mirror of
https://github.com/SheffieldML/GPy.git
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Merge branch 'devel' of github.com:SheffieldML/GPy into devel
This commit is contained in:
Zhenwen Dai
commit
f71fd8445d
16 changed files with 141 additions and 1021 deletions
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@ -8,5 +8,4 @@ from parameterization.observable_array import ObsAr
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from gp import GP
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from gp import GP
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from sparse_gp import SparseGP
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from sparse_gp import SparseGP
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from svigp import SVIGP
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from mapping import *
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from mapping import *
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130
GPy/core/gp.py
130
GPy/core/gp.py
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@ -26,7 +26,7 @@ class GP(Model):
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:param Y: output observations
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:param Y: output observations
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:param kernel: a GPy kernel, defaults to rbf+white
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:param kernel: a GPy kernel, defaults to rbf+white
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:param likelihood: a GPy likelihood
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:param likelihood: a GPy likelihood
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:param :class:`~GPy.inference.latent_function_inference.LatentFunctionInference` inference_method: The inference method to use for this GP
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:param inference_method: The :class:`~GPy.inference.latent_function_inference.LatentFunctionInference` inference method to use for this GP
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:rtype: model object
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:rtype: model object
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:param Norm normalizer:
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:param Norm normalizer:
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normalize the outputs Y.
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normalize the outputs Y.
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@ -95,10 +95,13 @@ class GP(Model):
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def set_XY(self, X=None, Y=None):
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def set_XY(self, X=None, Y=None):
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"""
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"""
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Set the input / output of the model
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Set the input / output data of the model
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This is useful if we wish to change our existing data but maintain the same model
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:param X: input observations
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:param X: input observations
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:type X: np.ndarray
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:param Y: output observations
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:param Y: output observations
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:type Y: np.ndarray
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"""
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"""
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self.update_model(False)
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self.update_model(False)
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if Y is not None:
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if Y is not None:
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@ -129,22 +132,39 @@ class GP(Model):
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def set_X(self,X):
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def set_X(self,X):
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"""
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"""
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Set the input of the model
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Set the input data of the model
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:param X: input observations
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:type X: np.ndarray
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"""
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"""
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self.set_XY(X=X)
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self.set_XY(X=X)
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def set_Y(self,Y):
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def set_Y(self,Y):
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"""
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"""
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Set the input of the model
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Set the output data of the model
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:param X: output observations
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:type X: np.ndarray
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"""
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"""
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self.set_XY(Y=Y)
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self.set_XY(Y=Y)
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def parameters_changed(self):
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def parameters_changed(self):
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"""
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Method that is called upon any changes to :class:`~GPy.core.parameterization.param.Param` variables within the model.
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In particular in the GP class this method reperforms inference, recalculating the posterior and log marginal likelihood and gradients of the model
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.. warning::
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This method is not designed to be called manually, the framework is set up to automatically call this method upon changes to parameters, if you call
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this method yourself, there may be unexpected consequences.
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"""
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self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.likelihood, self.Y_normalized, self.Y_metadata)
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self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.likelihood, self.Y_normalized, self.Y_metadata)
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self.likelihood.update_gradients(self.grad_dict['dL_dthetaL'])
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self.likelihood.update_gradients(self.grad_dict['dL_dthetaL'])
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self.kern.update_gradients_full(self.grad_dict['dL_dK'], self.X)
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self.kern.update_gradients_full(self.grad_dict['dL_dK'], self.X)
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def log_likelihood(self):
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def log_likelihood(self):
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"""
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The log marginal likelihood of the model, :math:`p(\mathbf{y})`, this is the objective function of the model being optimised
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"""
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return self._log_marginal_likelihood
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return self._log_marginal_likelihood
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def _raw_predict(self, _Xnew, full_cov=False, kern=None):
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def _raw_predict(self, _Xnew, full_cov=False, kern=None):
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@ -155,12 +175,10 @@ class GP(Model):
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of the prediction is computed. If full_cov is False (default), only the
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of the prediction is computed. If full_cov is False (default), only the
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diagonal of the covariance is returned.
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diagonal of the covariance is returned.
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$$
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.. math::
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p(f*|X*, X, Y) = \int^{\inf}_{\inf} p(f*|f,X*)p(f|X,Y) df
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p(f*|X*, X, Y) = \int^{\inf}_{\inf} p(f*|f,X*)p(f|X,Y) df
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= N(f*| K_{x*x}(K_{xx} + \Sigma)^{-1}Y, K_{x*x*} - K_{xx*}(K_{xx} + \Sigma)^{-1}K_{xx*}
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= N(f*| K_{x*x}(K_{xx} + \Sigma)^{-1}Y, K_{x*x*} - K_{xx*}(K_{xx} + \Sigma)^{-1}K_{xx*}
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\Sigma := \texttt{Likelihood.variance / Approximate likelihood covariance}
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\Sigma := \texttt{Likelihood.variance / Approximate likelihood covariance}
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$$
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"""
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"""
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if kern is None:
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if kern is None:
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kern = self.kern
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kern = self.kern
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@ -185,23 +203,20 @@ class GP(Model):
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Predict the function(s) at the new point(s) Xnew.
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Predict the function(s) at the new point(s) Xnew.
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:param Xnew: The points at which to make a prediction
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:param Xnew: The points at which to make a prediction
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:type Xnew: np.ndarray, Nnew x self.input_dim
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:type Xnew: np.ndarray (Nnew x self.input_dim)
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:param full_cov: whether to return the full covariance matrix, or just
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:param full_cov: whether to return the full covariance matrix, or just
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the diagonal
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the diagonal
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:type full_cov: bool
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:type full_cov: bool
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:param Y_metadata: metadata about the predicting point to pass to the likelihood
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:param Y_metadata: metadata about the predicting point to pass to the likelihood
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:param kern: The kernel to use for prediction (defaults to the model
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:param kern: The kernel to use for prediction (defaults to the model
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kern). this is useful for examining e.g. subprocesses.
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kern). this is useful for examining e.g. subprocesses.
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:returns: mean: posterior mean, a Numpy array, Nnew x self.input_dim
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:returns: (mean, var, lower_upper):
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:returns: var: posterior variance, a Numpy array, Nnew x 1 if
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mean: posterior mean, a Numpy array, Nnew x self.input_dim
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full_cov=False, Nnew x Nnew otherwise
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var: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
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:returns: lower and upper boundaries of the 95% confidence intervals,
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lower_upper: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.input_dim
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Numpy arrays, Nnew x self.input_dim
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If full_cov and self.input_dim > 1, the return shape of var is Nnew x Nnew x self.input_dim. If self.input_dim == 1, the return shape is Nnew x Nnew.
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If full_cov and self.input_dim > 1, the return shape of var is Nnew x Nnew x self.input_dim. If self.input_dim == 1, the return shape is Nnew x Nnew.
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This is to allow for different normalizations of the output dimensions.
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This is to allow for different normalizations of the output dimensions.
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"""
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"""
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#predict the latent function values
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#predict the latent function values
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mu, var = self._raw_predict(Xnew, full_cov=full_cov, kern=kern)
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mu, var = self._raw_predict(Xnew, full_cov=full_cov, kern=kern)
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@ -213,6 +228,16 @@ class GP(Model):
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return mean, var
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return mean, var
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def predict_quantiles(self, X, quantiles=(2.5, 97.5), Y_metadata=None):
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def predict_quantiles(self, X, quantiles=(2.5, 97.5), Y_metadata=None):
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"""
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Get the predictive quantiles around the prediction at X
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:param X: The points at which to make a prediction
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:type X: np.ndarray (Xnew x self.input_dim)
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:param quantiles: tuple of quantiles, default is (2.5, 97.5) which is the 95% interval
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:type quantiles: tuple
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:returns: list of quantiles for each X and predictive quantiles for interval combination
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:rtype: [np.ndarray (Xnew x self.input_dim), np.ndarray (Xnew x self.input_dim)]
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"""
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m, v = self._raw_predict(X, full_cov=False)
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m, v = self._raw_predict(X, full_cov=False)
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if self.normalizer is not None:
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if self.normalizer is not None:
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m, v = self.normalizer.inverse_mean(m), self.normalizer.inverse_variance(v)
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m, v = self.normalizer.inverse_mean(m), self.normalizer.inverse_variance(v)
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@ -225,7 +250,12 @@ class GP(Model):
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Given a set of points at which to predict X* (size [N*,Q]), compute the
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Given a set of points at which to predict X* (size [N*,Q]), compute the
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derivatives of the mean and variance. Resulting arrays are sized:
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derivatives of the mean and variance. Resulting arrays are sized:
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dmu_dX* -- [N*, Q ,D], where D is the number of output in this GP (usually one).
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dmu_dX* -- [N*, Q ,D], where D is the number of output in this GP (usually one).
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dv_dX* -- [N*, Q], (since all outputs have the same variance)
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dv_dX* -- [N*, Q], (since all outputs have the same variance)
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:param X: The points at which to get the predictive gradients
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:type X: np.ndarray (Xnew x self.input_dim)
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:returns: dmu_dX, dv_dX
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:rtype: [np.ndarray (N*, Q ,D), np.ndarray (N*,Q) ]
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"""
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"""
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dmu_dX = np.empty((Xnew.shape[0],Xnew.shape[1],self.output_dim))
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dmu_dX = np.empty((Xnew.shape[0],Xnew.shape[1],self.output_dim))
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@ -245,12 +275,13 @@ class GP(Model):
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Samples the posterior GP at the points X.
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Samples the posterior GP at the points X.
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:param X: The points at which to take the samples.
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:param X: The points at which to take the samples.
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:type X: np.ndarray, Nnew x self.input_dim.
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:type X: np.ndarray (Nnew x self.input_dim)
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:param size: the number of a posteriori samples.
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:param size: the number of a posteriori samples.
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:type size: int.
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:type size: int.
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:param full_cov: whether to return the full covariance matrix, or just the diagonal.
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:param full_cov: whether to return the full covariance matrix, or just the diagonal.
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:type full_cov: bool.
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:type full_cov: bool.
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:returns: Ysim: set of simulations, a Numpy array (N x samples).
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:returns: Ysim: set of simulations
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:rtype: np.ndarray (N x samples)
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"""
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"""
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m, v = self._raw_predict(X, full_cov=full_cov)
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m, v = self._raw_predict(X, full_cov=full_cov)
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if self.normalizer is not None:
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if self.normalizer is not None:
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@ -268,7 +299,7 @@ class GP(Model):
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Samples the posterior GP at the points X.
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Samples the posterior GP at the points X.
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:param X: the points at which to take the samples.
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:param X: the points at which to take the samples.
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:type X: np.ndarray, Nnew x self.input_dim.
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:type X: np.ndarray (Nnew x self.input_dim.)
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:param size: the number of a posteriori samples.
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:param size: the number of a posteriori samples.
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:type size: int.
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:type size: int.
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:param full_cov: whether to return the full covariance matrix, or just the diagonal.
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:param full_cov: whether to return the full covariance matrix, or just the diagonal.
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@ -292,6 +323,37 @@ class GP(Model):
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This is a call to plot with plot_raw=True.
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This is a call to plot with plot_raw=True.
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Data will not be plotted in this, as the GP's view of the world
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Data will not be plotted in this, as the GP's view of the world
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may live in another space, or units then the data.
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may live in another space, or units then the data.
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Can plot only part of the data and part of the posterior functions
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using which_data_rowsm which_data_ycols.
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:param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits
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:type plot_limits: np.array
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:param which_data_rows: which of the training data to plot (default all)
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:type which_data_rows: 'all' or a slice object to slice model.X, model.Y
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:param which_data_ycols: when the data has several columns (independant outputs), only plot these
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:type which_data_ycols: 'all' or a list of integers
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:param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v.
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:type fixed_inputs: a list of tuples
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:param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
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:type resolution: int
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:param levels: number of levels to plot in a contour plot.
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:param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure
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:type levels: int
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:param samples: the number of a posteriori samples to plot
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:type samples: int
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:param fignum: figure to plot on.
