mirror of
https://github.com/SheffieldML/GPy.git
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recover the ss_gplvm.py
This commit is contained in:
Zhenwen Dai
parent
0947112f3c
commit
a853d060fb
1 changed files with 92 additions and 263 deletions
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@ -2,18 +2,14 @@
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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import numpy as np
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import itertools
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from matplotlib import pyplot
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from ..core.sparse_gp import SparseGP
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from .. import kern
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from ..likelihoods import Gaussian
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from ..inference.optimization import SCG
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from ..util import linalg
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from ..core.parameterization.variational import SpikeAndSlabPrior, SpikeAndSlabPosterior
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from ..inference.latent_function_inference.var_dtc_parallel import update_gradients, VarDTC_minibatch
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from ..inference.latent_function_inference.var_dtc_gpu import VarDTC_GPU
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from ..kern._src.psi_comp.ssrbf_psi_gpucomp import PSICOMP_SSRBF_GPU
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class SSGPLVM(SparseGP):
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"""
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@ -27,9 +23,13 @@ class SSGPLVM(SparseGP):
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:type init: 'PCA'|'random'
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"""
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def __init__(self, Y, input_dim, X=None, X_variance=None, init='PCA', num_inducing=10,
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Z=None, kernel=None, inference_method=None, likelihood=None, name='Spike-and-Slab GPLVM', group_spike=False, **kwargs):
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def __init__(self, Y, input_dim, X=None, X_variance=None, Gamma=None, init='PCA', num_inducing=10,
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Z=None, kernel=None, inference_method=None, likelihood=None, name='Spike_and_Slab GPLVM', group_spike=False, mpi_comm=None, pi=None, learnPi=True, **kwargs):
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self.mpi_comm = mpi_comm
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self.__IN_OPTIMIZATION__ = False
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self.group_spike = group_spike
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if X == None:
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from ..util.initialization import initialize_latent
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X, fracs = initialize_latent(init, input_dim, Y)
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@ -40,49 +40,66 @@ class SSGPLVM(SparseGP):
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if X_variance is None: # The variance of the variational approximation (S)
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X_variance = np.random.uniform(0,.1,X.shape)
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gamma = np.empty_like(X, order='F') # The posterior probabilities of the binary variable in the variational approximation
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gamma[:] = 0.5 + 0.01 * np.random.randn(X.shape[0], input_dim)
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if group_spike:
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gamma[:] = gamma.mean(axis=0)
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if Gamma is None:
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gamma = np.empty_like(X) # The posterior probabilities of the binary variable in the variational approximation
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gamma[:] = 0.5 + 0.1 * np.random.randn(X.shape[0], input_dim)
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gamma[gamma>1.-1e-9] = 1.-1e-9
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gamma[gamma<1e-9] = 1e-9
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else:
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gamma = Gamma.copy()
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if Z is None:
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Z = np.random.permutation(X.copy())[:num_inducing]
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assert Z.shape[1] == X.shape[1]
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if likelihood is None:
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likelihood = Gaussian()
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if kernel is None:
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kernel = kern.RBF(input_dim, lengthscale=fracs, ARD=True) # + kern.white(input_dim)
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if kernel.useGPU:
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kernel.psicomp = PSICOMP_SSRBF_GPU()
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if inference_method is None:
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inference_method = VarDTC_minibatch(mpi_comm=mpi_comm)
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pi = np.empty((input_dim))
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pi[:] = 0.5
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self.variational_prior = SpikeAndSlabPrior(pi=pi) # the prior probability of the latent binary variable b
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X = np.asfortranarray(X)
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X_variance = np.asfortranarray(X_variance)
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gamma = np.asfortranarray(gamma)
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if pi is None:
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pi = np.empty((input_dim))
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pi[:] = 0.5
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self.variational_prior = SpikeAndSlabPrior(pi=pi,learnPi=learnPi) # the prior probability of the latent binary variable b
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X = SpikeAndSlabPosterior(X, X_variance, gamma)
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if group_spike:
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kernel.group_spike_prob = True
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self.variational_prior.group_spike_prob = True
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SparseGP.__init__(self, X, Y, Z, kernel, likelihood, inference_method, name, **kwargs)
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self.add_parameter(self.X, index=0)
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self.add_parameter(self.variational_prior)
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if mpi_comm != None:
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from ..util.mpi import divide_data
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N_start, N_end, N_list = divide_data(Y.shape[0], mpi_comm)
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self.N_range = (N_start, N_end)
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self.N_list = np.array(N_list)
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self.Y_local = self.Y[N_start:N_end]
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print 'MPI RANK: '+str(self.mpi_comm.rank)+' with datasize: '+str(self.N_range)
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mpi_comm.Bcast(self.param_array, root=0)
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if self.group_spike:
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[self.X.gamma[:,i].tie('tieGamma'+str(i)) for i in xrange(self.X.gamma.shape[1])] # Tie columns together
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def set_X_gradients(self, X, X_grad):
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"""Set the gradients of the posterior distribution of X in its specific form."""
