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dimensionality reduction merge
This commit is contained in:
Max Zwiessele
commit
7f63849dd2
9 changed files with 28 additions and 87 deletions
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@ -96,8 +96,7 @@ class GP(GPBase):
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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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return (-0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) -
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0.5 * self.output_dim * self.K_logdet + self._model_fit_term() + self.likelihood.Z)
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return - 0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) - 0.5 * self.output_dim * self.K_logdet + self._model_fit_term() + self.likelihood.Z
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def _log_likelihood_gradients(self):
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@ -108,7 +108,7 @@ class SparseGP(GPBase):
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self.B = np.eye(self.num_inducing) + self.A
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self.LB = jitchol(self.B)
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# VVT_factor is a matrix such that tdot(VVT_factor) = VVT...this is for efficiency!
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#VVT_factor is a matrix such that tdot(VVT_factor) = VVT...this is for efficiency!
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self.psi1Vf = np.dot(self.psi1.T, self.likelihood.VVT_factor)
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# back substutue C into psi1Vf
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@ -163,7 +163,7 @@ class SparseGP(GPBase):
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def log_likelihood(self):
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""" Compute the (lower bound on the) log marginal likelihood """
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if self.likelihood.is_heteroscedastic:
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A = -0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.likelihood.precision)) - 0.5 * np.sum(self.likelihood.V * self.likelihood.Y)
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A = -0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.likelihood.precision)) - 0.5 * np.sum(self.likelihood.V*self.likelihood.Y)
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B = -0.5 * self.output_dim * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A))
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else:
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A = -0.5 * self.num_data * self.output_dim * (np.log(2.*np.pi) - np.log(self.likelihood.precision)) - 0.5 * self.likelihood.precision * self.likelihood.trYYT
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@ -246,7 +246,7 @@ class SparseGP(GPBase):
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Kmmi_LmiBLmi = backsub_both_sides(self.Lm, np.eye(self.num_inducing) - Bi)
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if self.Cpsi1V is None:
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psi1V = np.dot(self.psi1.T, self.likelihood.V)
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psi1V = np.dot(self.psi1.T,self.likelihood.V)
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tmp, _ = dtrtrs(self.Lm, np.asfortranarray(psi1V), lower=1, trans=0)
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tmp, _ = dpotrs(self.LB, tmp, lower=1)
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self.Cpsi1V, _ = dtrtrs(self.Lm, tmp, lower=1, trans=1)
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@ -4,7 +4,7 @@
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import numpy as np
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import pylab as pb
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from .. import kern
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from ..util.linalg import pdinv, mdot, tdot, dpotrs, dtrtrs, jitchol, backsub_both_sides
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from ..util.linalg import linalg, pdinv, mdot, tdot, dpotrs, dtrtrs, jitchol, backsub_both_sides
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from ..likelihoods import EP
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from gp_base import GPBase
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from model import Model
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@ -269,7 +269,6 @@ class SVIGP(GPBase):
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def optimize(self, iterations, print_interval=10, callback=lambda:None, callback_interval=5):
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param_step = 0.
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#Iterate!
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for i in range(iterations):
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@ -288,6 +287,7 @@ class SVIGP(GPBase):
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#compute the steps in all parameters
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vb_step = self.vb_steplength*natgrads[0]
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if (self.epochs>=1):#only move the parameters after the first epoch
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# print "it {} ep {} par {}".format(self.iterations, self.epochs, param_step)
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param_step = self.momentum*param_step + self.param_steplength*grads
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else:
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param_step = 0.
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@ -295,8 +295,8 @@ class SVIGP(GPBase):
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self.set_vb_param(self.get_vb_param() + vb_step)
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#Note: don't recompute everything here, wait until the next iteration when we have a new batch
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self._set_params(self._untransform_params(self._get_params_transformed() + param_step), computations=False)
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#print messages if desired
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if i and (not i%print_interval):
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print i, np.mean(self._ll_trace[-print_interval:]) #, self.log_likelihood()
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print np.round(np.mean(self._grad_trace[-print_interval:],0),3)
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@ -24,7 +24,7 @@ def BGPLVM(seed=default_seed):
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Y = np.random.multivariate_normal(np.zeros(N), K, Q).T
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lik = Gaussian(Y, normalize=True)
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k = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q) + GPy.kern.white(Q)
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k = GPy.kern.rbf_inv(Q, ARD=True) + GPy.kern.bias(Q) + GPy.kern.white(Q)
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# k = GPy.kern.rbf(Q) + GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001)
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# k = GPy.kern.rbf(Q, ARD = False) + GPy.kern.white(Q, 0.00001)
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@ -145,6 +145,7 @@ def BGPLVM_oil(optimize=True, N=200, Q=10, num_inducing=15, max_iters=150, plot=
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# create simple GP model
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kernel = GPy.kern.rbf_inv(Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) + GPy.kern.white(Q, np.exp(-2))
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Y = data['X'][:N]
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Yn = Y - Y.mean(0)
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Yn /= Yn.std(0)
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@ -375,11 +376,12 @@ def stick():
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def stick_bgplvm(model=None):
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data = GPy.util.datasets.stick()
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Q = 6
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kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) + GPy.kern.white(Q, np.exp(-2))
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m = BayesianGPLVM(data['Y'], Q, init="PCA", num_inducing=20, kernel=kernel)
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kernel = GPy.kern.rbf_inv(Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) + GPy.kern.white(Q, np.exp(-2))
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m = BayesianGPLVM(data['Y'], Q, init="PCA", num_inducing=35,kernel=kernel)
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# optimize
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m.ensure_default_constraints()
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m.optimize(messages=1, max_f_eval=3000, xtol=1e-300, ftol=1e-300)
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m.constrain_bounded('.*rbf_inv',1e-5, 100)
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m.optimize(messages=1, max_iters=3000,xtol=1e-300,ftol=1e-300)
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m._set_params(m._get_params())
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plt.clf, (latent_axes, sense_axes) = plt.subplots(1, 2)
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plt.sca(latent_axes)
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@ -67,8 +67,8 @@ def toy_ARD(optim_iters=1000, kernel_type='linear', N=300, D=4):
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X4 = np.log(np.sort(np.random.rand(N,1),0))
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X = np.hstack((X1, X2, X3, X4))
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Y1 = np.asarray(2*X[:,0]+3).T
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Y2 = np.asarray(4*(X[:,2]-1.5*X[:,0])).T
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Y1 = np.asmatrix(2*X[:,0]+3).T
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Y2 = np.asmatrix(4*(X[:,2]-1.5*X[:,0])).T
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Y = np.hstack((Y1, Y2))
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Y = np.dot(Y, np.random.rand(2,D));
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@ -66,26 +66,12 @@ class kern(Parameterized):
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Parameterized.setstate(self, state)
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def plot_ARD(self, fignum=None, ax=None, title='', legend=False):
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"""If an ARD kernel is present, it bar-plots the ARD parameters,
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:param fignum: figure number of the plot
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:param ax: matplotlib axis to plot on
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:param title:
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title of the plot,
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pass '' to not print a title
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pass None for a generic title
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"""
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def plot_ARD(self, fignum=None, ax=None, title=None):
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"""If an ARD kernel is present, it bar-plots the ARD parameters"""
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if ax is None:
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fig = pb.figure(fignum)
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ax = fig.add_subplot(111)
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from GPy.util import Tango
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from matplotlib.textpath import TextPath
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Tango.reset()
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xticklabels = []
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bars = []
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x0 = 0
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for p in self.parts:
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c = Tango.nextMedium()
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if hasattr(p, 'ARD') and p.ARD:
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if title is None:
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ax.set_title('ARD parameters, %s kernel' % p.name)
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@ -96,32 +82,10 @@ class kern(Parameterized):
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else:
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ard_params = 1. / p.lengthscale
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x = np.arange(x0, x0 + len(ard_params))
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bars.append(ax.bar(x, ard_params, align='center', color=c, edgecolor='k', linewidth=1.2, label=p.name))
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xticklabels.extend([r"$\mathrm{{{name}}}\ {x}$".format(name=p.name, x=i) for i in np.arange(len(ard_params))])
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x0 += len(ard_params)
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x = np.arange(x0)
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for bar in bars:
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for patch, num in zip(bar.patches, np.arange(len(bar.patches))):
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height = patch.get_height()
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xi = patch.get_x() + patch.get_width() / 2.
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va = 'top'
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c = 'w'
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t = TextPath((0, 0), "${xi}$".format(xi=xi), rotation=0, usetex=True, ha='center')
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if patch.get_extents().height <= t.get_extents().height + 2:
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va = 'bottom'
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c = 'k'
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ax.text(xi, height, "${xi}$".format(xi=int(num)), color=c, rotation=0, ha='center', va=va)
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# for xi, t in zip(x, xticklabels):
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# ax.text(xi, maxi / 2, t, rotation=90, ha='center', va='center')
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# ax.set_xticklabels(xticklabels, rotation=17)
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ax.set_xticks([])
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ax.set_xlim(-.5, x0 - .5)
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if title is '':
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ax.legend(bbox_to_anchor=(0., 1.02, 1., .102), loc=3,
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ncol=len(bars), mode="expand", borderaxespad=0.)
