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much tidying and breakage in the GP class
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James Hensman
parent
791d240d96
commit
ea0802d938
2 changed files with 72 additions and 126 deletions
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@ -196,6 +196,9 @@ class gaussian(likelihood):
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Gaussian likelihood
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Y is expected to take values in (-inf,inf)
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"""
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self.variance = variance
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self._data = Y
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self.
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def moments_match(self,i,tau_i,v_i):
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"""
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Moments match of the marginal approximation in EP algorithm
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@ -219,8 +222,8 @@ class gaussian(likelihood):
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if U is not None:
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pb.plot(U,np.ones(U.shape[0])*self.Y.min()*.8,'r|',mew=1.5,markersize=12)
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def predictive_mean(self,mu,Sigma):
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return mu
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def _log_likelihood_gradients():
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raise NotImplementedError
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else:
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var = var[:,None] * np.square(self._Ystd)
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189
GPy/models/GP.py
189
GPy/models/GP.py
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@ -8,23 +8,22 @@ from .. import kern
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from ..core import model
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from ..util.linalg import pdinv,mdot
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from ..util.plot import gpplot, Tango
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from ..inference.EP import Full
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from ..inference.likelihoods import likelihood,probit,poisson,gaussian
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from ..inference.EP import Full # TODO: tidy
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from ..inference import likelihoods
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class GP(model):
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"""
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Gaussian Process model for regression and EP
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:param X: input observations
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:param Y: observed values
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:param kernel: a GPy kernel, defaults to rbf+white
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:parm likelihood: a GPy likelihood
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:param normalize_X: whether to normalize the input data before computing (predictions will be in original scales)
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:type normalize_X: False|True
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:param normalize_Y: whether to normalize the input data before computing (predictions will be in original scales)
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:type normalize_Y: False|True
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:param Xslices: how the X,Y data co-vary in the kernel (i.e. which "outputs" they correspond to). See (link:slicing)
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:rtype: model object
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:parm likelihood: a GPy likelihood, defaults to gaussian
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:param epsilon_ep: convergence criterion for the Expectation Propagation algorithm, defaults to 0.1
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:param powerep: power-EP parameters [$\eta$,$\delta$], defaults to [1.,1.]
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:type powerep: list
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@ -32,23 +31,19 @@ class GP(model):
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.. Note:: Multiple independent outputs are allowed using columns of Y
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"""
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#TODO: make beta parameter explicit
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#TODO: when using EP, predict needs to return 3 values otherwise it just needs 2. At the moment predict returns 3 values in any case.
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def __init__(self,X,Y=None,kernel=None,normalize_X=False,normalize_Y=False, Xslices=None,likelihood=None,epsilon_ep=1e-3,power_ep=[1.,1.]):
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def __init__(self, X, kernel, likelihood, normalize_X=False, Xslices=None):
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# parse arguments
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self.Xslices = Xslices
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self.X = X
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self.N, self.Q = self.X.shape
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assert len(self.X.shape)==2
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if kernel is None:
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kernel = kern.rbf(X.shape[1]) + kern.bias(X.shape[1]) + kern.white(X.shape[1])
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else:
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assert isinstance(kernel, kern.kern)
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self.N, self.Q = self.X.shape
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assert isinstance(kernel, kern.kern)
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self.kern = kernel
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#here's some simple normalisation
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#here's some simple normalisation for the inputs
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if normalize_X:
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self._Xmean = X.mean(0)[None,:]
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self._Xstd = X.std(0)[None,:]
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@ -59,82 +54,48 @@ class GP(model):
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self._Xmean = np.zeros((1,self.X.shape[1]))
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self._Xstd = np.ones((1,self.X.shape[1]))
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# Y - likelihood related variables, these might change whether using EP or not
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if likelihood is None:
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assert Y is not None, "Either Y or likelihood must be defined"
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self.likelihood = gaussian(Y)
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else:
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self.likelihood = likelihood
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assert len(self.likelihood.Y.shape)==2
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self.likelihood = likelihood
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self.Y = self.likelihood.Y
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self.YYT = self.likelihood.YYT # TODO: this is ugly. what about sufficient_stats?