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X.mean.gradient, X.variance.gradient, X.binary_prob.gradient = X_grad
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def get_X_gradients(self, X):
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"""Get the gradients of the posterior distribution of X in its specific form."""
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return X.mean.gradient, X.variance.gradient, X.binary_prob.gradient
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def parameters_changed(self):
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if isinstance(self.inference_method, VarDTC_GPU) or isinstance(self.inference_method, VarDTC_minibatch):
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update_gradients(self)
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update_gradients(self, mpi_comm=self.mpi_comm)
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return
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super(SSGPLVM, self).parameters_changed()
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self._log_marginal_likelihood -= self.variational_prior.KL_divergence(self.X)
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@ -91,7 +108,7 @@ class SSGPLVM(SparseGP):
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# update for the KL divergence
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self.variational_prior.update_gradients_KL(self.X)
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def input_sensitivity(self, summarize=True):
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def input_sensitivity(self):
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if self.kern.ARD:
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return self.kern.input_sensitivity()
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else:
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@ -104,235 +121,47 @@ class SSGPLVM(SparseGP):
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return dim_reduction_plots.plot_latent(self, plot_inducing=plot_inducing, *args, **kwargs)
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def do_test_latents(self, Y):
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"""
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Compute the latent representation for a set of new points Y
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Notes:
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This will only work with a univariate Gaussian likelihood (for now)
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"""
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assert not self.likelihood.is_heteroscedastic
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N_test = Y.shape[0]
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input_dim = self.Z.shape[1]
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means = np.zeros((N_test, input_dim))
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covars = np.zeros((N_test, input_dim))
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dpsi0 = -0.5 * self.output_dim * self.likelihood.precision
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dpsi2 = self.dL_dpsi2[0][None, :, :] # TODO: this may change if we ignore het. likelihoods
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V = self.likelihood.precision * Y
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#compute CPsi1V
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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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tmp, _ = linalg.dtrtrs(self._Lm, np.asfortranarray(psi1V), lower=1, trans=0)
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tmp, _ = linalg.dpotrs(self.LB, tmp, lower=1)
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self.Cpsi1V, _ = linalg.dtrtrs(self._Lm, tmp, lower=1, trans=1)
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dpsi1 = np.dot(self.Cpsi1V, V.T)
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start = np.zeros(self.input_dim * 2)
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for n, dpsi1_n in enumerate(dpsi1.T[:, :, None]):
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args = (self.kern, self.Z, dpsi0, dpsi1_n.T, dpsi2)
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xopt, fopt, neval, status = SCG(f=latent_cost, gradf=latent_grad, x=start, optargs=args, display=False)
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mu, log_S = xopt.reshape(2, 1, -1)
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means[n] = mu[0].copy()
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covars[n] = np.exp(log_S[0]).copy()
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return means, covars
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def dmu_dX(self, Xnew):
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"""
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Calculate the gradient of the prediction at Xnew w.r.t Xnew.