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:type fignum: figure number
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:param ax: axes to plot on.
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:type ax: axes handle
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:param linecol: color of line to plot [Tango.colorsHex['darkBlue']]
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:type linecol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) as is standard in matplotlib
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:param fillcol: color of fill [Tango.colorsHex['lightBlue']]
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:type fillcol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) as is standard in matplotlib
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:param Y_metadata: additional data associated with Y which may be needed
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:type Y_metadata: dict
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:param data_symbol: symbol as used matplotlib, by default this is a black cross ('kx')
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:type data_symbol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) alongside marker type, as is standard in matplotlib.
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"""
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"""
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assert "matplotlib" in sys.modules, "matplotlib package has not been imported."
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assert "matplotlib" in sys.modules, "matplotlib package has not been imported."
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from ..plotting.matplot_dep import models_plots
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from ..plotting.matplot_dep import models_plots
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@ -325,12 +387,13 @@ class GP(Model):
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:param which_data_rows: which of the training data to plot (default all)
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:param which_data_rows: which of the training data to plot (default all)
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:type which_data_rows: 'all' or a slice object to slice model.X, model.Y
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:type which_data_rows: 'all' or a slice object to slice model.X, model.Y
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:param which_data_ycols: when the data has several columns (independant outputs), only plot these
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:param which_data_ycols: when the data has several columns (independant outputs), only plot these
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:type which_data_rows: 'all' or a list of integers
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:type which_data_ycols: 'all' or a list of integers
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:param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v.
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:param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v.
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:type fixed_inputs: a list of tuples
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:type fixed_inputs: a list of tuples
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:param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
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:param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
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:type resolution: int
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:type resolution: int
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:param levels: number of levels to plot in a contour plot.
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:param levels: number of levels to plot in a contour plot.
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:param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure
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:type levels: int
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:type levels: int
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:param samples: the number of a posteriori samples to plot
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:param samples: the number of a posteriori samples to plot
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:type samples: int
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:type samples: int
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@ -338,11 +401,14 @@ class GP(Model):
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:type fignum: figure number
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:type fignum: figure number
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:param ax: axes to plot on.
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:param ax: axes to plot on.
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:type ax: axes handle
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:type ax: axes handle
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:type output: integer (first output is 0)
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:param linecol: color of line to plot [Tango.colorsHex['darkBlue']]
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:param linecol: color of line to plot [Tango.colorsHex['darkBlue']]
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:type linecol:
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:type linecol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) as is standard in matplotlib
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:param fillcol: color of fill [Tango.colorsHex['lightBlue']]
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:param fillcol: color of fill [Tango.colorsHex['lightBlue']]
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:param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure
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:type fillcol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) as is standard in matplotlib
|
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|
:param Y_metadata: additional data associated with Y which may be needed
|
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|
:type Y_metadata: dict
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||||||
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:param data_symbol: symbol as used matplotlib, by default this is a black cross ('kx')
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:type data_symbol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) alongside marker type, as is standard in matplotlib.
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"""
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"""
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assert "matplotlib" in sys.modules, "matplotlib package has not been imported."
|
assert "matplotlib" in sys.modules, "matplotlib package has not been imported."
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from ..plotting.matplot_dep import models_plots
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from ..plotting.matplot_dep import models_plots
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@ -372,10 +438,8 @@ class GP(Model):
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:type max_f_eval: int
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:type max_f_eval: int
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:messages: whether to display during optimisation
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:messages: whether to display during optimisation
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:type messages: bool
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:type messages: bool
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:param optimizer: which optimizer to use (defaults to self.preferred optimizer)
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:param optimizer: which optimizer to use (defaults to self.preferred optimizer), a range of optimisers can be found in :module:`~GPy.inference.optimization`, they include 'scg', 'lbfgs', 'tnc'.
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:type optimizer: string
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:type optimizer: string
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TODO: valid args
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"""
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"""
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self.inference_method.on_optimization_start()
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self.inference_method.on_optimization_start()
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try:
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try:
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||||||
|
|
@ -384,17 +448,17 @@ class GP(Model):
|
||||||
print "KeyboardInterrupt caught, calling on_optimization_end() to round things up"
|
print "KeyboardInterrupt caught, calling on_optimization_end() to round things up"
|
||||||
self.inference_method.on_optimization_end()
|
self.inference_method.on_optimization_end()
|
||||||
raise
|
raise
|
||||||
|
|
||||||
def infer_newX(self, Y_new, optimize=True, ):
|
def infer_newX(self, Y_new, optimize=True, ):
|
||||||
"""
|
"""
|
||||||
Infer the distribution of X for the new observed data *Y_new*.
|
Infer the distribution of X for the new observed data *Y_new*.
|
||||||
|
|
||||||
:param Y_new: the new observed data for inference
|
:param Y_new: the new observed data for inference
|
||||||
:type Y_new: numpy.ndarray
|
:type Y_new: numpy.ndarray
|
||||||
:param optimize: whether to optimize the location of new X (True by default)
|
:param optimize: whether to optimize the location of new X (True by default)
|
||||||
:type optimize: boolean
|
:type optimize: boolean
|
||||||
:return: a tuple containing the posterior estimation of X and the model that optimize X
|
:return: a tuple containing the posterior estimation of X and the model that optimize X
|
||||||
:rtype: (GPy.core.parameterization.variational.VariationalPosterior or numpy.ndarray, GPy.core.Model)
|
:rtype: (:class:`~GPy.core.parameterization.variational.VariationalPosterior` or numpy.ndarray, :class:`~GPy.core.model.Model`)
|
||||||
"""
|
"""
|
||||||
from ..inference.latent_function_inference.inferenceX import infer_newX
|
from ..inference.latent_function_inference.inferenceX import infer_newX
|
||||||
return infer_newX(self, Y_new, optimize=optimize)
|
return infer_newX(self, Y_new, optimize=optimize)
|
||||||
|
|
|
||||||
|
|
@ -1,434 +0,0 @@
|
||||||
# Copyright (c) 2012, James Hensman and Nicolo' Fusi
|
|
||||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
|
||||||
|
|
||||||
import numpy as np
|
|
||||||
from ..util.linalg import pdinv, mdot, tdot, dpotrs, dtrtrs, jitchol, backsub_both_sides
|
|
||||||
from gp import GP
|
|
||||||
import time
|
|
||||||
import sys
|
|
||||||
|
|
||||||
|
|
||||||
class SVIGP(GP):
|
|
||||||
"""
|
|
||||||
|
|
||||||
Stochastic Variational inference in a Gaussian Process
|
|
||||||
|
|
||||||
:param X: inputs
|
|
||||||
:type X: np.ndarray (N x Q)
|
|
||||||
:param Y: observed data
|
|
||||||
:type Y: np.ndarray of observations (N x D)
|
|
||||||
:param batchsize: the size of a h
|
|
||||||
|
|
||||||
Additional kwargs are used as for a sparse GP. They include:
|
|
||||||
|
|
||||||
:param q_u: canonical parameters of the distribution sqehd into a 1D array
|
|
||||||
:type q_u: np.ndarray
|
|
||||||
:param M: Number of inducing points (optional, default 10. Ignored if Z is not None)
|
|
||||||
:type M: int
|
|
||||||
:param kernel: the kernel/covariance function. See link kernels
|
|
||||||
:type kernel: a GPy kernel
|
|
||||||
:param Z: inducing inputs (optional, see note)
|
|
||||||
:type Z: np.ndarray (M x Q) | None
|
|
||||||
:param X_uncertainty: The uncertainty in the measurements of X (Gaussian variance)
|
|
||||||
:type X_uncertainty: np.ndarray (N x Q) | None
|
|
||||||
:param Zslices: slices for the inducing inputs (see slicing TODO: link)
|
|
||||||
:param M: Number of inducing points (optional, default 10. Ignored if Z is not None)
|
|
||||||
:type M: int
|
|
||||||
:param beta: noise precision. TODO: ignore beta if doing EP
|
|
||||||
:type beta: float
|
|
||||||
:param normalize_(X|Y): whether to normalize the data before computing (predictions will be in original scales)
|
|
||||||
:type normalize_(X|Y): bool
|
|
||||||
|
|
||||||
"""
|
|
||||||
|
|
||||||
|
|
||||||
def __init__(self, X, Y, kernel, Z, q_u=None, batchsize=10):
|
|
||||||
raise NotImplementedError, "This is a work in progress, see github issue "
|
|
||||||
GP.__init__(self, X, Y, kernel)
|
|
||||||
self.batchsize=batchsize
|
|
||||||
self.Z = Z
|
|
||||||
self.num_inducing = Z.shape[0]
|
|
||||||
|
|
||||||
self.batchcounter = 0
|
|
||||||
self.epochs = 0
|
|
||||||
self.iterations = 0
|
|
||||||
|
|
||||||
self.vb_steplength = 0.05
|
|
||||||
self.param_steplength = 1e-5
|
|
||||||
self.momentum = 0.9
|
|
||||||
|
|
||||||
if q_u is None:
|
|
||||||
q_u = np.hstack((np.random.randn(self.num_inducing*self.output_dim),-.5*np.eye(self.num_inducing).flatten()))
|
|
||||||
|
|
||||||
self.set_vb_param(q_u)
|
|
||||||
|
|
||||||
self._permutation = np.random.permutation(self.num_data)
|
|
||||||
self.load_batch()
|
|
||||||
|
|
||||||
self._param_trace = []
|
|
||||||
self._ll_trace = []
|
|
||||||
self._grad_trace = []
|
|
||||||
|
|
||||||
#set the adaptive steplength parameters
|
|
||||||
#self.hbar_t = 0.0
|
|
||||||
#self.tau_t = 100.0
|
|
||||||
#self.gbar_t = 0.0
|
|
||||||
#self.gbar_t1 = 0.0
|
|
||||||
#self.gbar_t2 = 0.0
|
|
||||||
#self.hbar_tp = 0.0
|
|
||||||
#self.tau_tp = 10000.0
|
|
||||||
#self.gbar_tp = 0.0
|
|
||||||
#self.adapt_param_steplength = True
|
|
||||||
#self.adapt_vb_steplength = True
|
|
||||||
#self._param_steplength_trace = []
|
|
||||||
#self._vb_steplength_trace = []
|
|
||||||
|
|
||||||
def _compute_kernel_matrices(self):
|
|
||||||
# kernel computations, using BGPLVM notation
|
|
||||||
self.Kmm = self.kern.K(self.Z)
|
|
||||||
self.psi0 = self.kern.Kdiag(self.X_batch)
|
|
||||||
self.psi1 = self.kern.K(self.X_batch, self.Z)
|
|
||||||
self.psi2 = None
|
|
||||||
|
|
||||||
def dL_dtheta(self):
|
|
||||||
dL_dtheta = self.kern._param_grad_helper(self.dL_dKmm, self.Z)
|
|
||||||
if self.has_uncertain_inputs:
|
|
||||||
dL_dtheta += self.kern.dpsi0_dtheta(self.dL_dpsi0, self.Z, self.X_batch, self.X_variance_batch)
|
|
||||||
dL_dtheta += self.kern.dpsi1_dtheta(self.dL_dpsi1, self.Z, self.X_batch, self.X_variance_batch)
|
|
||||||
dL_dtheta += self.kern.dpsi2_dtheta(self.dL_dpsi2, self.Z, self.X_batch, self.X_variance_batch)
|
|
||||||
else:
|
|
||||||
dL_dtheta += self.kern._param_grad_helper(self.dL_dpsi1, self.X_batch, self.Z)
|
|
||||||
dL_dtheta += self.kern.dKdiag_dtheta(self.dL_dpsi0, self.X_batch)
|
|
||||||
return dL_dtheta
|
|
||||||
|
|
||||||
def _set_params(self, p, computations=True):
|
|
||||||
self.kern._set_params_transformed(p[:self.kern.num_params])
|
|
||||||
self.likelihood._set_params(p[self.kern.num_params:])
|
|
||||||
if computations:
|
|
||||||
self._compute_kernel_matrices()
|
|
||||||
self._computations()
|
|
||||||
|
|
||||||
def _get_params(self):
|
|
||||||
return np.hstack((self.kern._get_params_transformed() , self.likelihood._get_params()))
|
|
||||||
|
|
||||||
def _get_param_names(self):
|
|
||||||
return self.kern._get_param_names_transformed() + self.likelihood._get_param_names()
|
|
||||||
|
|
||||||
def load_batch(self):
|
|
||||||
"""
|
|
||||||
load a batch of data (set self.X_batch and self.Y_batch from self.X, self.Y)
|
|
||||||
"""
|
|
||||||
|
|
||||||
#if we've seen all the data, start again with them in a new random order
|
|
||||||
if self.batchcounter+self.batchsize > self.num_data:
|
|
||||||
self.batchcounter = 0
|
|
||||||
self.epochs += 1
|
|
||||||
self._permutation = np.random.permutation(self.num_data)
|
|
||||||
|
|
||||||
this_perm = self._permutation[self.batchcounter:self.batchcounter+self.batchsize]
|
|
||||||
|
|
||||||
self.X_batch = self.X[this_perm]
|
|
||||||
self.Y_batch = self.Y[this_perm]
|
|
||||||
|
|
||||||
self.batchcounter += self.batchsize
|
|
||||||
|
|
||||||
self.data_prop = float(self.batchsize)/self.num_data
|
|
||||||
|
|
||||||
self._compute_kernel_matrices()
|
|
||||||
self._computations()
|
|
||||||
|
|
||||||
def _computations(self,do_Kmm=True, do_Kmm_grad=True):
|
|
||||||
"""
|
|
||||||
All of the computations needed. Some are optional, see kwargs.
|
|
||||||
"""
|
|
||||||
|
|
||||||
if do_Kmm:
|
|
||||||
self.Lm = jitchol(self.Kmm)
|
|
||||||
|
|
||||||
# The rather complex computations of self.A
|
|
||||||
if self.has_uncertain_inputs:
|
|
||||||
if self.likelihood.is_heteroscedastic:
|
|
||||||
psi2_beta = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.batchsize, 1, 1))).sum(0)
|
|
||||||
else:
|
|
||||||
psi2_beta = self.psi2.sum(0) * self.likelihood.precision
|
|
||||||
evals, evecs = np.linalg.eigh(psi2_beta)
|
|
||||||
clipped_evals = np.clip(evals, 0., 1e6) # TODO: make clipping configurable
|
|
||||||
tmp = evecs * np.sqrt(clipped_evals)
|
|
||||||
else:
|
|
||||||
if self.likelihood.is_heteroscedastic:
|
|
||||||
tmp = self.psi1.T * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.batchsize)))
|
|
||||||
else:
|
|
||||||
tmp = self.psi1.T * (np.sqrt(self.likelihood.precision))
|
|
||||||
tmp, _ = dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
|
|
||||||
self.A = tdot(tmp)
|
|
||||||
|
|
||||||
self.V = self.likelihood.precision*self.likelihood.Y
|
|
||||||
self.VmT = np.dot(self.V,self.q_u_expectation[0].T)
|
|
||||||
self.psi1V = np.dot(self.psi1.T, self.V)
|
|
||||||
|
|
||||||
self.B = np.eye(self.num_inducing)*self.data_prop + self.A
|
|
||||||
self.Lambda = backsub_both_sides(self.Lm, self.B.T)
|
|
||||||
self.LQL = backsub_both_sides(self.Lm,self.q_u_expectation[1].T,transpose='right')
|
|
||||||
|
|
||||||
self.trace_K = self.psi0.sum() - np.trace(self.A)/self.likelihood.precision
|
|
||||||
self.Kmmi_m, _ = dpotrs(self.Lm, self.q_u_expectation[0], lower=1)
|
|
||||||
self.projected_mean = np.dot(self.psi1,self.Kmmi_m)
|
|
||||||
|
|
||||||
# Compute dL_dpsi
|
|
||||||
self.dL_dpsi0 = - 0.5 * self.output_dim * self.likelihood.precision * np.ones(self.batchsize)
|
|
||||||
self.dL_dpsi1, _ = dpotrs(self.Lm,np.asfortranarray(self.VmT.T),lower=1)
|
|
||||||
self.dL_dpsi1 = self.dL_dpsi1.T
|
|
||||||
|
|
||||||
dL_dpsi2 = -0.5 * self.likelihood.precision * backsub_both_sides(self.Lm, self.LQL - self.output_dim * np.eye(self.num_inducing))
|
|
||||||
if self.has_uncertain_inputs:
|
|
||||||
self.dL_dpsi2 = np.repeat(dL_dpsi2[None,:,:],self.batchsize,axis=0)
|
|
||||||
else:
|
|
||||||
self.dL_dpsi1 += 2.*np.dot(dL_dpsi2,self.psi1.T).T
|
|
||||||
self.dL_dpsi2 = None
|
|
||||||
|
|
||||||
# Compute dL_dKmm
|
|
||||||
if do_Kmm_grad:
|
|
||||||
tmp = np.dot(self.LQL,self.A) - backsub_both_sides(self.Lm,np.dot(self.q_u_expectation[0],self.psi1V.T),transpose='right')
|
|
||||||
tmp += tmp.T
|
|
||||||
tmp += -self.output_dim*self.B
|
|
||||||
tmp += self.data_prop*self.LQL
|
|
||||||
self.dL_dKmm = 0.5*backsub_both_sides(self.Lm,tmp)
|
|
||||||
|
|
||||||
#Compute the gradient of the log likelihood wrt noise variance
|
|
||||||
self.partial_for_likelihood = -0.5*(self.batchsize*self.output_dim - np.sum(self.A*self.LQL))*self.likelihood.precision
|
|
||||||
self.partial_for_likelihood += (0.5*self.output_dim*self.trace_K + 0.5 * self.likelihood.trYYT - np.sum(self.likelihood.Y*self.projected_mean))*self.likelihood.precision**2
|
|
||||||
|
|
||||||
|
|
||||||
def log_likelihood(self):
|
|
||||||
"""
|
|
||||||
As for uncollapsed sparse GP, but account for the proportion of data we're looking at right now.
|
|
||||||
|
|
||||||
NB. self.batchsize is the size of the batch, not the size of X_all
|
|
||||||
"""
|
|
||||||
assert not self.likelihood.is_heteroscedastic
|
|
||||||
A = -0.5*self.batchsize*self.output_dim*(np.log(2.*np.pi) - np.log(self.likelihood.precision))
|
|
||||||
B = -0.5*self.likelihood.precision*self.output_dim*self.trace_K
|
|
||||||
Kmm_logdet = 2.*np.sum(np.log(np.diag(self.Lm)))
|
|
||||||
C = -0.5*self.output_dim*self.data_prop*(Kmm_logdet-self.q_u_logdet - self.num_inducing)
|
|
||||||
C += -0.5*np.sum(self.LQL * self.B)
|
|
||||||
D = -0.5*self.likelihood.precision*self.likelihood.trYYT
|
|
||||||
E = np.sum(self.V*self.projected_mean)
|
|
||||||
return (A+B+C+D+E)/self.data_prop
|
|
||||||
|
|
||||||
def _log_likelihood_gradients(self):
|
|
||||||
return np.hstack((self.dL_dtheta(), self.likelihood._gradients(partial=self.partial_for_likelihood)))/self.data_prop
|
|
||||||
|
|
||||||
def vb_grad_natgrad(self):
|
|
||||||
"""
|
|
||||||
Compute the gradients of the lower bound wrt the canonical and
|
|
||||||
Expectation parameters of u.
|
|
||||||
|
|
||||||
Note that the natural gradient in either is given by the gradient in
|
|
||||||
the other (See Hensman et al 2012 Fast Variational inference in the
|
|
||||||
conjugate exponential Family)
|
|
||||||
"""
|
|
||||||
|
|
||||||
# Gradient for eta
|
|
||||||
dL_dmmT_S = -0.5*self.Lambda/self.data_prop + 0.5*self.q_u_prec
|
|
||||||
Kmmipsi1V,_ = dpotrs(self.Lm,self.psi1V,lower=1)
|
|
||||||
dL_dm = (Kmmipsi1V - np.dot(self.Lambda,self.q_u_mean))/self.data_prop
|
|
||||||
|
|
||||||
# Gradients for theta
|
|
||||||
S = self.q_u_cov
|
|
||||||
Si = self.q_u_prec
|
|
||||||
m = self.q_u_mean
|
|
||||||
dL_dSi = -mdot(S,dL_dmmT_S, S)
|
|
||||||
|
|
||||||
dL_dmhSi = -2*dL_dSi
|
|
||||||
dL_dSim = np.dot(dL_dSi,m) + np.dot(Si, dL_dm)
|
|
||||||
|
|
||||||
return np.hstack((dL_dm.flatten(),dL_dmmT_S.flatten())) , np.hstack((dL_dSim.flatten(), dL_dmhSi.flatten()))
|
|
||||||
|
|
||||||
|
|
||||||
def optimize(self, iterations, print_interval=10, callback=lambda:None, callback_interval=5):
|
|
||||||
|
|
||||||
param_step = 0.
|
|
||||||
|
|
||||||
#Iterate!
|
|
||||||
for i in range(iterations):
|
|
||||||
|
|
||||||
#store the current configuration for plotting later
|
|
||||||
self._param_trace.append(self._get_params())
|
|
||||||
self._ll_trace.append(self.log_likelihood() + self.log_prior())
|
|
||||||
|
|
||||||
#load a batch
|
|
||||||
self.load_batch()
|
|
||||||
|
|
||||||
#compute the (stochastic) gradient
|
|
||||||
natgrads = self.vb_grad_natgrad()
|
|
||||||
grads = self._transform_gradients(self._log_likelihood_gradients() + self._log_prior_gradients())
|
|
||||||
self._grad_trace.append(grads)
|
|
||||||
|
|
||||||
#compute the steps in all parameters
|
|
||||||
vb_step = self.vb_steplength*natgrads[0]
|
|
||||||
if (self.epochs>=1):#only move the parameters after the first epoch
|
|
||||||
param_step = self.momentum*param_step + self.param_steplength*grads
|
|
||||||
else:
|
|
||||||
param_step = 0.
|
|
||||||
|
|
||||||
self.set_vb_param(self.get_vb_param() + vb_step)
|
|
||||||
#Note: don't recompute everything here, wait until the next iteration when we have a new batch
|
|
||||||
self._set_params(self._untransform_params(self._get_params_transformed() + param_step), computations=False)
|
|
||||||
|
|
||||||
#print messages if desired
|
|
||||||
if i and (not i%print_interval):
|
|
||||||
print i, np.mean(self._ll_trace[-print_interval:]) #, self.log_likelihood()
|
|
||||||
print np.round(np.mean(self._grad_trace[-print_interval:],0),3)
|
|
||||||
sys.stdout.flush()
|
|
||||||
|
|
||||||
#callback
|
|
||||||
if i and not i%callback_interval:
|
|
||||||
callback(self) # Change this to callback()
|
|
||||||
time.sleep(0.01)
|
|
||||||
|
|
||||||
if self.epochs > 10:
|
|
||||||
self._adapt_steplength()
|
|
||||||
|
|
||||||
self.iterations += 1
|
|
||||||
|
|
||||||
|
|
||||||
def _adapt_steplength(self):
|
|
||||||
if self.adapt_vb_steplength:
|
|
||||||
# self._adaptive_vb_steplength()
|
|
||||||
self._adaptive_vb_steplength_KL()
|
|
||||||
self._vb_steplength_trace.append(self.vb_steplength)
|
|
||||||
assert self.vb_steplength > 0
|
|
||||||
|
|
||||||
if self.adapt_param_steplength:
|
|
||||||
self._adaptive_param_steplength()
|
|
||||||
# self._adaptive_param_steplength_log()
|
|
||||||
# self._adaptive_param_steplength_from_vb()
|
|
||||||
self._param_steplength_trace.append(self.param_steplength)
|
|
||||||
|
|
||||||
def _adaptive_param_steplength(self):
|
|
||||||
decr_factor = 0.02
|
|
||||||
g_tp = self._transform_gradients(self._log_likelihood_gradients())
|
|
||||||
self.gbar_tp = (1-1/self.tau_tp)*self.gbar_tp + 1/self.tau_tp * g_tp
|
|
||||||
self.hbar_tp = (1-1/self.tau_tp)*self.hbar_tp + 1/self.tau_tp * np.dot(g_tp.T, g_tp)
|
|
||||||
new_param_steplength = np.dot(self.gbar_tp.T, self.gbar_tp) / self.hbar_tp
|
|
||||||
#- hack
|
|
||||||
new_param_steplength *= decr_factor
|
|
||||||
self.param_steplength = (self.param_steplength + new_param_steplength)/2
|
|
||||||
#-
|
|
||||||
self.tau_tp = self.tau_tp*(1-self.param_steplength) + 1
|
|
||||||
|
|
||||||
def _adaptive_param_steplength_log(self):
|
|
||||||
stp = np.logspace(np.log(0.0001), np.log(1e-6), base=np.e, num=18000)
|
|
||||||
self.param_steplength = stp[self.iterations]
|
|
||||||
|
|
||||||
def _adaptive_param_steplength_log2(self):
|
|
||||||
self.param_steplength = (self.iterations + 0.001)**-0.5
|
|
||||||
|
|
||||||
def _adaptive_param_steplength_from_vb(self):
|
|
||||||
self.param_steplength = self.vb_steplength * 0.01
|
|
||||||
|
|
||||||
def _adaptive_vb_steplength(self):
|
|
||||||
decr_factor = 0.1
|
|
||||||
g_t = self.vb_grad_natgrad()[0]
|
|
||||||
self.gbar_t = (1-1/self.tau_t)*self.gbar_t + 1/self.tau_t * g_t
|
|
||||||
self.hbar_t = (1-1/self.tau_t)*self.hbar_t + 1/self.tau_t * np.dot(g_t.T, g_t)
|
|
||||||
new_vb_steplength = np.dot(self.gbar_t.T, self.gbar_t) / self.hbar_t
|
|
||||||
#- hack
|
|
||||||
new_vb_steplength *= decr_factor
|
|
||||||
self.vb_steplength = (self.vb_steplength + new_vb_steplength)/2
|
|
||||||
#-
|
|
||||||
self.tau_t = self.tau_t*(1-self.vb_steplength) + 1
|
|
||||||
|
|
||||||
def _adaptive_vb_steplength_KL(self):
|
|
||||||
decr_factor = 0.1
|
|
||||||
natgrad = self.vb_grad_natgrad()
|
|
||||||
g_t1 = natgrad[0]
|
|
||||||
g_t2 = natgrad[1]
|
|
||||||
self.gbar_t1 = (1-1/self.tau_t)*self.gbar_t1 + 1/self.tau_t * g_t1
|
|
||||||
self.gbar_t2 = (1-1/self.tau_t)*self.gbar_t2 + 1/self.tau_t * g_t2
|
|
||||||
self.hbar_t = (1-1/self.tau_t)*self.hbar_t + 1/self.tau_t * np.dot(g_t1.T, g_t2)
|
|
||||||
self.vb_steplength = np.dot(self.gbar_t1.T, self.gbar_t2) / self.hbar_t
|
|
||||||
self.vb_steplength *= decr_factor
|
|
||||||
self.tau_t = self.tau_t*(1-self.vb_steplength) + 1
|
|
||||||
|
|
||||||
def _raw_predict(self, X_new, X_variance_new=None, which_parts='all',full_cov=False):
|
|
||||||
"""Internal helper function for making predictions, does not account for normalization"""
|
|
||||||
|
|
||||||
#TODO: make this more efficient!
|
|
||||||
self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
|
|
||||||
tmp = self.Kmmi- mdot(self.Kmmi,self.q_u_cov,self.Kmmi)
|
|
||||||
|
|
||||||
if X_variance_new is None:
|
|
||||||
Kx = self.kern.K(X_new,self.Z)
|
|
||||||
mu = np.dot(Kx,self.Kmmi_m)
|
|
||||||
if full_cov:
|
|
||||||
Kxx = self.kern.K(X_new)
|
|
||||||
var = Kxx - mdot(Kx,tmp,Kx.T)
|
|
||||||
else:
|
|
||||||
Kxx = self.kern.Kdiag(X_new)
|
|
||||||
var = (Kxx - np.sum(Kx*np.dot(Kx,tmp),1))[:,None]
|
|
||||||
return mu, var
|
|
||||||
else:
|
|
||||||
assert X_variance_new.shape == X_new.shape
|
|
||||||
Kx = self.kern.psi1(self.Z,X_new, X_variance_new)
|
|
||||||
mu = np.dot(Kx,self.Kmmi_m)
|
|
||||||
Kxx = self.kern.psi0(self.Z,X_new,X_variance_new)
|
|
||||||
psi2 = self.kern.psi2(self.Z,X_new,X_variance_new)
|
|
||||||
diag_var = Kxx - np.sum(np.sum(psi2*tmp[None,:,:],1),1)
|
|
||||||
if full_cov:
|
|
||||||
raise NotImplementedError
|
|
||||||
else:
|
|
||||||
return mu, diag_var[:,None]
|
|
||||||
|
|
||||||
def predict(self, Xnew, X_variance_new=None, which_parts='all', full_cov=False):
|
|
||||||
# normalize X values
|
|
||||||
Xnew = (Xnew.copy() - self._Xoffset) / self._Xscale
|
|
||||||
if X_variance_new is not None:
|
|
||||||
X_variance_new = X_variance_new / self._Xscale ** 2
|
|
||||||
|
|
||||||
# here's the actual prediction by the GP model
|
|
||||||
mu, var = self._raw_predict(Xnew, X_variance_new, full_cov=full_cov, which_parts=which_parts)
|
|
||||||
|
|
||||||
# now push through likelihood
|
|
||||||
mean, var, _025pm, _975pm = self.likelihood.predictive_values(mu, var, full_cov)
|
|
||||||
|
|
||||||
return mean, var, _025pm, _975pm
|
|
||||||
|
|
||||||
|
|
||||||
def set_vb_param(self,vb_param):
|
|
||||||
"""set the distribution q(u) from the canonical parameters"""
|
|
||||||
self.q_u_canonical_flat = vb_param.copy()
|
|
||||||
self.q_u_canonical = self.q_u_canonical_flat[:self.num_inducing*self.output_dim].reshape(self.num_inducing,self.output_dim),self.q_u_canonical_flat[self.num_inducing*self.output_dim:].reshape(self.num_inducing,self.num_inducing)
|
|
||||||
|
|
||||||
self.q_u_prec = -2.*self.q_u_canonical[1]
|
|
||||||
self.q_u_cov, q_u_Li, q_u_L, tmp = pdinv(self.q_u_prec)
|
|
||||||
self.q_u_Li = q_u_Li
|
|
||||||
self.q_u_logdet = -tmp
|
|
||||||
self.q_u_mean, _ = dpotrs(q_u_Li, np.asfortranarray(self.q_u_canonical[0]),lower=1)
|
|
||||||
|
|
||||||
self.q_u_expectation = (self.q_u_mean, np.dot(self.q_u_mean,self.q_u_mean.T)+self.q_u_cov*self.output_dim)
|
|
||||||
|
|
||||||
|
|
||||||
def get_vb_param(self):
|
|
||||||
"""
|
|
||||||
Return the canonical parameters of the distribution q(u)
|
|
||||||
"""
|
|
||||||
return self.q_u_canonical_flat
|
|
||||||
|
|
||||||
|
|
||||||
def plot(self, *args, **kwargs):
|
|
||||||
"""
|
|
||||||
See GPy.plotting.matplot_dep.svig_plots.plot
|
|
||||||
"""
|
|
||||||
assert "matplotlib" in sys.modules, "matplotlib package has not been imported."
|
|
||||||
from ..plotting.matplot_dep import svig_plots
|
|
||||||
svig_plots.plot(self,*args,**kwargs)
|
|
||||||
|
|
||||||
|
|
||||||
def plot_traces(self):
|
|
||||||
"""
|
|
||||||
See GPy.plotting.matplot_dep.svig_plots.plot_traces
|
|
||||||
"""
|
|
||||||
assert "matplotlib" in sys.modules, "matplotlib package has not been imported."
|
|
||||||
from ..plotting.matplot_dep import svig_plots
|
|
||||||
svig_plots.plot_traces(self)
|
|
||||||
|
|
@ -4,6 +4,4 @@
|
||||||
import classification
|
import classification
|
||||||
import regression
|
import regression
|
||||||
import dimensionality_reduction
|
import dimensionality_reduction
|
||||||
import tutorials
|
|
||||||
import stochastic
|
|
||||||
import non_gaussian
|
import non_gaussian
|
||||||
|
|
|
||||||
|
|
@ -28,13 +28,13 @@ def oil(num_inducing=50, max_iters=100, kernel=None, optimize=True, plot=True):
|
||||||
m = GPy.models.SparseGPClassification(X, Y, kernel=kernel, num_inducing=num_inducing)
|
m = GPy.models.SparseGPClassification(X, Y, kernel=kernel, num_inducing=num_inducing)
|
||||||
|
|
||||||
# Contrain all parameters to be positive
|
# Contrain all parameters to be positive
|
||||||
m.tie_params('.*len')
|
#m.tie_params('.*len')
|
||||||
m['.*len'] = 10.
|
m['.*len'] = 10.
|
||||||
m.update_likelihood_approximation()
|
|
||||||
|
|
||||||
# Optimize
|
# Optimize
|
||||||
if optimize:
|
if optimize:
|
||||||
m.optimize(max_iters=max_iters)
|
for _ in range(5):
|
||||||
|
m.optimize(max_iters=int(max_iters/5))
|
||||||
print(m)
|
print(m)
|
||||||
|
|
||||||
#Test
|
#Test
|
||||||
|
|
@ -150,7 +150,7 @@ def sparse_toy_linear_1d_classification(num_inducing=10, seed=default_seed, opti
|
||||||
print m
|
print m
|
||||||
return m
|
return m
|
||||||
|
|
||||||
def toy_heaviside(seed=default_seed, optimize=True, plot=True):
|
def toy_heaviside(seed=default_seed, max_iters=100, optimize=True, plot=True):
|
||||||
"""
|
"""
|
||||||
Simple 1D classification example using a heavy side gp transformation
|
Simple 1D classification example using a heavy side gp transformation
|
||||||
|
|
||||||
|
|
@ -166,16 +166,18 @@ def toy_heaviside(seed=default_seed, optimize=True, plot=True):
|
||||||
Y[Y.flatten() == -1] = 0
|
Y[Y.flatten() == -1] = 0
|
||||||
|
|
||||||
# Model definition
|
# Model definition
|
||||||
noise_model = GPy.likelihoods.bernoulli(GPy.likelihoods.noise_models.gp_transformations.Heaviside())
|
kernel = GPy.kern.RBF(1)
|
||||||
likelihood = GPy.likelihoods.EP(Y, noise_model)
|
likelihood = GPy.likelihoods.Bernoulli(gp_link=GPy.likelihoods.link_functions.Heaviside())
|
||||||
m = GPy.models.GPClassification(data['X'], likelihood=likelihood)
|
ep = GPy.inference.latent_function_inference.expectation_propagation.EP()
|
||||||
|
m = GPy.core.GP(X=data['X'], Y=Y, kernel=kernel, likelihood=likelihood, inference_method=ep, name='gp_classification_heaviside')
|
||||||
|
#m = GPy.models.GPClassification(data['X'], likelihood=likelihood)
|
||||||
|
|
||||||
# Optimize
|
# Optimize
|
||||||
if optimize:
|
if optimize:
|
||||||
m.update_likelihood_approximation()
|
|
||||||
# Parameters optimization:
|
# Parameters optimization:
|
||||||
m.optimize()
|
for _ in range(5):
|
||||||
#m.pseudo_EM()
|
m.optimize(max_iters=int(max_iters/5))
|
||||||
|
print m
|
||||||
|
|
||||||
# Plot
|
# Plot
|
||||||
if plot:
|
if plot:
|
||||||
|
|
|
||||||
|
|
@ -368,7 +368,7 @@ def bgplvm_simulation_missing_data(optimize=True, verbose=1,
|
||||||
max_iters=2e4,
|
max_iters=2e4,
|
||||||
):
|
):
|
||||||
from GPy import kern
|
from GPy import kern
|
||||||
from GPy.models import BayesianGPLVM
|
from GPy.models.bayesian_gplvm_minibatch import BayesianGPLVMMiniBatch
|
||||||
|
|
||||||
D1, D2, D3, N, num_inducing, Q = 13, 5, 8, 400, 3, 4
|
D1, D2, D3, N, num_inducing, Q = 13, 5, 8, 400, 3, 4
|
||||||
_, _, Ylist = _simulate_matern(D1, D2, D3, N, num_inducing, plot_sim)
|
_, _, Ylist = _simulate_matern(D1, D2, D3, N, num_inducing, plot_sim)
|
||||||
|
|
@ -379,7 +379,7 @@ def bgplvm_simulation_missing_data(optimize=True, verbose=1,
|
||||||
Ymissing = Y.copy()
|
Ymissing = Y.copy()
|
||||||
Ymissing[inan] = _np.nan
|
Ymissing[inan] = _np.nan
|
||||||
|
|
||||||
m = BayesianGPLVM(Ymissing, Q, init="random", num_inducing=num_inducing,
|
m = BayesianGPLVMMiniBatch(Ymissing, Q, init="random", num_inducing=num_inducing,
|
||||||
kernel=k, missing_data=True)
|
kernel=k, missing_data=True)
|
||||||
|
|
||||||
m.Yreal = Y
|
m.Yreal = Y
|
||||||
|
|
@ -624,7 +624,10 @@ def cmu_mocap(subject='35', motion=['01'], in_place=True, optimize=True, verbose
|
||||||
if in_place:
|
if in_place:
|
||||||
# Make figure move in place.
|
# Make figure move in place.
|
||||||
data['Y'][:, 0:3] = 0.0
|
data['Y'][:, 0:3] = 0.0
|
||||||
m = GPy.models.GPLVM(data['Y'], 2, normalize_Y=True)
|
Y = data['Y']
|
||||||
|
Y_mean = Y.mean(0)
|
||||||
|
Y_std = Y.std(0)
|
||||||
|
m = GPy.models.GPLVM((Y-Y_mean)/Y_std, 2)
|
||||||
|
|
||||||
if optimize: m.optimize(messages=verbose, max_f_eval=10000)
|
if optimize: m.optimize(messages=verbose, max_f_eval=10000)
|
||||||
if plot:
|
if plot:
|
||||||
|
|
|
||||||
|
|
@ -59,7 +59,7 @@ def student_t_approx(optimize=True, plot=True):
|
||||||
t_distribution = GPy.likelihoods.StudentT(deg_free=deg_free, sigma2=edited_real_sd)
|
t_distribution = GPy.likelihoods.StudentT(deg_free=deg_free, sigma2=edited_real_sd)
|
||||||
laplace_inf = GPy.inference.latent_function_inference.Laplace()
|
laplace_inf = GPy.inference.latent_function_inference.Laplace()
|
||||||
m3 = GPy.core.GP(X, Y.copy(), kernel3, likelihood=t_distribution, inference_method=laplace_inf)
|
m3 = GPy.core.GP(X, Y.copy(), kernel3, likelihood=t_distribution, inference_method=laplace_inf)
|
||||||
m3['.*t_noise'].constrain_bounded(1e-6, 10.)
|
m3['.*t_scale2'].constrain_bounded(1e-6, 10.)
|
||||||
m3['.*white'].constrain_fixed(1e-5)
|
m3['.*white'].constrain_fixed(1e-5)
|
||||||
m3.randomize()
|
m3.randomize()
|
||||||
|
|
||||||
|
|
@ -67,7 +67,7 @@ def student_t_approx(optimize=True, plot=True):
|
||||||
t_distribution = GPy.likelihoods.StudentT(deg_free=deg_free, sigma2=edited_real_sd)
|
t_distribution = GPy.likelihoods.StudentT(deg_free=deg_free, sigma2=edited_real_sd)
|
||||||
laplace_inf = GPy.inference.latent_function_inference.Laplace()
|
laplace_inf = GPy.inference.latent_function_inference.Laplace()
|
||||||
m4 = GPy.core.GP(X, Yc.copy(), kernel4, likelihood=t_distribution, inference_method=laplace_inf)
|
m4 = GPy.core.GP(X, Yc.copy(), kernel4, likelihood=t_distribution, inference_method=laplace_inf)
|
||||||
m4['.*t_noise'].constrain_bounded(1e-6, 10.)
|
m4['.*t_scale2'].constrain_bounded(1e-6, 10.)
|
||||||
m4['.*white'].constrain_fixed(1e-5)
|
m4['.*white'].constrain_fixed(1e-5)
|
||||||
m4.randomize()
|
m4.randomize()
|
||||||
print m4
|
print m4
|
||||||
|
|
@ -124,6 +124,7 @@ def student_t_approx(optimize=True, plot=True):
|
||||||
return m1, m2, m3, m4
|
return m1, m2, m3, m4
|
||||||
|
|
||||||
def boston_example(optimize=True, plot=True):
|
def boston_example(optimize=True, plot=True):
|
||||||
|
raise NotImplementedError("Needs updating")
|
||||||
import sklearn
|
import sklearn
|
||||||
from sklearn.cross_validation import KFold
|
from sklearn.cross_validation import KFold
|
||||||
optimizer='bfgs'
|
optimizer='bfgs'
|
||||||
|
|
@ -152,8 +153,8 @@ def boston_example(optimize=True, plot=True):
|
||||||
noise = 1e-1 #np.exp(-2)
|
noise = 1e-1 #np.exp(-2)
|
||||||
rbf_len = 0.5
|
rbf_len = 0.5
|
||||||
data_axis_plot = 4
|
data_axis_plot = 4
|
||||||
kernelstu = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1]) + GPy.kern.bias(X.shape[1])
|
kernelstu = GPy.kern.RBF(X.shape[1]) + GPy.kern.white(X.shape[1]) + GPy.kern.bias(X.shape[1])
|
||||||
kernelgp = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1]) + GPy.kern.bias(X.shape[1])
|
kernelgp = GPy.kern.RBF(X.shape[1]) + GPy.kern.white(X.shape[1]) + GPy.kern.bias(X.shape[1])
|
||||||
|
|
||||||
#Baseline
|
#Baseline
|
||||||
score_folds[0, n] = rmse(Y_test, np.mean(Y_train))
|
score_folds[0, n] = rmse(Y_test, np.mean(Y_train))
|
||||||
|
|
@ -162,8 +163,8 @@ def boston_example(optimize=True, plot=True):
|
||||||
print "Gauss GP"
|
print "Gauss GP"
|
||||||
mgp = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelgp.copy())
|
mgp = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelgp.copy())
|
||||||
mgp.constrain_fixed('.*white', 1e-5)
|
mgp.constrain_fixed('.*white', 1e-5)
|
||||||
mgp['rbf_len'] = rbf_len
|
mgp['.*len'] = rbf_len
|
||||||
mgp['noise'] = noise
|
mgp['.*noise'] = noise
|
||||||
print mgp
|
print mgp
|
||||||
if optimize:
|
if optimize:
|
||||||
mgp.optimize(optimizer=optimizer, messages=messages)
|
mgp.optimize(optimizer=optimizer, messages=messages)
|
||||||
|
|
@ -198,9 +199,9 @@ def boston_example(optimize=True, plot=True):
|
||||||
stu_t_likelihood = GPy.likelihoods.Laplace(Y_train.copy(), t_distribution)
|
stu_t_likelihood = GPy.likelihoods.Laplace(Y_train.copy(), t_distribution)
|
||||||
mstu_t = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelstu.copy(), likelihood=stu_t_likelihood)
|
mstu_t = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelstu.copy(), likelihood=stu_t_likelihood)
|
||||||
mstu_t.constrain_fixed('.*white', 1e-5)
|
mstu_t.constrain_fixed('.*white', 1e-5)
|
||||||
mstu_t.constrain_bounded('.*t_noise', 0.0001, 1000)
|
mstu_t.constrain_bounded('.*t_scale2', 0.0001, 1000)
|
||||||
mstu_t['rbf_len'] = rbf_len
|
mstu_t['rbf_len'] = rbf_len
|
||||||
mstu_t['.*t_noise'] = noise
|
mstu_t['.*t_scale2'] = noise
|
||||||
print mstu_t
|
print mstu_t
|
||||||
if optimize:
|
if optimize:
|
||||||
mstu_t.optimize(optimizer=optimizer, messages=messages)
|
mstu_t.optimize(optimizer=optimizer, messages=messages)
|
||||||
|
|
|
||||||
|
|
@ -1,40 +0,0 @@
|
||||||
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
|
|
||||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
|
||||||
|
|
||||||
try:
|
|
||||||
import pylab as pb
|
|
||||||
except:
|
|
||||||
pass
|
|
||||||
import numpy as np
|
|
||||||
import GPy
|
|
||||||
|
|
||||||
def toy_1d(optimize=True, plot=True):
|
|
||||||
N = 2000
|
|
||||||
M = 20
|
|
||||||
|
|
||||||
#create data
|
|
||||||
X = np.linspace(0,32,N)[:,None]
|
|
||||||
Z = np.linspace(0,32,M)[:,None]
|
|
||||||
Y = np.sin(X) + np.cos(0.3*X) + np.random.randn(*X.shape)/np.sqrt(50.)
|
|
||||||
|
|
||||||
m = GPy.models.SVIGPRegression(X,Y, batchsize=10, Z=Z)
|
|
||||||
m.constrain_bounded('noise_variance',1e-3,1e-1)
|
|
||||||
m.constrain_bounded('white_variance',1e-3,1e-1)
|
|
||||||
|
|
||||||
m.param_steplength = 1e-4
|
|
||||||
|
|
||||||
if plot:
|
|
||||||
fig = pb.figure()
|
|
||||||
ax = fig.add_subplot(111)
|
|
||||||
def cb(foo):
|
|
||||||
ax.cla()
|
|
||||||
m.plot(ax=ax,Z_height=-3)
|
|
||||||
ax.set_ylim(-3,3)
|
|
||||||
fig.canvas.draw()
|
|
||||||
|
|
||||||
if optimize:
|
|
||||||
m.optimize(500, callback=cb, callback_interval=1)
|
|
||||||
|
|
||||||
if plot:
|
|
||||||
m.plot_traces()
|
|
||||||
return m
|
|
||||||
|
|
@ -1,156 +0,0 @@
|
||||||
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
|
|
||||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
|
||||||
|
|
||||||
|
|
||||||
"""
|
|
||||||
Code of Tutorials
|
|
||||||
"""
|
|
||||||
|
|
||||||
try:
|
|
||||||
import pylab as pb
|
|
||||||
pb.ion()
|
|
||||||
except:
|
|
||||||
pass
|
|
||||||
import numpy as np
|
|
||||||
import GPy
|
|
||||||
|
|
||||||
def tuto_GP_regression(optimize=True, plot=True):
|
|
||||||
"""The detailed explanations of the commands used in this file can be found in the tutorial section"""
|
|
||||||
|
|
||||||
X = np.random.uniform(-3.,3.,(20,1))
|
|
||||||
Y = np.sin(X) + np.random.randn(20,1)*0.05
|
|
||||||
|
|
||||||
kernel = GPy.kern.rbf(input_dim=1, variance=1., lengthscale=1.)
|
|
||||||
|
|
||||||
m = GPy.models.GPRegression(X, Y, kernel)
|
|
||||||
|
|
||||||
print m
|
|
||||||
if plot:
|
|
||||||
m.plot()
|
|
||||||
|
|
||||||
m.constrain_positive('')
|
|
||||||
|
|
||||||
m.unconstrain('') # may be used to remove the previous constrains
|
|
||||||
m.constrain_positive('.*rbf_variance')
|
|
||||||
m.constrain_bounded('.*lengthscale',1.,10. )
|
|
||||||
m.constrain_fixed('.*noise',0.0025)
|
|
||||||
|
|
||||||
if optimize:
|
|
||||||
m.optimize()
|
|
||||||
m.optimize_restarts(num_restarts = 10)
|
|
||||||
|
|
||||||
#######################################################
|
|
||||||
#######################################################
|
|
||||||
# sample inputs and outputs
|
|
||||||
X = np.random.uniform(-3.,3.,(50,2))
|
|
||||||
Y = np.sin(X[:,0:1]) * np.sin(X[:,1:2])+np.random.randn(50,1)*0.05
|
|
||||||
|
|
||||||
# define kernel
|
|
||||||
ker = GPy.kern.Matern52(2,ARD=True) + GPy.kern.white(2)
|
|
||||||
|
|
||||||
# create simple GP model
|
|
||||||
m = GPy.models.GPRegression(X, Y, ker)
|
|
||||||
|
|
||||||
# contrain all parameters to be positive
|
|
||||||
m.constrain_positive('')
|
|
||||||
|
|
||||||
# optimize and plot
|
|
||||||
if optimize:
|
|
||||||
m.optimize('tnc', max_f_eval = 1000)
|
|
||||||
if plot:
|
|
||||||
m.plot()
|
|
||||||
|
|
||||||
print m
|
|
||||||
return(m)
|
|
||||||
|
|
||||||
def tuto_kernel_overview(optimize=True, plot=True):
|
|
||||||
"""The detailed explanations of the commands used in this file can be found in the tutorial section"""
|
|
||||||
ker1 = GPy.kern.rbf(1) # Equivalent to ker1 = GPy.kern.rbf(input_dim=1, variance=1., lengthscale=1.)
|
|
||||||
ker2 = GPy.kern.rbf(input_dim=1, variance = .75, lengthscale=2.)
|
|
||||||
ker3 = GPy.kern.rbf(1, .5, .5)
|
|
||||||
|
|
||||||
print ker2
|
|
||||||
|
|
||||||
if plot:
|
|
||||||
ker1.plot()
|
|
||||||
ker2.plot()
|
|
||||||
ker3.plot()
|
|
||||||
|
|
||||||
k1 = GPy.kern.rbf(1,1.,2.)
|
|
||||||
k2 = GPy.kern.Matern32(1, 0.5, 0.2)
|
|
||||||
|
|
||||||
# Product of kernels
|
|
||||||
k_prod = k1.prod(k2) # By default, tensor=False
|
|
||||||
k_prodtens = k1.prod(k2,tensor=True)
|
|
||||||
|
|
||||||
# Sum of kernels
|
|
||||||
k_add = k1.add(k2) # By default, tensor=False
|
|
||||||
k_addtens = k1.add(k2,tensor=True)
|
|
||||||
|
|
||||||
k1 = GPy.kern.rbf(1,1.,2)
|
|
||||||
k2 = GPy.kern.periodic_Matern52(1,variance=1e3, lengthscale=1, period = 1.5, lower=-5., upper = 5)
|
|
||||||
|
|
||||||
k = k1 * k2 # equivalent to k = k1.prod(k2)
|
|
||||||
print k
|
|
||||||
|
|
||||||
# Simulate sample paths
|
|
||||||
X = np.linspace(-5,5,501)[:,None]
|
|
||||||
Y = np.random.multivariate_normal(np.zeros(501),k.K(X),1)
|
|
||||||
|
|
||||||
k1 = GPy.kern.rbf(1)
|
|
||||||
k2 = GPy.kern.Matern32(1)
|
|
||||||
k3 = GPy.kern.white(1)
|
|
||||||
|
|
||||||
k = k1 + k2 + k3
|
|
||||||
print k
|
|
||||||
|
|
||||||
k.constrain_positive('.*var')
|
|
||||||
k.constrain_fixed(np.array([1]),1.75)
|
|
||||||
k.tie_params('.*len')
|
|
||||||
k.unconstrain('white')
|
|
||||||
k.constrain_bounded('white',lower=1e-5,upper=.5)
|
|
||||||
print k
|
|
||||||
|
|
||||||
k_cst = GPy.kern.bias(1,variance=1.)
|
|
||||||
k_mat = GPy.kern.Matern52(1,variance=1., lengthscale=3)
|
|
||||||
Kanova = (k_cst + k_mat).prod(k_cst + k_mat,tensor=True)
|
|
||||||
print Kanova
|
|
||||||
|
|
||||||
# sample inputs and outputs
|
|
||||||
X = np.random.uniform(-3.,3.,(40,2))
|
|
||||||
Y = 0.5*X[:,:1] + 0.5*X[:,1:] + 2*np.sin(X[:,:1]) * np.sin(X[:,1:])
|
|
||||||
|
|
||||||
# Create GP regression model
|
|
||||||
m = GPy.models.GPRegression(X, Y, Kanova)
|
|
||||||
|
|
||||||
if plot:
|
|
||||||
fig = pb.figure(figsize=(5,5))
|
|
||||||
ax = fig.add_subplot(111)
|
|
||||||
m.plot(ax=ax)
|
|
||||||
|
|
||||||
pb.figure(figsize=(20,3))
|
|
||||||
pb.subplots_adjust(wspace=0.5)
|
|
||||||
axs = pb.subplot(1,5,1)
|
|
||||||
m.plot(ax=axs)
|
|
||||||
pb.subplot(1,5,2)
|
|
||||||
pb.ylabel("= ",rotation='horizontal',fontsize='30')
|
|
||||||
axs = pb.subplot(1,5,3)
|
|
||||||
m.plot(ax=axs, which_parts=[False,True,False,False])
|
|
||||||
pb.ylabel("cst +",rotation='horizontal',fontsize='30')
|
|
||||||
axs = pb.subplot(1,5,4)
|
|
||||||
m.plot(ax=axs, which_parts=[False,False,True,False])
|
|
||||||
pb.ylabel("+ ",rotation='horizontal',fontsize='30')
|
|
||||||
axs = pb.subplot(1,5,5)
|
|
||||||
pb.ylabel("+ ",rotation='horizontal',fontsize='30')
|
|
||||||
m.plot(ax=axs, which_parts=[False,False,False,True])
|
|
||||||
|
|
||||||
return(m)
|
|
||||||
|
|
||||||
|
|
||||||
def model_interaction(optimize=True, plot=True):
|
|
||||||
X = np.random.randn(20,1)
|
|
||||||
Y = np.sin(X) + np.random.randn(*X.shape)*0.01 + 5.
|
|
||||||
k = GPy.kern.rbf(1) + GPy.kern.bias(1)
|
|
||||||
m = GPy.models.GPRegression(X, Y, kernel=k)
|
|
||||||
return m
|
|
||||||
|
|
||||||
|
|
@ -4,7 +4,6 @@
|
||||||
from gp_regression import GPRegression
|
from gp_regression import GPRegression
|
||||||
from gp_classification import GPClassification
|
from gp_classification import GPClassification
|
||||||
from sparse_gp_regression import SparseGPRegression, SparseGPRegressionUncertainInput
|
from sparse_gp_regression import SparseGPRegression, SparseGPRegressionUncertainInput
|
||||||
from svigp_regression import SVIGPRegression
|
|
||||||
from sparse_gp_classification import SparseGPClassification
|
from sparse_gp_classification import SparseGPClassification
|
||||||
from gplvm import GPLVM
|
from gplvm import GPLVM
|
||||||
from bcgplvm import BCGPLVM
|
from bcgplvm import BCGPLVM
|
||||||
|
|
|
||||||
|
|
@ -1,171 +0,0 @@
|
||||||
# Copyright (c) 2013, Ricardo Andrade
|
|
||||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
|
||||||
|
|
||||||
import numpy as np
|
|
||||||
from ..core import GP
|
|
||||||
from .. import likelihoods
|
|
||||||
from .. import kern
|
|
||||||
|
|
||||||
class GPMultioutputRegression(GP):
|
|
||||||
"""
|
|
||||||
Multiple output Gaussian process with Gaussian noise
|
|
||||||
|
|
||||||
This is a wrapper around the models.GP class, with a set of sensible defaults
|
|
||||||
|
|
||||||
:param X_list: input observations
|
|
||||||
:type X_list: list of numpy arrays (num_data_output_i x input_dim), one array per output
|
|
||||||
:param Y_list: observed values
|
|
||||||
:type Y_list: list of numpy arrays (num_data_output_i x 1), one array per output
|
|
||||||
:param kernel_list: GPy kernels, defaults to rbf
|
|
||||||
:type kernel_list: list of GPy kernels
|
|
||||||
:param noise_variance_list: noise parameters per output, defaults to 1.0 for every output
|
|
||||||
:type noise_variance_list: list of floats
|
|
||||||
:param normalize_X: whether to normalize the input data before computing (predictions will be in original scales)
|
|
||||||
:type normalize_X: False|True
|
|
||||||
:param normalize_Y: whether to normalize the input data before computing (predictions will be in original scales)
|
|
||||||
:type normalize_Y: False|True
|
|
||||||
:param rank: number tuples of the corregionalization parameters 'coregion_W' (see coregionalize kernel documentation)
|
|
||||||
:type rank: integer
|
|
||||||
"""
|
|
||||||
|
|
||||||
def __init__(self,X_list,Y_list,kernel_list=None,noise_variance_list=None,normalize_X=False,normalize_Y=False,rank=1):
|
|
||||||
|
|
||||||
self.output_dim = len(Y_list)
|
|
||||||
assert len(X_list) == self.output_dim, 'Number of outputs do not match length of inputs list.'
|
|
||||||
|
|
||||||
#Inputs indexing
|
|
||||||
i = 0
|
|
||||||
index = []
|
|
||||||
for x,y in zip(X_list,Y_list):
|
|
||||||
assert x.shape[0] == y.shape[0]
|
|
||||||
index.append(np.repeat(i,x.size)[:,None])
|
|
||||||
i += 1
|
|
||||||
index = np.vstack(index)
|
|
||||||
X = np.hstack([np.vstack(X_list),index])
|
|
||||||
original_dim = X.shape[1] - 1
|
|
||||||
|
|
||||||
#Mixed noise likelihood definition
|
|
||||||
likelihood = likelihoods.Gaussian_Mixed_Noise(Y_list,noise_params=noise_variance_list,normalize=normalize_Y)
|
|
||||||
|
|
||||||
#Coregionalization kernel definition
|
|
||||||
if kernel_list is None:
|
|
||||||
kernel_list = [kern.rbf(original_dim)]
|
|
||||||
mkernel = kern.build_lcm(input_dim=original_dim, output_dim=self.output_dim, kernel_list = kernel_list, rank=rank)
|
|
||||||
|
|
||||||
self.multioutput = True
|
|
||||||
GP.__init__(self, X, likelihood, mkernel, normalize_X=normalize_X)
|
|
||||||
self.ensure_default_constraints()
|
|
||||||
|
|
||||||
def _add_output_index(self,X,output):
|
|
||||||
"""
|
|
||||||
In a multioutput model, appends an index column to X to specify the output it is related to.
|
|
||||||
|
|
||||||
:param X: Input data
|
|
||||||
:type X: np.ndarray, N x self.input_dim
|
|
||||||
:param output: output X is related to
|
|
||||||
:type output: integer in {0,..., output_dim-1}
|
|
||||||
|
|
||||||
.. Note:: For multiple non-independent outputs models only.
|
|
||||||
"""
|
|
||||||
|
|
||||||
assert hasattr(self,'multioutput'), 'This function is for multiple output models only.'
|
|
||||||
|
|
||||||
index = np.ones((X.shape[0],1))*output
|
|
||||||
return np.hstack((X,index))
|
|
||||||
|
|
||||||
def plot_single_output(self, X, output):
|
|
||||||
"""
|
|
||||||
A simple wrapper around self.plot, with appropriate setting of the fixed_inputs argument
|
|
||||||
"""
|
|
||||||
raise NotImplementedError
|
|
||||||
|
|
||||||
def _raw_predict_single_output(self, _Xnew, output, which_parts='all', full_cov=False,stop=False):
|
|
||||||
"""
|
|
||||||
For a specific output, calls _raw_predict() at the new point(s) _Xnew.
|
|
||||||
This functions calls _add_output_index(), so _Xnew should not have an index column specifying the output.
|
|
||||||
---------
|
|
||||||
|
|
||||||
:param Xnew: The points at which to make a prediction
|
|
||||||
:type Xnew: np.ndarray, Nnew x self.input_dim
|
|
||||||
:param output: output to predict
|
|
||||||
:type output: integer in {0,..., output_dim-1}
|
|
||||||
:param which_parts: specifies which outputs kernel(s) to use in prediction
|
|
||||||
:type which_parts: ('all', list of bools)
|
|
||||||
:param full_cov: whether to return the full covariance matrix, or just the diagonal
|
|
||||||
|
|
||||||
.. Note:: For multiple non-independent outputs models only.
|
|
||||||
"""
|
|
||||||
_Xnew = self._add_output_index(_Xnew, output)
|
|
||||||
return self._raw_predict(_Xnew, which_parts=which_parts,full_cov=full_cov, stop=stop)
|
|
||||||
|
|
||||||
def predict_single_output(self, Xnew,output=0, which_parts='all', full_cov=False, likelihood_args=dict()):
|
|
||||||
"""
|
|
||||||
For a specific output, calls predict() at the new point(s) Xnew.
|
|
||||||
This functions calls _add_output_index(), so Xnew should not have an index column specifying the output.
|
|
||||||
|
|
||||||
:param Xnew: The points at which to make a prediction
|
|
||||||
:type Xnew: np.ndarray, Nnew x self.input_dim
|
|
||||||
:param which_parts: specifies which outputs kernel(s) to use in prediction
|
|
||||||
:type which_parts: ('all', list of bools)
|
|
||||||
:param full_cov: whether to return the full covariance matrix, or just the diagonal
|
|
||||||
:type full_cov: bool
|
|
||||||
:returns: mean: posterior mean, a Numpy array, Nnew x self.input_dim
|
|
||||||
:returns: var: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
|
|
||||||
:returns: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.input_dim
|
|
||||||
|
|
||||||
.. Note:: For multiple non-independent outputs models only.
|
|
||||||
"""
|
|
||||||
Xnew = self._add_output_index(Xnew, output)
|
|
||||||
return self.predict(Xnew, which_parts=which_parts, full_cov=full_cov, likelihood_args=likelihood_args)
|
|
||||||
|
|
||||||
def plot_single_output_f(self, output=None, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, full_cov=False, fignum=None, ax=None):
|
|
||||||
"""
|
|
||||||
For a specific output, in a multioutput model, this function works just as plot_f on single output models.
|
|
||||||
|
|
||||||
:param output: which output to plot (for multiple output models only)
|
|
||||||
:type output: integer (first output is 0)
|
|
||||||
:param samples: the number of a posteriori samples to plot
|
|
||||||
:param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits
|
|
||||||
:param which_data: which if the training data to plot (default all)
|
|
||||||
:type which_data: 'all' or a slice object to slice self.X, self.Y
|
|
||||||
:param which_parts: which of the kernel functions to plot (additively)
|
|
||||||
:type which_parts: 'all', or list of bools
|
|
||||||
:param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
|
|
||||||
:type resolution: int
|
|
||||||
:param full_cov:
|
|
||||||
:type full_cov: bool
|
|
||||||
:param fignum: figure to plot on.
|
|
||||||
:type fignum: figure number
|
|
||||||
:param ax: axes to plot on.
|
|
||||||
:type ax: axes handle
|
|
||||||
"""
|
|
||||||
assert output is not None, "An output must be specified."
|
|
||||||
assert len(self.likelihood.noise_model_list) > output, "The model has only %s outputs." %(self.output_dim + 1)
|
|
||||||
|
|
||||||
if which_data == 'all':
|
|
||||||
which_data = slice(None)
|
|
||||||
|
|
||||||
if ax is None:
|
|
||||||
fig = pb.figure(num=fignum)
|
|
||||||
ax = fig.add_subplot(111)
|
|
||||||
|
|
||||||
if self.X.shape[1] == 2:
|
|
||||||
Xu = self.X[self.X[:,-1]==output ,0:1]
|
|
||||||
Xnew, xmin, xmax = x_frame1D(Xu, plot_limits=plot_limits)
|
|
||||||
Xnew_indexed = self._add_output_index(Xnew,output)
|
|
||||||
|
|
||||||
m, v = self._raw_predict(Xnew_indexed, which_parts=which_parts)
|
|
||||||
|
|
||||||
if samples:
|
|
||||||
Ysim = self.posterior_samples_f(Xnew_indexed, samples, which_parts=which_parts, full_cov=True)
|
|
||||||
for yi in Ysim.T:
|
|
||||||
ax.plot(Xnew, yi[:,None], Tango.colorsHex['darkBlue'], linewidth=0.25)
|
|
||||||
|
|
||||||
gpplot(Xnew, m, m - 2 * np.sqrt(v), m + 2 * np.sqrt(v), axes=ax)
|
|
||||||
ax.plot(Xu[which_data], self.likelihood.Y[self.likelihood.index==output][:,None], 'kx', mew=1.5)
|
|
||||||
ax.set_xlim(xmin, xmax)
|
|
||||||
ymin, ymax = min(np.append(self.likelihood.Y, m - 2 * np.sqrt(np.diag(v)[:, None]))), max(np.append(self.likelihood.Y, m + 2 * np.sqrt(np.diag(v)[:, None])))
|
|
||||||
ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
|
|
||||||
ax.set_ylim(ymin, ymax)
|
|
||||||
|
|
||||||
|
|
||||||
|
|
@ -1,80 +0,0 @@
|
||||||
# Copyright (c) 2013, Ricardo Andrade
|
|
||||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
|
||||||
|
|
||||||
|
|
||||||
import numpy as np
|
|
||||||
from ..core import SparseGP
|
|
||||||
from .. import likelihoods
|
|
||||||
from .. import kern
|
|
||||||
from ..util import multioutput
|
|
||||||
|
|
||||||
class SparseGPMultioutputRegression(SparseGP):
|
|
||||||
"""
|
|
||||||
Sparse multiple output Gaussian process with Gaussian noise
|
|
||||||
|
|
||||||
This is a wrapper around the models.SparseGP class, with a set of sensible defaults
|
|
||||||
|
|
||||||
:param X_list: input observations
|
|
||||||
:type X_list: list of numpy arrays (num_data_output_i x input_dim), one array per output
|
|
||||||
:param Y_list: observed values
|
|
||||||
:type Y_list: list of numpy arrays (num_data_output_i x 1), one array per output
|
|
||||||
:param kernel_list: GPy kernels, defaults to rbf
|
|
||||||
:type kernel_list: list of GPy kernels
|
|
||||||
:param noise_variance_list: noise parameters per output, defaults to 1.0 for every output
|
|
||||||
:type noise_variance_list: list of floats
|
|
||||||
:param normalize_X: whether to normalize the input data before computing (predictions will be in original scales)
|
|
||||||
:type normalize_X: False|True
|
|
||||||
:param normalize_Y: whether to normalize the input data before computing (predictions will be in original scales)
|
|
||||||
:type normalize_Y: False|True
|
|
||||||
:param Z_list: inducing inputs (optional)
|
|
||||||
:type Z_list: list of numpy arrays (num_inducing_output_i x input_dim), one array per output | empty list
|
|
||||||
:param num_inducing: number of inducing inputs per output, defaults to 10 (ignored if Z_list is not empty)
|
|
||||||
:type num_inducing: integer
|
|
||||||
:param rank: number tuples of the corregionalization parameters 'coregion_W' (see coregionalize kernel documentation)
|
|
||||||
:type rank: integer
|
|
||||||
"""
|
|
||||||
#NOTE not tested with uncertain inputs
|
|
||||||
def __init__(self,X_list,Y_list,kernel_list=None,noise_variance_list=None,normalize_X=False,normalize_Y=False,Z_list=[],num_inducing=10,rank=1):
|
|
||||||
|
|
||||||
self.output_dim = len(Y_list)
|
|
||||||
assert len(X_list) == self.output_dim, 'Number of outputs do not match length of inputs list.'
|
|
||||||
|
|
||||||
#Inducing inputs list
|
|
||||||
if len(Z_list):
|
|
||||||
assert len(Z_list) == self.output_dim, 'Number of outputs do not match length of inducing inputs list.'
|
|
||||||
else:
|
|
||||||
if isinstance(num_inducing,np.int):
|
|
||||||
num_inducing = [num_inducing] * self.output_dim
|
|
||||||
num_inducing = np.asarray(num_inducing)
|
|
||||||
assert num_inducing.size == self.output_dim, 'Number of outputs do not match length of inducing inputs list.'
|
|
||||||
for ni,X in zip(num_inducing,X_list):
|
|
||||||
i = np.random.permutation(X.shape[0])[:ni]
|
|
||||||
Z_list.append(X[i].copy())
|
|
||||||
|
|
||||||
#Inputs and inducing inputs indexing
|
|
||||||
i = 0
|
|
||||||
index = []
|
|
||||||
index_z = []
|
|
||||||
for x,y,z in zip(X_list,Y_list,Z_list):
|
|
||||||
assert x.shape[0] == y.shape[0]
|
|
||||||
index.append(np.repeat(i,x.size)[:,None])
|
|
||||||
index_z.append(np.repeat(i,z.size)[:,None])
|
|
||||||
i += 1
|
|
||||||
index = np.vstack(index)
|
|
||||||
index_z = np.vstack(index_z)
|
|
||||||
X = np.hstack([np.vstack(X_list),index])
|
|
||||||
Z = np.hstack([np.vstack(Z_list),index_z])
|
|
||||||
original_dim = X.shape[1] - 1
|
|
||||||
|
|
||||||
#Mixed noise likelihood definition
|
|
||||||
likelihood = likelihoods.Gaussian_Mixed_Noise(Y_list,noise_params=noise_variance_list,normalize=normalize_Y)
|
|
||||||
|
|
||||||
#Coregionalization kernel definition
|
|
||||||
if kernel_list is None:
|
|
||||||
kernel_list = [kern.rbf(original_dim)]
|
|
||||||
mkernel = kern.build_lcm(input_dim=original_dim, output_dim=self.output_dim, kernel_list = kernel_list, rank=rank)
|
|
||||||
|
|
||||||
self.multioutput = True
|
|
||||||
SparseGP.__init__(self, X, likelihood, mkernel, Z=Z, normalize_X=normalize_X)
|
|
||||||
self.constrain_fixed('.*iip_\d+_1')
|
|
||||||
self.ensure_default_constraints()
|
|
||||||
|
|
@ -1,45 +0,0 @@
|
||||||
# Copyright (c) 2012, James Hensman
|
|
||||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
|
||||||
|
|
||||||
import numpy as np
|
|
||||||
from ..core import SVIGP
|
|
||||||
from .. import likelihoods
|
|
||||||
from .. import kern
|
|
||||||
|
|
||||||
class SVIGPRegression(SVIGP):
|
|
||||||
"""
|
|
||||||
Gaussian Process model for regression
|
|
||||||
|
|
||||||
This is a thin wrapper around the SVIGP class, with a set of sensible defalts
|
|
||||||
|
|
||||||
:param X: input observations
|
|
||||||
:param Y: observed values
|
|
||||||
:param kernel: a GPy kernel, defaults to rbf+white
|
|
||||||
:param normalize_X: whether to normalize the input data before computing (predictions will be in original scales)
|
|
||||||
:type normalize_X: False|True
|
|
||||||
:param normalize_Y: whether to normalize the input data before computing (predictions will be in original scales)
|
|
||||||
:type normalize_Y: False|True
|
|
||||||
:rtype: model object
|
|
||||||
|
|
||||||
.. Note:: Multiple independent outputs are allowed using columns of Y
|
|
||||||
|
|
||||||
"""
|
|
||||||
|
|
||||||
def __init__(self, X, Y, kernel=None, Z=None, num_inducing=10, q_u=None, batchsize=10, normalize_Y=False):
|
|
||||||
# kern defaults to rbf (plus white for stability)
|
|
||||||
if kernel is None:
|
|
||||||
kernel = kern.rbf(X.shape[1], variance=1., lengthscale=4.) + kern.white(X.shape[1], 1e-3)
|
|
||||||
|
|
||||||
# Z defaults to a subset of the data
|
|
||||||
if Z is None:
|
|
||||||
i = np.random.permutation(X.shape[0])[:num_inducing]
|
|
||||||
Z = X[i].copy()
|
|
||||||
else:
|
|
||||||
assert Z.shape[1] == X.shape[1]
|
|
||||||
|
|
||||||
# likelihood defaults to Gaussian
|
|
||||||
likelihood = likelihoods.Gaussian(Y, normalize=normalize_Y)
|
|
||||||
|
|
||||||
SVIGP.__init__(self, X, likelihood, kernel, Z, q_u=q_u, batchsize=batchsize)
|
|
||||||
self.load_batch()
|
|
||||||
|
|
||||||
|
|
@ -6,7 +6,6 @@ import models_plots
|
||||||
import priors_plots
|
import priors_plots
|
||||||
import variational_plots
|
import variational_plots
|
||||||
import kernel_plots
|
import kernel_plots
|
||||||
import svig_plots
|
|
||||||
import dim_reduction_plots
|
import dim_reduction_plots
|
||||||
import mapping_plots
|
import mapping_plots
|
||||||
import Tango
|
import Tango
|
||||||
|
|
|
||||||
|
|
@ -5,23 +5,28 @@
|
||||||
|
|
||||||
Welcome to GPy's documentation!
|
Welcome to GPy's documentation!
|
||||||
===============================
|
===============================
|
||||||
For a quick start, you can have a look at one of the tutorials:
|
|
||||||
|
|
||||||
* `Basic Gaussian process regression <tuto_GP_regression.html>`_
|
`GPy <http://sheffieldml.github.io/GPy/>`_ is a Gaussian Process (GP) framework written in Python, from the Sheffield machine learning group.
|
||||||
* `Interacting with models <tuto_interacting_with_models.html>`_
|
|
||||||
* `A kernel overview <tuto_kernel_overview.html>`_
|
|
||||||
* `Writing new kernels <tuto_creating_new_kernels.html>`_
|
|
||||||
* `Writing new models <tuto_creating_new_models.html>`_
|
|
||||||
* `Parameterization handles <tuto_parameterized.html>`_
|
|
||||||
|
|
||||||
You may also be interested by some examples in the GPy/examples folder.
|
The `GPy homepage <http://sheffieldml.github.io/GPy/>`_ contains tutorials for users and further information on the project, including installation instructions.
|
||||||
|
This documentation is mostly aimed at developers interacting closely with the code-base.
|
||||||
|
|
||||||
|
The code can be found on our `Github project page <https://github.com/SheffieldML/GPy>`_. It is open source and provided under the BSD license.
|
||||||
|
|
||||||
|
.. * `Basic Gaussian process regression <tuto_GP_regression.html>`_
|
||||||
|
.. * `Interacting with models <tuto_interacting_with_models.html>`_
|
||||||
|
.. * `A kernel overview <tuto_kernel_overview.html>`_
|
||||||
|
.. * `Writing new kernels <tuto_creating_new_kernels.html>`_
|
||||||
|
.. * `Writing new models <tuto_creating_new_models.html>`_
|
||||||
|
.. * `Parameterization handles <tuto_parameterized.html>`_
|
||||||
|
|
||||||
|
.. You may also be interested by some examples in the GPy/examples folder.
|
||||||
|
|
||||||
Contents:
|
Contents:
|
||||||
|
|
||||||
.. toctree::
|
.. toctree::
|
||||||
:maxdepth: 2
|
:maxdepth: 2
|
||||||
|
|
||||||
installation
|
|
||||||
GPy
|
GPy
|
||||||
|
|
||||||
|
|
||||||
|
|
|
||||||
30
doc/log.txt
30
doc/log.txt
|
|
@ -1,7 +1,7 @@
|
||||||
/home/alans/Work/GPy/GPy/__init__.py:docstring of GPy.load:1: WARNING: Inline interpreted text or phrase reference start-string without end-string.
|
/home/alans/Work/GPy/GPy/__init__.py:docstring of GPy.load:1: WARNING: Inline interpreted text or phrase reference start-string without end-string.
|
||||||
/home/alans/Work/GPy/GPy/core/gp.py:docstring of GPy.core.gp.GP:7: WARNING: Field list ends without a blank line; unexpected unindent.
|
/home/alans/Work/GPy/GPy/core/gp.py:docstring of GPy.core.gp.GP.optimize:8: ERROR: Unknown interpreted text role "module".
|
||||||
/home/alans/Work/GPy/GPy/core/gp.py:docstring of GPy.core.gp.GP:10: ERROR: Unexpected indentation.
|
|
||||||
/home/alans/Work/GPy/GPy/core/gp.py:docstring of GPy.core.gp.GP.predictive_gradients:5: ERROR: Unexpected indentation.
|
/home/alans/Work/GPy/GPy/core/gp.py:docstring of GPy.core.gp.GP.predictive_gradients:5: ERROR: Unexpected indentation.
|
||||||
|
/home/alans/Work/GPy/GPy/core/gp.py:docstring of GPy.core.gp.GP.predictive_gradients:8: WARNING: Block quote ends without a blank line; unexpected unindent.
|
||||||
/home/alans/Work/GPy/GPy/core/model.py:docstring of GPy.core.model.Model.optimize_restarts:29: WARNING: Explicit markup ends without a blank line; unexpected unindent.
|
/home/alans/Work/GPy/GPy/core/model.py:docstring of GPy.core.model.Model.optimize_restarts:29: WARNING: Explicit markup ends without a blank line; unexpected unindent.
|
||||||
/home/alans/Work/GPy/doc/GPy.core.rst:65: WARNING: autodoc: failed to import module u'GPy.core.symbolic'; the following exception was raised:
|
/home/alans/Work/GPy/doc/GPy.core.rst:65: WARNING: autodoc: failed to import module u'GPy.core.symbolic'; the following exception was raised:
|
||||||
Traceback (most recent call last):
|
Traceback (most recent call last):
|
||||||
|
|
@ -23,31 +23,6 @@ ImportError: No module named lambdify
|
||||||
/home/alans/Work/GPy/GPy/core/parameterization/ties_and_remappings.py:docstring of GPy.core.parameterization.ties_and_remappings.Tie:18: SEVERE: Unexpected section title or transition.
|
/home/alans/Work/GPy/GPy/core/parameterization/ties_and_remappings.py:docstring of GPy.core.parameterization.ties_and_remappings.Tie:18: SEVERE: Unexpected section title or transition.
|
||||||
|
|
||||||
================================
|
================================
|
||||||
/home/alans/Work/GPy/doc/GPy.examples.rst:18: WARNING: autodoc: failed to import module u'GPy.examples.coreg_example'; the following exception was raised:
|
|
||||||
Traceback (most recent call last):
|
|
||||||
File "/home/alans/anaconda/envs/GPy/lib/python2.7/site-packages/sphinx/ext/autodoc.py", line 335, in import_object
|
|
||||||
__import__(self.modname)
|
|
||||||
File "/home/alans/Work/GPy/GPy/examples/coreg_example.py", line 44, in <module>
|
|
||||||
m = GPy.models.SparseGPCoregionalizedRegression(X_list=[X1], Y_list=[Y1], Z_list = [Z1], kernel=kern)
|
|
||||||
File "/home/alans/Work/GPy/GPy/core/parameterization/parameterized.py", line 19, in __call__
|
|
||||||
self = super(ParametersChangedMeta, self).__call__(*args, **kw)
|
|
||||||
File "/home/alans/Work/GPy/GPy/models/sparse_gp_coregionalized_regression.py", line 66, in __init__
|
|
||||||
self['.*inducing'][:,-1].fix()
|
|
||||||
File "/home/alans/Work/GPy/GPy/core/parameterization/parameter_core.py", line 444, in constrain_fixed
|
|
||||||
self.notify_observers(self, None if trigger_parent else -np.inf)
|
|
||||||
File "/home/alans/Work/GPy/GPy/core/parameterization/parameter_core.py", line 148, in notify_observers
|
|
||||||
[callble(self, which=which) for _, _, callble in self.observers]
|
|
||||||
File "/home/alans/Work/GPy/GPy/core/parameterization/parameter_core.py", line 1077, in _pass_through_notify_observers
|
|
||||||
self.notify_observers(which=which)
|
|
||||||
File "/home/alans/Work/GPy/GPy/core/parameterization/parameter_core.py", line 148, in notify_observers
|
|
||||||
[callble(self, which=which) for _, _, callble in self.observers]
|
|
||||||
File "/home/alans/Work/GPy/GPy/core/parameterization/parameter_core.py", line 1075, in _parameters_changed_notification
|
|
||||||
self.parameters_changed()
|
|
||||||
File "/home/alans/Work/GPy/GPy/core/sparse_gp.py", line 66, in parameters_changed
|
|
||||||
self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.Z, self.likelihood, self.Y, self.Y_metadata)
|
|
||||||
File "/home/alans/Work/GPy/GPy/inference/latent_function_inference/var_dtc.py", line 170, in inference
|
|
||||||
import ipdb; ipdb.set_trace()
|
|
||||||
ImportError: No module named ipdb
|
|
||||||
/home/alans/Work/GPy/GPy/kern/_src/coregionalize.py:docstring of GPy.kern._src.coregionalize.Coregionalize:5: ERROR: Unexpected indentation.
|
/home/alans/Work/GPy/GPy/kern/_src/coregionalize.py:docstring of GPy.kern._src.coregionalize.Coregionalize:5: ERROR: Unexpected indentation.
|
||||||
/home/alans/Work/GPy/doc/GPy.kern._src.rst:73: WARNING: autodoc: failed to import module u'GPy.kern._src.hierarchical'; the following exception was raised:
|
/home/alans/Work/GPy/doc/GPy.kern._src.rst:73: WARNING: autodoc: failed to import module u'GPy.kern._src.hierarchical'; the following exception was raised:
|
||||||
Traceback (most recent call last):
|
Traceback (most recent call last):
|
||||||
|
|
@ -187,6 +162,7 @@ Parameter handles
|
||||||
|
|
||||||
:py:class:`~GPy.core.parameterization.param.Param`
|
:py:class:`~GPy.core.parameterization.param.Param`
|
||||||
===========
|
===========
|
||||||
|
/home/alans/Work/GPy/doc/installation.rst:: WARNING: document isn't included in any toctree
|
||||||
/home/alans/Work/GPy/doc/kernel_implementation.rst:: WARNING: document isn't included in any toctree
|
/home/alans/Work/GPy/doc/kernel_implementation.rst:: WARNING: document isn't included in any toctree
|
||||||
/home/alans/Work/GPy/doc/modules.rst:: WARNING: document isn't included in any toctree
|
/home/alans/Work/GPy/doc/modules.rst:: WARNING: document isn't included in any toctree
|
||||||
/home/alans/Work/GPy/doc/tuto_GP_regression.rst:: WARNING: document isn't included in any toctree
|
/home/alans/Work/GPy/doc/tuto_GP_regression.rst:: WARNING: document isn't included in any toctree
|
||||||
|
|
|
||||||
Loading…
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