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assert self.X.shape[0] == self.likelihood.Y.shape[0]
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self.N, self.D = self.likelihood.Y.shape
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if isinstance(self.likelihood,gaussian):
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self.EP = False
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self.Y = Y
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self.beta = 100.#FIXME beta should be an explicit parameter for this model
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# Here's some simple normalisation
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if normalize_Y:
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self._Ymean = Y.mean(0)[None,:]
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self._Ystd = Y.std(0)[None,:]
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self.Y = (Y.copy()- self._Ymean) / self._Ystd
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else:
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self._Ymean = np.zeros((1,self.Y.shape[1]))
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self._Ystd = np.ones((1,self.Y.shape[1]))
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if self.D > self.N:
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# then it's more efficient to store YYT
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self.YYT = np.dot(self.Y, self.Y.T)
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else:
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self.YYT = None
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else:
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if self.D > 1:
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raise NotImplementedError, "EP is not implemented for D > 1"
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# Y is defined after approximating the likelihood
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self.EP = True
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self.eta,self.delta = power_ep
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self.epsilon_ep = epsilon_ep
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self.beta = np.ones([self.N,self.D])
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self.Z_ep = 0
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self.Y = None
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self._Ymean = np.zeros((1,self.D))
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self._Ystd = np.ones((1,self.D))
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model.__init__(self)
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def _set_params(self,p):
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# TODO: add beta when not using EP
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self.kern._set_params_transformed(p)
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self.kern._set_params_transformed(p[:self.kern.Nparam])
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self.likelihood._set_params(p[self.kern.Nparam:])
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self.K = self.kern.K(self.X,slices1=self.Xslices)
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if self.EP:
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self.K += np.diag(1./self.beta.flatten())
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#else:
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# self.beta = p[-1]
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self.K += np.diag(self.likelihood_variance)
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self.Ki, self.L, self.Li, self.K_logdet = pdinv(self.K)
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#the gradient of the likelihood wrt the covariance matrix
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if self.YYT is None:
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self._alpha = np.dot(self.Ki,self.Y)
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self._alpha2 = np.square(self._alpha)
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self.dL_dK = 0.5*(np.dot(self._alpha,self._alpha.T)-self.D*self.Ki)
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else:
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tmp = mdot(self.Ki, self.YYT, self.Ki)
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self._alpha2 = np.diag(tmp)
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self.dL_dK = 0.5*(tmp - self.D*self.Ki)
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def _get_params(self):
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# TODO: add beta when not using EP
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return self.kern._get_params_transformed()
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return np.hstack((self.kern._get_params_transformed(), self.likelihood._get_params()))
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def _get_param_names(self):
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# TODO: add beta when not using EP
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return self.kern._get_param_names_transformed()
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return self.kern._get_param_names_transformed() + self.likelihood._get_param_names()
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def approximate_likelihood(self):
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def update_likelihood_approximation(self):
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"""
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Approximates a non-gaussian likelihood using Expectation Propagation
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For a Gaussian (or direct: TODO) likelihood, no iteration is required:
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this function does nothing
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"""
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assert not isinstance(self.likelihood, gaussian), "EP is only available for non-gaussian likelihoods"
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self.ep_approx = Full(self.K,self.likelihood,epsilon = self.epsilon_ep,power_ep=[self.eta,self.delta])
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self.beta, self.Y, self.Z_ep = self.ep_approx.fit_EP()
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if self.D > self.N:
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# then it's more efficient to store YYT
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self.YYT = np.dot(self.Y, self.Y.T)
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else:
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self.YYT = None
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# Kernel plus noise variance term
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self.K = self.kern.K(self.X,slices1=self.Xslices) + np.diag(1./self.beta.flatten())
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self.Ki, self.L, self.Li, self.K_logdet = pdinv(self.K)
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self.likelihood.fit(self.K)
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self.Y, self.YYT, self.likelihood_variance, self.likelihood_Z = self.likelihood.sufficient_stats() # TODO: just store these in the likelihood?
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def _model_fit_term(self):
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"""
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@ -147,29 +108,41 @@ class GP(model):
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def log_likelihood(self):
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"""
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The log marginal likelihood for an EP model can be written as the log likelihood of
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a regression model for a new variable Y* = v_tilde/tau_tilde, with a covariance
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The log marginal likelihood of the GP.
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For an EP model, can be written as the log likelihood of a regression
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model for a new variable Y* = v_tilde/tau_tilde, with a covariance
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matrix K* = K + diag(1./tau_tilde) plus a normalization term.
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"""
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L = -0.5*selff.D*self.K_logdet + self.model_fit_term()
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if self.EP:
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L += self.normalisation_term()
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return L
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return -0.5*self.D*self.K_logdet + self.model_fit_term() + self.likelihood.Z
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def log_likelihood(self):
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complexity_term = -0.5*self.N*self.D*np.log(2.*np.pi) - 0.5*self.D*self.K_logdet
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return complexity_term + self._model_fit_term()
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def dL_dK(self):
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if self.YYT is None:
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alpha = np.dot(self.Ki,self.Y)
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dL_dK = 0.5*(np.dot(alpha,alpha.T)-self.D*self.Ki)
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else:
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dL_dK = 0.5*(mdot(self.Ki, self.YYT, self.Ki) - self.D*self.Ki)
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return dL_dK
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def _log_likelihood_gradients(self):
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return self.kern.dK_dtheta(partial=self.dL_dK(),X=self.X)
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"""
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The gradient of all parameters.
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For the kernel parameters, use the chain rule via dL_dK
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For the likelihood parameters, pass in alpha = K^-1 y
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"""
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return np.hstack((self.kern.dK_dtheta(partial=self.dL_dK(),X=self.X), self.likelihood._gradients(self.alpha2)))
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def _raw_predict(self,_Xnew,slices, full_cov=False):
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"""
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Internal helper function for making predictions, does not account
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for normalisation or likelihood
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"""
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Kx = self.kern.K(self.X,_Xnew, slices1=self.Xslices,slices2=slices)
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mu = np.dot(np.dot(Kx.T,self.Ki),self.Y)
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KiKx = np.dot(self.Ki,Kx)
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if full_cov:
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Kxx = self.kern.K(_Xnew, slices1=slices,slices2=slices)
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var = Kxx - np.dot(KiKx.T,Kx)
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else:
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Kxx = self.kern.Kdiag(_Xnew, slices=slices)
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var = Kxx - np.sum(np.multiply(KiKx,Kx),0)
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return mu, var
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def predict(self,Xnew, slices=None, full_cov=False):
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"""
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@ -198,41 +171,11 @@ class GP(model):
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"""
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#normalise X values
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Xnew = (Xnew.copy() - self._Xmean) / self._Xstd
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mu, var, phi = self._raw_predict(Xnew, slices, full_cov)
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mu, var, phi = self._raw_predict(Xnew, slices, full_cov=full_cov)
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#un-normalise
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mu = mu*self._Ystd + self._Ymean
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if full_cov:
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if self.D==1:
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var *= np.square(self._Ystd)
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else:
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var = var[:,:,None] * np.square(self._Ystd)
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else:
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if self.D==1:
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var *= np.square(np.squeeze(self._Ystd))
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else:
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var = var[:,None] * np.square(self._Ystd)
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#now push through likelihood TODO
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return mu,var,phi
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def _raw_predict(self,_Xnew,slices, full_cov=False):
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"""Internal helper function for making predictions, does not account for normalisation"""
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Kx = self.kern.K(self.X,_Xnew, slices1=self.Xslices,slices2=slices)
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mu = np.dot(np.dot(Kx.T,self.Ki),self.Y)
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KiKx = np.dot(self.Ki,Kx)
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if full_cov:
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Kxx = self.kern.K(_Xnew, slices1=slices,slices2=slices)
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var = Kxx - np.dot(KiKx.T,Kx)
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if self.EP:
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raise NotImplementedError, "full_cov = True not implemented for EP"
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#var = np.diag(var)[:,None]
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#phi = self.likelihood.predictive_mean(mu,var)
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else:
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Kxx = self.kern.Kdiag(_Xnew, slices=slices)
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var = Kxx - np.sum(np.multiply(KiKx,Kx),0)
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if self.EP:
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phi = self.likelihood.predictive_mean(mu,var)
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return mu, var, phi
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return mean, _5pc, _95pc
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def plot(self,samples=0,plot_limits=None,which_data='all',which_functions='all',resolution=None,full_cov=False):
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"""
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