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"""
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dmu_dX = np.zeros_like(Xnew)
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for i in range(self.Z.shape[0]):
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dmu_dX += self.kern.dK_dX(self.Cpsi1Vf[i:i + 1, :], Xnew, self.Z[i:i + 1, :])
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return dmu_dX
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def dmu_dXnew(self, Xnew):
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"""
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Individual gradient of prediction at Xnew w.r.t. each sample in Xnew
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"""
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dK_dX = np.zeros((Xnew.shape[0], self.num_inducing))
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ones = np.ones((1, 1))
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for i in range(self.Z.shape[0]):
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dK_dX[:, i] = self.kern.dK_dX(ones, Xnew, self.Z[i:i + 1, :]).sum(-1)
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return np.dot(dK_dX, self.Cpsi1Vf)
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def plot_steepest_gradient_map(self, fignum=None, ax=None, which_indices=None, labels=None, data_labels=None, data_marker='o', data_s=40, resolution=20, aspect='auto', updates=False, ** kwargs):
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input_1, input_2 = significant_dims = most_significant_input_dimensions(self, which_indices)
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X = np.zeros((resolution ** 2, self.input_dim))
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indices = np.r_[:X.shape[0]]
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if labels is None:
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labels = range(self.output_dim)
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def plot_function(x):
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X[:, significant_dims] = x
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dmu_dX = self.dmu_dXnew(X)
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argmax = np.argmax(dmu_dX, 1)
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return dmu_dX[indices, argmax], np.array(labels)[argmax]
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if ax is None:
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fig = pyplot.figure(num=fignum)
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ax = fig.add_subplot(111)
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if data_labels is None:
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data_labels = np.ones(self.num_data)
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ulabels = []
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for lab in data_labels:
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if not lab in ulabels:
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ulabels.append(lab)
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marker = itertools.cycle(list(data_marker))
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from GPy.util import Tango
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for i, ul in enumerate(ulabels):
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if type(ul) is np.string_:
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this_label = ul
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elif type(ul) is np.int64:
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this_label = 'class %i' % ul
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else:
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this_label = 'class %i' % i
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m = marker.next()
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index = np.nonzero(data_labels == ul)[0]
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x = self.X[index, input_1]
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y = self.X[index, input_2]
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ax.scatter(x, y, marker=m, s=data_s, color=Tango.nextMedium(), label=this_label)
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ax.set_xlabel('latent dimension %i' % input_1)
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ax.set_ylabel('latent dimension %i' % input_2)
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from matplotlib.cm import get_cmap
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from GPy.util.latent_space_visualizations.controllers.imshow_controller import ImAnnotateController
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if not 'cmap' in kwargs.keys():
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kwargs.update(cmap=get_cmap('jet'))
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controller = ImAnnotateController(ax,
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plot_function,
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tuple(self.X.min(0)[:, significant_dims]) + tuple(self.X.max(0)[:, significant_dims]),
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resolution=resolution,
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aspect=aspect,
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**kwargs)
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ax.legend()
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ax.figure.tight_layout()
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if updates:
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pyplot.show()
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clear = raw_input('Enter to continue')
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if clear.lower() in 'yes' or clear == '':
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controller.deactivate()
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return controller.view
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def plot_X_1d(self, fignum=None, ax=None, colors=None):
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"""
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Plot latent space X in 1D:
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- if fig is given, create input_dim subplots in fig and plot in these
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- if ax is given plot input_dim 1D latent space plots of X into each `axis`
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- if neither fig nor ax is given create a figure with fignum and plot in there
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colors:
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colors of different latent space dimensions input_dim
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"""
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import pylab
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if ax is None:
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fig = pylab.figure(num=fignum, figsize=(8, min(12, (2 * self.X.shape[1]))))
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if colors is None:
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colors = pylab.gca()._get_lines.color_cycle
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pylab.clf()
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else:
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colors = iter(colors)
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plots = []
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x = np.arange(self.X.shape[0])
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for i in range(self.X.shape[1]):
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if ax is None:
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a = fig.add_subplot(self.X.shape[1], 1, i + 1)
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elif isinstance(ax, (tuple, list)):
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a = ax[i]
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else:
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raise ValueError("Need one ax per latent dimnesion input_dim")
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a.plot(self.X, c='k', alpha=.3)
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plots.extend(a.plot(x, self.X.T[i], c=colors.next(), label=r"$\mathbf{{X_{{{}}}}}$".format(i)))
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a.fill_between(x,
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self.X.T[i] - 2 * np.sqrt(self.X_variance.T[i]),
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self.X.T[i] + 2 * np.sqrt(self.X_variance.T[i]),
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facecolor=plots[-1].get_color(),
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alpha=.3)
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a.legend(borderaxespad=0.)
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a.set_xlim(x.min(), x.max())
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if i < self.X.shape[1] - 1:
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a.set_xticklabels('')
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pylab.draw()
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if ax is None:
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fig.tight_layout(h_pad=.01) # , rect=(0, 0, 1, .95))
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return fig
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def getstate(self):
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"""
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Get the current state of the class,
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here just all the indices, rest can get recomputed
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"""
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return SparseGP._getstate(self) + [self.init]
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def setstate(self, state):
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self._const_jitter = None
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self.init = state.pop()
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SparseGP._setstate(self, state)
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def latent_cost_and_grad(mu_S, kern, Z, dL_dpsi0, dL_dpsi1, dL_dpsi2):
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"""
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objective function for fitting the latent variables for test points
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(negative log-likelihood: should be minimised!)