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else:
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ax.legend()
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x = np.arange(len(ard_params))
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ax.bar(x - 0.4, ard_params)
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ax.set_xticks(x)
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ax.set_xticklabels([r"${}$".format(i) for i in x])
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return ax
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def _transform_gradients(self, g):
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@ -397,7 +361,6 @@ class kern(Parameterized):
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# compute the "cross" terms
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# TODO: better looping, input_slices
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for i1, i2 in itertools.permutations(range(len(self.parts)), 2):
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p1, p2 = self.parts[i1], self.parts[i2]
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# ipsl1, ipsl2 = self.input_slices[i1], self.input_slices[i2]
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@ -115,8 +115,8 @@ class BayesianGPLVM(SparseGP, GPLVM):
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self.dbound_dZtheta = SparseGP._log_likelihood_gradients(self)
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return np.hstack((self.dbound_dmuS.flatten(), self.dbound_dZtheta))
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def plot_latent(self, plot_inducing=True, *args, **kwargs):
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return plot_latent.plot_latent(self, plot_inducing=plot_inducing, *args, **kwargs)
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def plot_latent(self, *args, **kwargs):
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return plot_latent.plot_latent(self, *args, **kwargs)
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def do_test_latents(self, Y):
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"""
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@ -36,10 +36,10 @@ class GPLVM(GP):
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self.ensure_default_constraints()
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def initialise_latent(self, init, input_dim, Y):
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Xr = np.random.randn(Y.shape[0], input_dim)
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if init == 'PCA':
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Xr[:, :Y.shape[1]] = PCA(Y, input_dim)[0]
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return Xr
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return PCA(Y, input_dim)[0]
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else:
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return np.random.randn(Y.shape[0], input_dim)
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def getstate(self):
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return GP.getstate(self)
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@ -23,7 +23,7 @@ class GradientTests(unittest.TestCase):
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self.X2D = np.random.uniform(-3., 3., (40, 2))
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self.Y2D = np.sin(self.X2D[:, 0:1]) * np.sin(self.X2D[:, 1:2]) + np.random.randn(40, 1) * 0.05
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def check_model_with_white(self, kern, model_type='GPRegression', dimension=1, uncertain_inputs=False):
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def check_model_with_white(self, kern, model_type='GPRegression', dimension=1):
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# Get the correct gradients
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if dimension == 1:
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X = self.X1D
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@ -36,10 +36,7 @@ class GradientTests(unittest.TestCase):
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noise = GPy.kern.white(dimension)
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kern = kern + noise
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if uncertain_inputs:
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m = model_fit(X, Y, kernel=kern, X_variance=np.random.rand(X.shape[0], X.shape[1]))
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else:
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m = model_fit(X, Y, kernel=kern)
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m = model_fit(X, Y, kernel=kern)
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m.randomize()
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# contrain all parameters to be positive
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self.assertTrue(m.checkgrad())
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@ -144,26 +141,6 @@ class GradientTests(unittest.TestCase):
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rbf = GPy.kern.rbf(2)
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self.check_model_with_white(rbf, model_type='SparseGPRegression', dimension=2)
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def test_SparseGPRegression_rbf_linear_white_kern_1D(self):
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''' Testing the sparse GP regression with rbf and white kernel on 2d data '''
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rbflin = GPy.kern.rbf(1) + GPy.kern.linear(1)
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self.check_model_with_white(rbflin, model_type='SparseGPRegression', dimension=1)
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def test_SparseGPRegression_rbf_linear_white_kern_2D(self):
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''' Testing the sparse GP regression with rbf and white kernel on 2d data '''
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rbflin = GPy.kern.rbf(2) + GPy.kern.linear(2)
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self.check_model_with_white(rbflin, model_type='SparseGPRegression', dimension=2)
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def test_SparseGPRegression_rbf_linear_white_kern_2D_uncertain_inputs(self):
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''' Testing the sparse GP regression with rbf, linear and white kernel on 2d data with uncertain inputs'''
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rbflin = GPy.kern.rbf(2) + GPy.kern.linear(2)
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self.check_model_with_white(rbflin, model_type='SparseGPRegression', dimension=2, uncertain_inputs=1)
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def test_SparseGPRegression_rbf_linear_white_kern_1D_uncertain_inputs(self):
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''' Testing the sparse GP regression with rbf, linear and white kernel on 1d data with uncertain inputs'''
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rbflin = GPy.kern.rbf(1) + GPy.kern.linear(1)
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self.check_model_with_white(rbflin, model_type='SparseGPRegression', dimension=1, uncertain_inputs=1)
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def test_GPLVM_rbf_bias_white_kern_2D(self):
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""" Testing GPLVM with rbf + bias and white kernel """
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N, input_dim, D = 50, 1, 2
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