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"""
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mu, log_S = mu_S.reshape(2, 1, -1)
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S = np.exp(log_S)
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psi0 = kern.psi0(Z, mu, S)
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psi1 = kern.psi1(Z, mu, S)
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psi2 = kern.psi2(Z, mu, S)
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lik = dL_dpsi0 * psi0 + np.dot(dL_dpsi1.flatten(), psi1.flatten()) + np.dot(dL_dpsi2.flatten(), psi2.flatten()) - 0.5 * np.sum(np.square(mu) + S) + 0.5 * np.sum(log_S)
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mu0, S0 = kern.dpsi0_dmuS(dL_dpsi0, Z, mu, S)
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mu1, S1 = kern.dpsi1_dmuS(dL_dpsi1, Z, mu, S)
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mu2, S2 = kern.dpsi2_dmuS(dL_dpsi2, Z, mu, S)
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dmu = mu0 + mu1 + mu2 - mu
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# dS = S0 + S1 + S2 -0.5 + .5/S
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dlnS = S * (S0 + S1 + S2 - 0.5) + .5
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return -lik, -np.hstack((dmu.flatten(), dlnS.flatten()))
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def latent_cost(mu_S, kern, Z, dL_dpsi0, dL_dpsi1, dL_dpsi2):
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"""
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objective function for fitting the latent variables (negative log-likelihood: should be minimised!)
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This is the same as latent_cost_and_grad but only for the objective
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"""
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mu, log_S = mu_S.reshape(2, 1, -1)
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S = np.exp(log_S)
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psi0 = kern.psi0(Z, mu, S)
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psi1 = kern.psi1(Z, mu, S)
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psi2 = kern.psi2(Z, mu, S)
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lik = dL_dpsi0 * psi0 + np.dot(dL_dpsi1.flatten(), psi1.flatten()) + np.dot(dL_dpsi2.flatten(), psi2.flatten()) - 0.5 * np.sum(np.square(mu) + S) + 0.5 * np.sum(log_S)
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return -float(lik)
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def latent_grad(mu_S, kern, Z, dL_dpsi0, dL_dpsi1, dL_dpsi2):
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"""
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This is the same as latent_cost_and_grad but only for the grad
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"""
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mu, log_S = mu_S.reshape(2, 1, -1)
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S = np.exp(log_S)
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mu0, S0 = kern.dpsi0_dmuS(dL_dpsi0, Z, mu, S)
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mu1, S1 = kern.dpsi1_dmuS(dL_dpsi1, Z, mu, S)
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mu2, S2 = kern.dpsi2_dmuS(dL_dpsi2, Z, mu, S)
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dmu = mu0 + mu1 + mu2 - mu
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# dS = S0 + S1 + S2 -0.5 + .5/S
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dlnS = S * (S0 + S1 + S2 - 0.5) + .5
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return -np.hstack((dmu.flatten(), dlnS.flatten()))
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def __getstate__(self):
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dc = super(SSGPLVM, self).__getstate__()
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dc['mpi_comm'] = None
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if self.mpi_comm != None:
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del dc['N_range']
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del dc['N_list']
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del dc['Y_local']
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return dc
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def __setstate__(self, state):
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return super(SSGPLVM, self).__setstate__(state)
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#=====================================================
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# The MPI parallelization
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# - can move to model at some point
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#=====================================================
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def _set_params_transformed(self, p):
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if self.mpi_comm != None:
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if self.__IN_OPTIMIZATION__ and self.mpi_comm.rank==0:
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self.mpi_comm.Bcast(np.int32(1),root=0)
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self.mpi_comm.Bcast(p, root=0)
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super(SSGPLVM, self)._set_params_transformed(p)
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def optimize(self, optimizer=None, start=None, **kwargs):
|
||||
self.__IN_OPTIMIZATION__ = True
|
||||
if self.mpi_comm==None:
|
||||
super(SSGPLVM, self).optimize(optimizer,start,**kwargs)
|
||||
elif self.mpi_comm.rank==0:
|
||||
super(SSGPLVM, self).optimize(optimizer,start,**kwargs)
|
||||
self.mpi_comm.Bcast(np.int32(-1),root=0)
|
||||
elif self.mpi_comm.rank>0:
|
||||
x = self._get_params_transformed().copy()
|
||||
flag = np.empty(1,dtype=np.int32)
|
||||
while True:
|
||||
self.mpi_comm.Bcast(flag,root=0)
|
||||
if flag==1:
|
||||
self._set_params_transformed(x)
|
||||
elif flag==-1:
|
||||
break
|
||||
else:
|
||||
self.__IN_OPTIMIZATION__ = False
|
||||
raise Exception("Unrecognizable flag for synchronization!")
|
||||
self.__IN_OPTIMIZATION__ = False
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue