mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-05-11 04:52:37 +02:00
REFACTORING: model names, lowercase, classes uppercase
This commit is contained in:
Max Zwiessele
parent
2a39440619
commit
2e5e8ac026
50 changed files with 436 additions and 3307 deletions
|
|
@ -1,588 +0,0 @@
|
|||
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
|
||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
||||
|
||||
import numpy as np
|
||||
import pylab as pb
|
||||
import sys, pdb
|
||||
from GPLVM import GPLVM
|
||||
from ..core import sparse_GP
|
||||
from GPy.util.linalg import pdinv
|
||||
from ..likelihoods import Gaussian
|
||||
from .. import kern
|
||||
from numpy.linalg.linalg import LinAlgError
|
||||
import itertools
|
||||
from matplotlib.colors import colorConverter
|
||||
from matplotlib.figure import SubplotParams
|
||||
from GPy.inference.optimization import SCG
|
||||
from GPy.util import plot_latent
|
||||
|
||||
class Bayesian_GPLVM(sparse_GP, GPLVM):
|
||||
"""
|
||||
Bayesian Gaussian Process Latent Variable Model
|
||||
|
||||
:param Y: observed data (np.ndarray) or GPy.likelihood
|
||||
:type Y: np.ndarray| GPy.likelihood instance
|
||||
:param input_dim: latent dimensionality
|
||||
:type input_dim: int
|
||||
:param init: initialisation method for the latent space
|
||||
:type init: 'PCA'|'random'
|
||||
|
||||
"""
|
||||
def __init__(self, likelihood_or_Y, input_dim, X=None, X_variance=None, init='PCA', M=10,
|
||||
Z=None, kernel=None, oldpsave=10, _debug=False,
|
||||
**kwargs):
|
||||
if type(likelihood_or_Y) is np.ndarray:
|
||||
likelihood = Gaussian(likelihood_or_Y)
|
||||
else:
|
||||
likelihood = likelihood_or_Y
|
||||
|
||||
if X == None:
|
||||
X = self.initialise_latent(init, input_dim, likelihood.Y)
|
||||
self.init = init
|
||||
|
||||
if X_variance is None:
|
||||
X_variance = np.clip((np.ones_like(X) * 0.5) + .01 * np.random.randn(*X.shape), 0.001, 1)
|
||||
|
||||
if Z is None:
|
||||
Z = np.random.permutation(X.copy())[:M]
|
||||
assert Z.shape[1] == X.shape[1]
|
||||
|
||||
if kernel is None:
|
||||
kernel = kern.rbf(input_dim) + kern.white(input_dim)
|
||||
|
||||
self.oldpsave = oldpsave
|
||||
self._oldps = []
|
||||
self._debug = _debug
|
||||
|
||||
if self._debug:
|
||||
self.f_call = 0
|
||||
self._count = itertools.count()
|
||||
self._savedklll = []
|
||||
self._savedparams = []
|
||||
self._savedgradients = []
|
||||
self._savederrors = []
|
||||
self._savedpsiKmm = []
|
||||
self._savedABCD = []
|
||||
|
||||
sparse_GP.__init__(self, X, likelihood, kernel, Z=Z, X_variance=X_variance, **kwargs)
|
||||
self._set_params(self._get_params())
|
||||
|
||||
@property
|
||||
def oldps(self):
|
||||
return self._oldps
|
||||
@oldps.setter
|
||||
def oldps(self, p):
|
||||
if len(self._oldps) == (self.oldpsave + 1):
|
||||
self._oldps.pop()
|
||||
# if len(self._oldps) == 0 or not np.any([np.any(np.abs(p - op) > 1e-5) for op in self._oldps]):
|
||||
self._oldps.insert(0, p.copy())
|
||||
|
||||
def _get_param_names(self):
|
||||
X_names = sum([['X_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.N)], [])
|
||||
S_names = sum([['X_variance_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.N)], [])
|
||||
return (X_names + S_names + sparse_GP._get_param_names(self))
|
||||
|
||||
def _get_params(self):
|
||||
"""
|
||||
Horizontally stacks the parameters in order to present them to the optimizer.
|
||||
The resulting 1-D array has this structure:
|
||||
|
||||
===============================================================
|
||||
| mu | S | Z | theta | beta |
|
||||
===============================================================
|
||||
|
||||
"""
|
||||
x = np.hstack((self.X.flatten(), self.X_variance.flatten(), sparse_GP._get_params(self)))
|
||||
return x
|
||||
|
||||
def _clipped(self, x):
|
||||
return x # np.clip(x, -1e300, 1e300)
|
||||
|
||||
def _set_params(self, x, save_old=True, save_count=0):
|
||||
# try:
|
||||
x = self._clipped(x)
|
||||
N, input_dim = self.N, self.input_dim
|
||||
self.X = x[:self.X.size].reshape(N, input_dim).copy()
|
||||
self.X_variance = x[(N * input_dim):(2 * N * input_dim)].reshape(N, input_dim).copy()
|
||||
sparse_GP._set_params(self, x[(2 * N * input_dim):])
|
||||
# self.oldps = x
|
||||
# except (LinAlgError, FloatingPointError, ZeroDivisionError):
|
||||
# print "\rWARNING: Caught LinAlgError, continueing without setting "
|
||||
# if self._debug:
|
||||
# self._savederrors.append(self.f_call)
|
||||
# if save_count > 10:
|
||||
# raise
|
||||
# self._set_params(self.oldps[-1], save_old=False, save_count=save_count + 1)
|
||||
|
||||
def dKL_dmuS(self):
|
||||
dKL_dS = (1. - (1. / (self.X_variance))) * 0.5
|
||||
dKL_dmu = self.X
|
||||
return dKL_dmu, dKL_dS
|
||||
|
||||
def dL_dmuS(self):
|
||||
dL_dmu_psi0, dL_dS_psi0 = self.kern.dpsi0_dmuS(self.dL_dpsi0, self.Z, self.X, self.X_variance)
|
||||
dL_dmu_psi1, dL_dS_psi1 = self.kern.dpsi1_dmuS(self.dL_dpsi1, self.Z, self.X, self.X_variance)
|
||||
dL_dmu_psi2, dL_dS_psi2 = self.kern.dpsi2_dmuS(self.dL_dpsi2, self.Z, self.X, self.X_variance)
|
||||
dL_dmu = dL_dmu_psi0 + dL_dmu_psi1 + dL_dmu_psi2
|
||||
dL_dS = dL_dS_psi0 + dL_dS_psi1 + dL_dS_psi2
|
||||
|
||||
return dL_dmu, dL_dS
|
||||
|
||||
def KL_divergence(self):
|
||||
var_mean = np.square(self.X).sum()
|
||||
var_S = np.sum(self.X_variance - np.log(self.X_variance))
|
||||
return 0.5 * (var_mean + var_S) - 0.5 * self.input_dim * self.N
|
||||
|
||||
def log_likelihood(self):
|
||||
ll = sparse_GP.log_likelihood(self)
|
||||
kl = self.KL_divergence()
|
||||
|
||||
# if ll < -2E4:
|
||||
# ll = -2E4 + np.random.randn()
|
||||
# if kl > 5E4:
|
||||
# kl = 5E4 + np.random.randn()
|
||||
|
||||
if self._debug:
|
||||
self.f_call = self._count.next()
|
||||
if self.f_call % 1 == 0:
|
||||
self._savedklll.append([self.f_call, ll, kl])
|
||||
self._savedparams.append([self.f_call, self._get_params()])
|
||||
self._savedgradients.append([self.f_call, self._log_likelihood_gradients()])
|
||||
self._savedpsiKmm.append([self.f_call, [self.Kmm, self.dL_dKmm]])
|
||||
# sf2 = self.scale_factor ** 2
|
||||
if self.likelihood.is_heteroscedastic:
|
||||
A = -0.5 * self.N * self.D * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.likelihood.precision)) - 0.5 * np.sum(self.V * self.likelihood.Y)
|
||||
# B = -0.5 * self.D * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A) * sf2)
|
||||
B = -0.5 * self.D * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A))
|
||||
else:
|
||||
A = -0.5 * self.N * self.D * (np.log(2.*np.pi) + np.log(self.likelihood._variance)) - 0.5 * self.likelihood.precision * self.likelihood.trYYT
|
||||
# B = -0.5 * self.D * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A) * sf2)
|
||||
B = -0.5 * self.D * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A))
|
||||
C = -self.D * (np.sum(np.log(np.diag(self.LB)))) # + 0.5 * self.M * np.log(sf2))
|
||||
D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
|
||||
self._savedABCD.append([self.f_call, A, B, C, D])
|
||||
|
||||
# print "\nkl:", kl, "ll:", ll
|
||||
return ll - kl
|
||||
|
||||
def _log_likelihood_gradients(self):
|
||||
dKL_dmu, dKL_dS = self.dKL_dmuS()
|
||||
dL_dmu, dL_dS = self.dL_dmuS()
|
||||
# TODO: find way to make faster
|
||||
|
||||
d_dmu = (dL_dmu - dKL_dmu).flatten()
|
||||
d_dS = (dL_dS - dKL_dS).flatten()
|
||||
# TEST KL: ====================
|
||||
# d_dmu = (dKL_dmu).flatten()
|
||||
# d_dS = (dKL_dS).flatten()
|
||||
# ========================
|
||||
# TEST L: ====================
|
||||
# d_dmu = (dL_dmu).flatten()
|
||||
# d_dS = (dL_dS).flatten()
|
||||
# ========================
|
||||
self.dbound_dmuS = np.hstack((d_dmu, d_dS))
|
||||
self.dbound_dZtheta = sparse_GP._log_likelihood_gradients(self)
|
||||
return self._clipped(np.hstack((self.dbound_dmuS.flatten(), self.dbound_dZtheta)))
|
||||
|
||||
def plot_latent(self, *args, **kwargs):
|
||||
return plot_latent.plot_latent_indices(self, *args, **kwargs)
|
||||
|
||||
def do_test_latents(self, Y):
|
||||
"""
|
||||
Compute the latent representation for a set of new points Y
|
||||
|
||||
Notes:
|
||||
This will only work with a univariate Gaussian likelihood (for now)
|
||||
"""
|
||||
assert not self.likelihood.is_heteroscedastic
|
||||
N_test = Y.shape[0]
|
||||
input_dim = self.Z.shape[1]
|
||||
means = np.zeros((N_test, input_dim))
|
||||
covars = np.zeros((N_test, input_dim))
|
||||
|
||||
dpsi0 = -0.5 * self.D * self.likelihood.precision
|
||||
dpsi2 = self.dL_dpsi2[0][None, :, :] # TODO: this may change if we ignore het. likelihoods
|
||||
V = self.likelihood.precision * Y
|
||||
dpsi1 = np.dot(self.Cpsi1V, V.T)
|
||||
|
||||
start = np.zeros(self.input_dim * 2)
|
||||
|
||||
for n, dpsi1_n in enumerate(dpsi1.T[:, :, None]):
|
||||
args = (self.kern, self.Z, dpsi0, dpsi1_n, dpsi2)
|
||||
xopt, fopt, neval, status = SCG(f=latent_cost, gradf=latent_grad, x=start, optargs=args, display=False)
|
||||
|
||||
mu, log_S = xopt.reshape(2, 1, -1)
|
||||
means[n] = mu[0].copy()
|
||||
covars[n] = np.exp(log_S[0]).copy()
|
||||
|
||||
return means, covars
|
||||
|
||||
|
||||
def plot_X_1d(self, fignum=None, ax=None, colors=None):
|
||||
"""
|
||||
Plot latent space X in 1D:
|
||||
|
||||
-if fig is given, create input_dim subplots in fig and plot in these
|
||||
-if ax is given plot input_dim 1D latent space plots of X into each `axis`
|
||||
-if neither fig nor ax is given create a figure with fignum and plot in there
|
||||
|
||||
colors:
|
||||
colors of different latent space dimensions input_dim
|
||||
"""
|
||||
import pylab
|
||||
if ax is None:
|
||||
fig = pylab.figure(num=fignum, figsize=(8, min(12, (2 * self.X.shape[1]))))
|
||||
if colors is None:
|
||||
colors = pylab.gca()._get_lines.color_cycle
|
||||
pylab.clf()
|
||||
else:
|
||||
colors = iter(colors)
|
||||
plots = []
|
||||
x = np.arange(self.X.shape[0])
|
||||
for i in range(self.X.shape[1]):
|
||||
if ax is None:
|
||||
a = fig.add_subplot(self.X.shape[1], 1, i + 1)
|
||||
elif isinstance(ax, (tuple, list)):
|
||||
a = ax[i]
|
||||
else:
|
||||
raise ValueError("Need one ax per latent dimnesion input_dim")
|
||||
a.plot(self.X, c='k', alpha=.3)
|
||||
plots.extend(a.plot(x, self.X.T[i], c=colors.next(), label=r"$\mathbf{{X_{{{}}}}}$".format(i)))
|
||||
a.fill_between(x,
|
||||
self.X.T[i] - 2 * np.sqrt(self.X_variance.T[i]),
|
||||
self.X.T[i] + 2 * np.sqrt(self.X_variance.T[i]),
|
||||
facecolor=plots[-1].get_color(),
|
||||
alpha=.3)
|
||||
a.legend(borderaxespad=0.)
|
||||
a.set_xlim(x.min(), x.max())
|
||||
if i < self.X.shape[1] - 1:
|
||||
a.set_xticklabels('')
|
||||
pylab.draw()
|
||||
fig.tight_layout(h_pad=.01) # , rect=(0, 0, 1, .95))
|
||||
return fig
|
||||
|
||||
def __getstate__(self):
|
||||
return (self.likelihood, self.input_dim, self.X, self.X_variance,
|
||||
self.init, self.M, self.Z, self.kern,
|
||||
self.oldpsave, self._debug)
|
||||
|
||||
def __setstate__(self, state):
|
||||
self.__init__(*state)
|
||||
|
||||
def _debug_filter_params(self, x):
|
||||
start, end = 0, self.X.size,
|
||||
X = x[start:end].reshape(self.N, self.input_dim)
|
||||
start, end = end, end + self.X_variance.size
|
||||
X_v = x[start:end].reshape(self.N, self.input_dim)
|
||||
start, end = end, end + (self.M * self.input_dim)
|
||||
Z = x[start:end].reshape(self.M, self.input_dim)
|
||||
start, end = end, end + self.input_dim
|
||||
theta = x[start:]
|
||||
return X, X_v, Z, theta
|
||||
|
||||
|
||||
def _debug_get_axis(self, figs):
|
||||
if figs[-1].axes:
|
||||
ax1 = figs[-1].axes[0]
|
||||
ax1.cla()
|
||||
else:
|
||||
ax1 = figs[-1].add_subplot(111)
|
||||
return ax1
|
||||
|
||||
def _debug_plot(self):
|
||||
assert self._debug, "must enable _debug, to debug-plot"
|
||||
import pylab
|
||||
# from mpl_toolkits.mplot3d import Axes3D
|
||||
figs = [pylab.figure('BGPLVM DEBUG', figsize=(12, 4))]
|
||||
# fig.clf()
|
||||
|
||||
# log like
|
||||
# splotshape = (6, 4)
|
||||
# ax1 = pylab.subplot2grid(splotshape, (0, 0), 1, 4)
|
||||
ax1 = self._debug_get_axis(figs)
|
||||
ax1.text(.5, .5, "Optimization", alpha=.3, transform=ax1.transAxes,
|
||||
ha='center', va='center')
|
||||
kllls = np.array(self._savedklll)
|
||||
LL, = ax1.plot(kllls[:, 0], kllls[:, 1] - kllls[:, 2], '-', label=r'$\log p(\mathbf{Y})$', mew=1.5)
|
||||
KL, = ax1.plot(kllls[:, 0], kllls[:, 2], '-', label=r'$\mathcal{KL}(p||q)$', mew=1.5)
|
||||
L, = ax1.plot(kllls[:, 0], kllls[:, 1], '-', label=r'$L$', mew=1.5) # \mathds{E}_{q(\mathbf{X})}[p(\mathbf{Y|X})\frac{p(\mathbf{X})}{q(\mathbf{X})}]
|
||||
|
||||
param_dict = dict(self._savedparams)
|
||||
gradient_dict = dict(self._savedgradients)
|
||||
# kmm_dict = dict(self._savedpsiKmm)
|
||||
iters = np.array(param_dict.keys())
|
||||
ABCD_dict = np.array(self._savedABCD)
|
||||
self.showing = 0
|
||||
|
||||
# ax2 = pylab.subplot2grid(splotshape, (1, 0), 2, 4)
|
||||
figs.append(pylab.figure("BGPLVM DEBUG X", figsize=(12, 4)))
|
||||
ax2 = self._debug_get_axis(figs)
|
||||
ax2.text(.5, .5, r"$\mathbf{X}$", alpha=.5, transform=ax2.transAxes,
|
||||
ha='center', va='center')
|
||||
figs[-1].canvas.draw()
|
||||
figs[-1].tight_layout(rect=(0, 0, 1, .86))
|
||||
# ax3 = pylab.subplot2grid(splotshape, (3, 0), 2, 4, sharex=ax2)
|
||||
figs.append(pylab.figure("BGPLVM DEBUG S", figsize=(12, 4)))
|
||||
ax3 = self._debug_get_axis(figs)
|
||||
ax3.text(.5, .5, r"$\mathbf{S}$", alpha=.5, transform=ax3.transAxes,
|
||||
ha='center', va='center')
|
||||
figs[-1].canvas.draw()
|
||||
figs[-1].tight_layout(rect=(0, 0, 1, .86))
|
||||
# ax4 = pylab.subplot2grid(splotshape, (5, 0), 2, 2)
|
||||
figs.append(pylab.figure("BGPLVM DEBUG Z", figsize=(6, 4)))
|
||||
ax4 = self._debug_get_axis(figs)
|
||||
ax4.text(.5, .5, r"$\mathbf{Z}$", alpha=.5, transform=ax4.transAxes,
|
||||
ha='center', va='center')
|
||||
figs[-1].canvas.draw()
|
||||
figs[-1].tight_layout(rect=(0, 0, 1, .86))
|
||||
# ax5 = pylab.subplot2grid(splotshape, (5, 2), 2, 2)
|
||||
figs.append(pylab.figure("BGPLVM DEBUG theta", figsize=(6, 4)))
|
||||
ax5 = self._debug_get_axis(figs)
|
||||
ax5.text(.5, .5, r"${\theta}$", alpha=.5, transform=ax5.transAxes,
|
||||
ha='center', va='center')
|
||||
figs[-1].canvas.draw()
|
||||
figs[-1].tight_layout(rect=(.15, 0, 1, .86))
|
||||
# figs.append(pylab.figure("BGPLVM DEBUG Kmm", figsize=(12, 6)))
|
||||
# fig = figs[-1]
|
||||
# ax6 = fig.add_subplot(121)
|
||||
# ax6.text(.5, .5, r"${\mathbf{K}_{mm}}$", color='magenta', alpha=.5, transform=ax6.transAxes,
|
||||
# ha='center', va='center')
|
||||
# ax7 = fig.add_subplot(122)
|
||||
# ax7.text(.5, .5, r"${\frac{dL}{dK_{mm}}}$", color='magenta', alpha=.5, transform=ax7.transAxes,
|
||||
# ha='center', va='center')
|
||||
figs.append(pylab.figure("BGPLVM DEBUG Kmm", figsize=(12, 6)))
|
||||
fig = figs[-1]
|
||||
ax8 = fig.add_subplot(121)
|
||||
ax8.text(.5, .5, r"${\mathbf{A,B,C,D}}$", color='k', alpha=.5, transform=ax8.transAxes,
|
||||
ha='center', va='center')
|
||||
ax8.plot(ABCD_dict[:, 0], ABCD_dict[:, 1], label='A')
|
||||
ax8.plot(ABCD_dict[:, 0], ABCD_dict[:, 2], label='B')
|
||||
ax8.plot(ABCD_dict[:, 0], ABCD_dict[:, 3], label='C')
|
||||
ax8.plot(ABCD_dict[:, 0], ABCD_dict[:, 4], label='D')
|
||||
ax8.legend()
|
||||
figs[-1].canvas.draw()
|
||||
figs[-1].tight_layout(rect=(.15, 0, 1, .86))
|
||||
|
||||
X, S, Z, theta = self._debug_filter_params(param_dict[self.showing])
|
||||
Xg, Sg, Zg, thetag = self._debug_filter_params(gradient_dict[self.showing])
|
||||
# Xg, Sg, Zg, thetag = -Xg, -Sg, -Zg, -thetag
|
||||
|
||||
quiver_units = 'xy'
|
||||
quiver_scale = 1
|
||||
quiver_scale_units = 'xy'
|
||||
Xlatentplts = ax2.plot(X, ls="-", marker="x")
|
||||
colors = colorConverter.to_rgba_array([p.get_color() for p in Xlatentplts], .4)
|
||||
Ulatent = np.zeros_like(X)
|
||||
xlatent = np.tile(np.arange(0, X.shape[0])[:, None], X.shape[1])
|
||||
Xlatentgrads = ax2.quiver(xlatent, X, Ulatent, Xg, color=colors,
|
||||
units=quiver_units, scale_units=quiver_scale_units,
|
||||
scale=quiver_scale)
|
||||
|
||||
Slatentplts = ax3.plot(S, ls="-", marker="x")
|
||||
Slatentgrads = ax3.quiver(xlatent, S, Ulatent, Sg, color=colors,
|
||||
units=quiver_units, scale_units=quiver_scale_units,
|
||||
scale=quiver_scale)
|
||||
ax3.set_ylim(0, 1.)
|
||||
|
||||
xZ = np.tile(np.arange(0, Z.shape[0])[:, None], Z.shape[1])
|
||||
UZ = np.zeros_like(Z)
|
||||
Zplts = ax4.plot(Z, ls="-", marker="x")
|
||||
Zgrads = ax4.quiver(xZ, Z, UZ, Zg, color=colors,
|
||||
units=quiver_units, scale_units=quiver_scale_units,
|
||||
scale=quiver_scale)
|
||||
|
||||
xtheta = np.arange(len(theta))
|
||||
Utheta = np.zeros_like(theta)
|
||||
thetaplts = ax5.bar(xtheta - .4, theta, color=colors)
|
||||
thetagrads = ax5.quiver(xtheta, theta, Utheta, thetag, color=colors,
|
||||
units=quiver_units, scale_units=quiver_scale_units,
|
||||
scale=quiver_scale,
|
||||
edgecolors=('k',), linewidths=[1])
|
||||
pylab.setp(thetaplts, zorder=0)
|
||||
pylab.setp(thetagrads, zorder=10)
|
||||
ax5.set_xticks(np.arange(len(theta)))
|
||||
ax5.set_xticklabels(self._get_param_names()[-len(theta):], rotation=17)
|
||||
|
||||
# imkmm = ax6.imshow(kmm_dict[self.showing][0])
|
||||
# from mpl_toolkits.axes_grid1 import make_axes_locatable
|
||||
# divider = make_axes_locatable(ax6)
|
||||
# caxkmm = divider.append_axes("right", "5%", pad="1%")
|
||||
# cbarkmm = pylab.colorbar(imkmm, cax=caxkmm)
|
||||
#
|
||||
# imkmmdl = ax7.imshow(kmm_dict[self.showing][1])
|
||||
# divider = make_axes_locatable(ax7)
|
||||
# caxkmmdl = divider.append_axes("right", "5%", pad="1%")
|
||||
# cbarkmmdl = pylab.colorbar(imkmmdl, cax=caxkmmdl)
|
||||
|
||||
# input_dimleg = ax1.legend(Xlatentplts, [r"$input_dim_{}$".format(i + 1) for i in range(self.input_dim)],
|
||||
# loc=3, ncol=self.input_dim, bbox_to_anchor=(0, 1.15, 1, 1.15),
|
||||
# borderaxespad=0, mode="expand")
|
||||
ax2.legend(Xlatentplts, [r"$input_dim_{}$".format(i + 1) for i in range(self.input_dim)],
|
||||
loc=3, ncol=self.input_dim, bbox_to_anchor=(0, 1.1, 1, 1.1),
|
||||
borderaxespad=0, mode="expand")
|
||||
ax3.legend(Xlatentplts, [r"$input_dim_{}$".format(i + 1) for i in range(self.input_dim)],
|
||||
loc=3, ncol=self.input_dim, bbox_to_anchor=(0, 1.1, 1, 1.1),
|
||||
borderaxespad=0, mode="expand")
|
||||
ax4.legend(Xlatentplts, [r"$input_dim_{}$".format(i + 1) for i in range(self.input_dim)],
|
||||
loc=3, ncol=self.input_dim, bbox_to_anchor=(0, 1.1, 1, 1.1),
|
||||
borderaxespad=0, mode="expand")
|
||||
ax5.legend(Xlatentplts, [r"$input_dim_{}$".format(i + 1) for i in range(self.input_dim)],
|
||||
loc=3, ncol=self.input_dim, bbox_to_anchor=(0, 1.1, 1, 1.1),
|
||||
borderaxespad=0, mode="expand")
|
||||
Lleg = ax1.legend()
|
||||
Lleg.draggable()
|
||||
# ax1.add_artist(input_dimleg)
|
||||
|
||||
indicatorKL, = ax1.plot(kllls[self.showing, 0], kllls[self.showing, 2], 'o', c=KL.get_color())
|
||||
indicatorLL, = ax1.plot(kllls[self.showing, 0], kllls[self.showing, 1] - kllls[self.showing, 2], 'o', c=LL.get_color())
|
||||
indicatorL, = ax1.plot(kllls[self.showing, 0], kllls[self.showing, 1], 'o', c=L.get_color())
|
||||
# for err in self._savederrors:
|
||||
# if err < kllls.shape[0]:
|
||||
# ax1.scatter(kllls[err, 0], kllls[err, 2], s=50, marker=(5, 2), c=KL.get_color())
|
||||
# ax1.scatter(kllls[err, 0], kllls[err, 1] - kllls[err, 2], s=50, marker=(5, 2), c=LL.get_color())
|
||||
# ax1.scatter(kllls[err, 0], kllls[err, 1], s=50, marker=(5, 2), c=L.get_color())
|
||||
|
||||
# try:
|
||||
# for f in figs:
|
||||
# f.canvas.draw()
|
||||
# f.tight_layout(box=(0, .15, 1, .9))
|
||||
# # pylab.draw()
|
||||
# # pylab.tight_layout(box=(0, .1, 1, .9))
|
||||
# except:
|
||||
# pass
|
||||
|
||||
# parameter changes
|
||||
# ax2 = pylab.subplot2grid((4, 1), (1, 0), 3, 1, projection='3d')
|
||||
button_options = [0, 0] # [0]: clicked -- [1]: dragged
|
||||
|
||||
def update_plots(event):
|
||||
if button_options[0] and not button_options[1]:
|
||||
# event.button, event.x, event.y, event.xdata, event.ydata)
|
||||
tmp = np.abs(iters - event.xdata)
|
||||
closest_hit = iters[tmp == tmp.min()][0]
|
||||
|
||||
if closest_hit != self.showing:
|
||||
self.showing = closest_hit
|
||||
# print closest_hit, iters, event.xdata
|
||||
|
||||
indicatorLL.set_data(self.showing, kllls[self.showing, 1] - kllls[self.showing, 2])
|
||||
indicatorKL.set_data(self.showing, kllls[self.showing, 2])
|
||||
indicatorL.set_data(self.showing, kllls[self.showing, 1])
|
||||
|
||||
X, S, Z, theta = self._debug_filter_params(param_dict[self.showing])
|
||||
Xg, Sg, Zg, thetag = self._debug_filter_params(gradient_dict[self.showing])
|
||||
# Xg, Sg, Zg, thetag = -Xg, -Sg, -Zg, -thetag
|
||||
|
||||
for i, Xlatent in enumerate(Xlatentplts):
|
||||
Xlatent.set_ydata(X[:, i])
|
||||
Xlatentgrads.set_offsets(np.array([xlatent.ravel(), X.ravel()]).T)
|
||||
Xlatentgrads.set_UVC(Ulatent, Xg)
|
||||
|
||||
for i, Slatent in enumerate(Slatentplts):
|
||||
Slatent.set_ydata(S[:, i])
|
||||
Slatentgrads.set_offsets(np.array([xlatent.ravel(), S.ravel()]).T)
|
||||
Slatentgrads.set_UVC(Ulatent, Sg)
|
||||
|
||||
for i, Zlatent in enumerate(Zplts):
|
||||
Zlatent.set_ydata(Z[:, i])
|
||||
Zgrads.set_offsets(np.array([xZ.ravel(), Z.ravel()]).T)
|
||||
Zgrads.set_UVC(UZ, Zg)
|
||||
|
||||
for p, t in zip(thetaplts, theta):
|
||||
p.set_height(t)
|
||||
thetagrads.set_offsets(np.array([xtheta.ravel(), theta.ravel()]).T)
|
||||
thetagrads.set_UVC(Utheta, thetag)
|
||||
|
||||
# imkmm.set_data(kmm_dict[self.showing][0])
|
||||
# imkmm.autoscale()
|
||||
# cbarkmm.update_normal(imkmm)
|
||||
#
|
||||
# imkmmdl.set_data(kmm_dict[self.showing][1])
|
||||
# imkmmdl.autoscale()
|
||||
# cbarkmmdl.update_normal(imkmmdl)
|
||||
|
||||
ax2.relim()
|
||||
# ax3.relim()
|
||||
ax4.relim()
|
||||
ax5.relim()
|
||||
ax2.autoscale()
|
||||
# ax3.autoscale()
|
||||
ax4.autoscale()
|
||||
ax5.autoscale()
|
||||
|
||||
[fig.canvas.draw() for fig in figs]
|
||||
button_options[0] = 0
|
||||
button_options[1] = 0
|
||||
|
||||
def onclick(event):
|
||||
if event.inaxes is ax1 and event.button == 1:
|
||||
button_options[0] = 1
|
||||
def motion(event):
|
||||
if button_options[0]:
|
||||
button_options[1] = 1
|
||||
|
||||
cidr = figs[0].canvas.mpl_connect('button_release_event', update_plots)
|
||||
cidp = figs[0].canvas.mpl_connect('button_press_event', onclick)
|
||||
cidd = figs[0].canvas.mpl_connect('motion_notify_event', motion)
|
||||
|
||||
return ax1, ax2, ax3, ax4, ax5 # , ax6, ax7
|
||||
|
||||
|
||||
|
||||
|
||||
def latent_cost_and_grad(mu_S, kern, Z, dL_dpsi0, dL_dpsi1, dL_dpsi2):
|
||||
"""
|
||||
objective function for fitting the latent variables for test points
|
||||
(negative log-likelihood: should be minimised!)
|
||||
"""
|
||||
mu, log_S = mu_S.reshape(2, 1, -1)
|
||||
S = np.exp(log_S)
|
||||
|
||||
psi0 = kern.psi0(Z, mu, S)
|
||||
psi1 = kern.psi1(Z, mu, S)
|
||||
psi2 = kern.psi2(Z, mu, S)
|
||||
|
||||
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)
|
||||
|
||||
mu0, S0 = kern.dpsi0_dmuS(dL_dpsi0, Z, mu, S)
|
||||
mu1, S1 = kern.dpsi1_dmuS(dL_dpsi1, Z, mu, S)
|
||||
mu2, S2 = kern.dpsi2_dmuS(dL_dpsi2, Z, mu, S)
|
||||
|
||||
dmu = mu0 + mu1 + mu2 - mu
|
||||
# dS = S0 + S1 + S2 -0.5 + .5/S
|
||||
dlnS = S * (S0 + S1 + S2 - 0.5) + .5
|
||||
return -lik, -np.hstack((dmu.flatten(), dlnS.flatten()))
|
||||
|
||||
def latent_cost(mu_S, kern, Z, dL_dpsi0, dL_dpsi1, dL_dpsi2):
|
||||
"""
|
||||
objective function for fitting the latent variables (negative log-likelihood: should be minimised!)
|
||||
This is the same as latent_cost_and_grad but only for the objective
|
||||
"""
|
||||
mu, log_S = mu_S.reshape(2, 1, -1)
|
||||
S = np.exp(log_S)
|
||||
|
||||
psi0 = kern.psi0(Z, mu, S)
|
||||
psi1 = kern.psi1(Z, mu, S)
|
||||
psi2 = kern.psi2(Z, mu, S)
|
||||
|
||||
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)
|
||||
return -float(lik)
|
||||
|
||||
def latent_grad(mu_S, kern, Z, dL_dpsi0, dL_dpsi1, dL_dpsi2):
|
||||
"""
|
||||
This is the same as latent_cost_and_grad but only for the grad
|
||||
"""
|
||||
mu, log_S = mu_S.reshape(2, 1, -1)
|
||||
S = np.exp(log_S)
|
||||
|
||||
mu0, S0 = kern.dpsi0_dmuS(dL_dpsi0, Z, mu, S)
|
||||
mu1, S1 = kern.dpsi1_dmuS(dL_dpsi1, Z, mu, S)
|
||||
mu2, S2 = kern.dpsi2_dmuS(dL_dpsi2, Z, mu, S)
|
||||
|
||||
dmu = mu0 + mu1 + mu2 - mu
|
||||
# dS = S0 + S1 + S2 -0.5 + .5/S
|
||||
dlnS = S * (S0 + S1 + S2 - 0.5) + .5
|
||||
|
||||
return -np.hstack((dmu.flatten(), dlnS.flatten()))
|
||||
|
||||
|
||||
|
|
@ -1,252 +0,0 @@
|
|||
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
|
||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
||||
|
||||
import numpy as np
|
||||
import pylab as pb
|
||||
from ..util.linalg import mdot, jitchol, chol_inv, tdot, symmetrify,pdinv
|
||||
from ..util.plot import gpplot
|
||||
from .. import kern
|
||||
from scipy import stats, linalg
|
||||
from ..core import sparse_GP
|
||||
|
||||
def backsub_both_sides(L,X):
|
||||
""" Return L^-T * X * L^-1, assumuing X is symmetrical and L is lower cholesky"""
|
||||
tmp,_ = linalg.lapack.flapack.dtrtrs(L,np.asfortranarray(X),lower=1,trans=1)
|
||||
return linalg.lapack.flapack.dtrtrs(L,np.asfortranarray(tmp.T),lower=1,trans=1)[0].T
|
||||
|
||||
class FITC(sparse_GP):
|
||||
|
||||
def __init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False):
|
||||
super(FITC, self).__init__(X, likelihood, kernel, normalize_X=normalize_X)
|
||||
|
||||
def update_likelihood_approximation(self):
|
||||
"""
|
||||
Approximates a non-gaussian likelihood using Expectation Propagation
|
||||
|
||||
For a Gaussian (or direct: TODO) likelihood, no iteration is required:
|
||||
this function does nothing
|
||||
|
||||
Diag(Knn - Qnn) is added to the noise term to use the tools already implemented in sparse_GP.
|
||||
The true precison is now 'true_precision' not 'precision'.
|
||||
"""
|
||||
if self.has_uncertain_inputs:
|
||||
raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
|
||||
else:
|
||||
self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
|
||||
self._set_params(self._get_params()) # update the GP
|
||||
|
||||
def _computations(self):
|
||||
|
||||
#factor Kmm
|
||||
self.Lm = jitchol(self.Kmm)
|
||||
self.Lmi,info = linalg.lapack.flapack.dtrtrs(self.Lm,np.eye(self.M),lower=1)
|
||||
Lmipsi1 = np.dot(self.Lmi,self.psi1)
|
||||
self.Qnn = np.dot(Lmipsi1.T,Lmipsi1).copy()
|
||||
self.Diag0 = self.psi0 - np.diag(self.Qnn)
|
||||
self.beta_star = self.likelihood.precision/(1. + self.likelihood.precision*self.Diag0[:,None]) #Includes Diag0 in the precision
|
||||
self.V_star = self.beta_star * self.likelihood.Y
|
||||
|
||||
# The rather complex computations of self.A
|
||||
if self.has_uncertain_inputs:
|
||||
raise NotImplementedError
|
||||
else:
|
||||
if self.likelihood.is_heteroscedastic:
|
||||
assert self.likelihood.D == 1
|
||||
tmp = self.psi1 * (np.sqrt(self.beta_star.flatten().reshape(1, self.N)))
|
||||
tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
|
||||
self.A = tdot(tmp)
|
||||
|
||||
# factor B
|
||||
self.B = np.eye(self.M) + self.A
|
||||
self.LB = jitchol(self.B)
|
||||
self.LBi = chol_inv(self.LB)
|
||||
self.psi1V = np.dot(self.psi1, self.V_star)
|
||||
|
||||
Lmi_psi1V, info = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(self.psi1V), lower=1, trans=0)
|
||||
self._LBi_Lmi_psi1V, _ = linalg.lapack.flapack.dtrtrs(self.LB, np.asfortranarray(Lmi_psi1V), lower=1, trans=0)
|
||||
|
||||
Kmmipsi1 = np.dot(self.Lmi.T,Lmipsi1)
|
||||
b_psi1_Ki = self.beta_star * Kmmipsi1.T
|
||||
Ki_pbp_Ki = np.dot(Kmmipsi1,b_psi1_Ki)
|
||||
Kmmi = np.dot(self.Lmi.T,self.Lmi)
|
||||
LBiLmi = np.dot(self.LBi,self.Lmi)
|
||||
LBL_inv = np.dot(LBiLmi.T,LBiLmi)
|
||||
VVT = np.outer(self.V_star,self.V_star)
|
||||
VV_p_Ki = np.dot(VVT,Kmmipsi1.T)
|
||||
Ki_pVVp_Ki = np.dot(Kmmipsi1,VV_p_Ki)
|
||||
psi1beta = self.psi1*self.beta_star.T
|
||||
H = self.Kmm + mdot(self.psi1,psi1beta.T)
|
||||
LH = jitchol(H)
|
||||
LHi = chol_inv(LH)
|
||||
Hi = np.dot(LHi.T,LHi)
|
||||
|
||||
betapsi1TLmiLBi = np.dot(psi1beta.T,LBiLmi.T)
|
||||
alpha = np.array([np.dot(a.T,a) for a in betapsi1TLmiLBi])[:,None]
|
||||
gamma_1 = mdot(VVT,self.psi1.T,Hi)
|
||||
pHip = mdot(self.psi1.T,Hi,self.psi1)
|
||||
gamma_2 = mdot(self.beta_star*pHip,self.V_star)
|
||||
gamma_3 = self.V_star * gamma_2
|
||||
|
||||
self._dL_dpsi0 = -0.5 * self.beta_star#dA_dpsi0: logdet(self.beta_star)
|
||||
self._dL_dpsi0 += .5 * self.V_star**2 #dA_psi0: yT*beta_star*y
|
||||
self._dL_dpsi0 += .5 *alpha #dC_dpsi0
|
||||
self._dL_dpsi0 += 0.5*mdot(self.beta_star*pHip,self.V_star)**2 - self.V_star * mdot(self.V_star.T,pHip*self.beta_star).T #dD_dpsi0
|
||||
|
||||
self._dL_dpsi1 = b_psi1_Ki.copy() #dA_dpsi1: logdet(self.beta_star)
|
||||
self._dL_dpsi1 += -np.dot(psi1beta.T,LBL_inv) #dC_dpsi1
|
||||
self._dL_dpsi1 += gamma_1 - mdot(psi1beta.T,Hi,self.psi1,gamma_1) #dD_dpsi1
|
||||
|
||||
self._dL_dKmm = -0.5 * np.dot(Kmmipsi1,b_psi1_Ki) #dA_dKmm: logdet(self.beta_star)
|
||||
self._dL_dKmm += .5*(LBL_inv - Kmmi) + mdot(LBL_inv,psi1beta,Kmmipsi1.T) #dC_dKmm
|
||||
self._dL_dKmm += -.5 * mdot(Hi,self.psi1,gamma_1) #dD_dKmm
|
||||
|
||||
self._dpsi1_dtheta = 0
|
||||
self._dpsi1_dX = 0
|
||||
self._dKmm_dtheta = 0
|
||||
self._dKmm_dX = 0
|
||||
|
||||
self._dpsi1_dX_jkj = 0
|
||||
self._dpsi1_dtheta_jkj = 0
|
||||
|
||||
for i,V_n,alpha_n,gamma_n,gamma_k in zip(range(self.N),self.V_star,alpha,gamma_2,gamma_3):
|
||||
K_pp_K = np.dot(Kmmipsi1[:,i:(i+1)],Kmmipsi1[:,i:(i+1)].T)
|
||||
|
||||
#Diag_dpsi1 = Diag_dA_dpsi1: yT*beta_star*y + Diag_dC_dpsi1 +Diag_dD_dpsi1
|
||||
_dpsi1 = (-V_n**2 - alpha_n + 2.*gamma_k - gamma_n**2) * Kmmipsi1.T[i:(i+1),:]
|
||||
|
||||
#Diag_dKmm = Diag_dA_dKmm: yT*beta_star*y +Diag_dC_dKmm +Diag_dD_dKmm
|
||||
_dKmm = .5*(V_n**2 + alpha_n + gamma_n**2 - 2.*gamma_k) * K_pp_K #Diag_dD_dKmm
|
||||
|
||||
self._dpsi1_dtheta += self.kern.dK_dtheta(_dpsi1,self.X[i:i+1,:],self.Z)
|
||||
self._dKmm_dtheta += self.kern.dK_dtheta(_dKmm,self.Z)
|
||||
|
||||
self._dKmm_dX += 2.*self.kern.dK_dX(_dKmm ,self.Z)
|
||||
self._dpsi1_dX += self.kern.dK_dX(_dpsi1.T,self.Z,self.X[i:i+1,:])
|
||||
|
||||
# the partial derivative vector for the likelihood
|
||||
if self.likelihood.Nparams == 0:
|
||||
# save computation here.
|
||||
self.partial_for_likelihood = None
|
||||
elif self.likelihood.is_heteroscedastic:
|
||||
raise NotImplementedError, "heteroscedatic derivates not implemented"
|
||||
else:
|
||||
# likelihood is not heterscedatic
|
||||
dbstar_dnoise = self.likelihood.precision * (self.beta_star**2 * self.Diag0[:,None] - self.beta_star)
|
||||
Lmi_psi1 = mdot(self.Lmi,self.psi1)
|
||||
LBiLmipsi1 = np.dot(self.LBi,Lmi_psi1)
|
||||
aux_0 = np.dot(self._LBi_Lmi_psi1V.T,LBiLmipsi1)
|
||||
aux_1 = self.likelihood.Y.T * np.dot(self._LBi_Lmi_psi1V.T,LBiLmipsi1)
|
||||
aux_2 = np.dot(LBiLmipsi1.T,self._LBi_Lmi_psi1V)
|
||||
|
||||
dA_dnoise = 0.5 * self.D * (dbstar_dnoise/self.beta_star).sum() - 0.5 * self.D * np.sum(self.likelihood.Y**2 * dbstar_dnoise)
|
||||
dC_dnoise = -0.5 * np.sum(mdot(self.LBi.T,self.LBi,Lmi_psi1) * Lmi_psi1 * dbstar_dnoise.T)
|
||||
dC_dnoise = -0.5 * np.sum(mdot(self.LBi.T,self.LBi,Lmi_psi1) * Lmi_psi1 * dbstar_dnoise.T)
|
||||
|
||||
dD_dnoise_1 = mdot(self.V_star*LBiLmipsi1.T,LBiLmipsi1*dbstar_dnoise.T*self.likelihood.Y.T)
|
||||
alpha = mdot(LBiLmipsi1,self.V_star)
|
||||
alpha_ = mdot(LBiLmipsi1.T,alpha)
|
||||
dD_dnoise_2 = -0.5 * self.D * np.sum(alpha_**2 * dbstar_dnoise )
|
||||
|
||||
dD_dnoise_1 = mdot(self.V_star.T,self.psi1.T,self.Lmi.T,self.LBi.T,self.LBi,self.Lmi,self.psi1,dbstar_dnoise*self.likelihood.Y)
|
||||
dD_dnoise_2 = 0.5*mdot(self.V_star.T,self.psi1.T,Hi,self.psi1,dbstar_dnoise*self.psi1.T,Hi,self.psi1,self.V_star)
|
||||
dD_dnoise = dD_dnoise_1 + dD_dnoise_2
|
||||
|
||||
self.partial_for_likelihood = dA_dnoise + dC_dnoise + dD_dnoise
|
||||
|
||||
def log_likelihood(self):
|
||||
""" Compute the (lower bound on the) log marginal likelihood """
|
||||
A = -0.5 * self.N * self.D * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.beta_star)) - 0.5 * np.sum(self.V_star * self.likelihood.Y)
|
||||
C = -self.D * (np.sum(np.log(np.diag(self.LB))))
|
||||
D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
|
||||
return A + C + D
|
||||
|
||||
def _log_likelihood_gradients(self):
|
||||
pass
|
||||
return np.hstack((self.dL_dZ().flatten(), self.dL_dtheta(), self.likelihood._gradients(partial=self.partial_for_likelihood)))
|
||||
|
||||
def dL_dtheta(self):
|
||||
if self.has_uncertain_inputs:
|
||||
raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
|
||||
else:
|
||||
dL_dtheta = self.kern.dKdiag_dtheta(self._dL_dpsi0,self.X)
|
||||
dL_dtheta += self.kern.dK_dtheta(self._dL_dpsi1,self.X,self.Z)
|
||||
dL_dtheta += self.kern.dK_dtheta(self._dL_dKmm,X=self.Z)
|
||||
dL_dtheta += self._dKmm_dtheta
|
||||
dL_dtheta += self._dpsi1_dtheta
|
||||
return dL_dtheta
|
||||
|
||||
def dL_dZ(self):
|
||||
if self.has_uncertain_inputs:
|
||||
raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
|
||||
else:
|
||||
dL_dZ = self.kern.dK_dX(self._dL_dpsi1.T,self.Z,self.X)
|
||||
dL_dZ += 2. * self.kern.dK_dX(self._dL_dKmm,X=self.Z)
|
||||
dL_dZ += self._dpsi1_dX
|
||||
dL_dZ += self._dKmm_dX
|
||||
return dL_dZ
|
||||
|
||||
def _raw_predict(self, Xnew, which_parts, full_cov=False):
|
||||
|
||||
if self.likelihood.is_heteroscedastic:
|
||||
Iplus_Dprod_i = 1./(1.+ self.Diag0 * self.likelihood.precision.flatten())
|
||||
self.Diag = self.Diag0 * Iplus_Dprod_i
|
||||
self.P = Iplus_Dprod_i[:,None] * self.psi1.T
|
||||
self.RPT0 = np.dot(self.Lmi,self.psi1)
|
||||
self.L = np.linalg.cholesky(np.eye(self.M) + np.dot(self.RPT0,((1. - Iplus_Dprod_i)/self.Diag0)[:,None]*self.RPT0.T))
|
||||
self.R,info = linalg.flapack.dtrtrs(self.L,self.Lmi,lower=1)
|
||||
self.RPT = np.dot(self.R,self.P.T)
|
||||
self.Sigma = np.diag(self.Diag) + np.dot(self.RPT.T,self.RPT)
|
||||
self.w = self.Diag * self.likelihood.v_tilde
|
||||
self.Gamma = np.dot(self.R.T, np.dot(self.RPT,self.likelihood.v_tilde))
|
||||
self.mu = self.w + np.dot(self.P,self.Gamma)
|
||||
|
||||
"""
|
||||
Make a prediction for the generalized FITC model
|
||||
|
||||
Arguments
|
||||
---------
|
||||
X : Input prediction data - Nx1 numpy array (floats)
|
||||
"""
|
||||
# q(u|f) = N(u| R0i*mu_u*f, R0i*C*R0i.T)
|
||||
|
||||
# Ci = I + (RPT0)Di(RPT0).T
|
||||
# C = I - [RPT0] * (D+[RPT0].T*[RPT0])^-1*[RPT0].T
|
||||
# = I - [RPT0] * (D + self.Qnn)^-1 * [RPT0].T
|
||||
# = I - [RPT0] * (U*U.T)^-1 * [RPT0].T
|
||||
# = I - V.T * V
|
||||
U = np.linalg.cholesky(np.diag(self.Diag0) + self.Qnn)
|
||||
V,info = linalg.flapack.dtrtrs(U,self.RPT0.T,lower=1)
|
||||
C = np.eye(self.M) - np.dot(V.T,V)
|
||||
mu_u = np.dot(C,self.RPT0)*(1./self.Diag0[None,:])
|
||||
#self.C = C
|
||||
#self.RPT0 = np.dot(self.R0,self.Knm.T) P0.T
|
||||
#self.mu_u = mu_u
|
||||
#self.U = U
|
||||
# q(u|y) = N(u| R0i*mu_H,R0i*Sigma_H*R0i.T)
|
||||
mu_H = np.dot(mu_u,self.mu)
|
||||
self.mu_H = mu_H
|
||||
Sigma_H = C + np.dot(mu_u,np.dot(self.Sigma,mu_u.T))
|
||||
# q(f_star|y) = N(f_star|mu_star,sigma2_star)
|
||||
Kx = self.kern.K(self.Z, Xnew, which_parts=which_parts)
|
||||
KR0T = np.dot(Kx.T,self.Lmi.T)
|
||||
mu_star = np.dot(KR0T,mu_H)
|
||||
if full_cov:
|
||||
Kxx = self.kern.K(Xnew,which_parts=which_parts)
|
||||
var = Kxx + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.M),KR0T.T))
|
||||
else:
|
||||
Kxx = self.kern.Kdiag(Xnew,which_parts=which_parts)
|
||||
var = (Kxx + np.sum(KR0T.T*np.dot(Sigma_H - np.eye(self.M),KR0T.T),0))[:,None]
|
||||
return mu_star[:,None],var
|
||||
else:
|
||||
raise NotImplementedError, "homoscedastic fitc not implemented"
|
||||
"""
|
||||
Kx = self.kern.K(self.Z, Xnew)
|
||||
mu = mdot(Kx.T, self.C/self.scale_factor, self.psi1V)
|
||||
if full_cov:
|
||||
Kxx = self.kern.K(Xnew)
|
||||
var = Kxx - mdot(Kx.T, (self.Kmmi - self.C/self.scale_factor**2), Kx) #NOTE this won't work for plotting
|
||||
else:
|
||||
Kxx = self.kern.Kdiag(Xnew)
|
||||
var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.C/self.scale_factor**2, Kx),0)
|
||||
return mu,var[:,None]
|
||||
"""
|
||||
|
|
@ -1,67 +0,0 @@
|
|||
### Copyright (c) 2012, GPy authors (see AUTHORS.txt).
|
||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
||||
|
||||
|
||||
import numpy as np
|
||||
import pylab as pb
|
||||
import sys, pdb
|
||||
from .. import kern
|
||||
from ..core import model
|
||||
from ..util.linalg import pdinv, PCA
|
||||
from ..core import GP
|
||||
from ..likelihoods import Gaussian
|
||||
from .. import util
|
||||
from GPy.util import plot_latent
|
||||
|
||||
|
||||
class GPLVM(GP):
|
||||
"""
|
||||
Gaussian Process Latent Variable Model
|
||||
|
||||
:param Y: observed data
|
||||
:type Y: np.ndarray
|
||||
:param input_dim: latent dimensionality
|
||||
:type input_dim: int
|
||||
:param init: initialisation method for the latent space
|
||||
:type init: 'PCA'|'random'
|
||||
|
||||
"""
|
||||
def __init__(self, Y, input_dim, init='PCA', X = None, kernel=None, normalize_Y=False):
|
||||
if X is None:
|
||||
X = self.initialise_latent(init, input_dim, Y)
|
||||
if kernel is None:
|
||||
kernel = kern.rbf(input_dim, ARD=input_dim>1) + kern.bias(input_dim, np.exp(-2)) + kern.white(input_dim, np.exp(-2))
|
||||
likelihood = Gaussian(Y, normalize=normalize_Y)
|
||||
GP.__init__(self, X, likelihood, kernel, normalize_X=False)
|
||||
self._set_params(self._get_params())
|
||||
|
||||
def initialise_latent(self, init, input_dim, Y):
|
||||
if init == 'PCA':
|
||||
return PCA(Y, input_dim)[0]
|
||||
else:
|
||||
return np.random.randn(Y.shape[0], input_dim)
|
||||
|
||||
def _get_param_names(self):
|
||||
return sum([['X_%i_%i'%(n,q) for q in range(self.input_dim)] for n in range(self.N)],[]) + GP._get_param_names(self)
|
||||
|
||||
def _get_params(self):
|
||||
return np.hstack((self.X.flatten(), GP._get_params(self)))
|
||||
|
||||
def _set_params(self,x):
|
||||
self.X = x[:self.N*self.input_dim].reshape(self.N,self.input_dim).copy()
|
||||
GP._set_params(self, x[self.X.size:])
|
||||
|
||||
def _log_likelihood_gradients(self):
|
||||
dL_dX = 2.*self.kern.dK_dX(self.dL_dK,self.X)
|
||||
|
||||
return np.hstack((dL_dX.flatten(),GP._log_likelihood_gradients(self)))
|
||||
|
||||
def plot(self):
|
||||
assert self.likelihood.Y.shape[1]==2
|
||||
pb.scatter(self.likelihood.Y[:,0],self.likelihood.Y[:,1],40,self.X[:,0].copy(),linewidth=0,cmap=pb.cm.jet)
|
||||
Xnew = np.linspace(self.X.min(),self.X.max(),200)[:,None]
|
||||
mu, var, upper, lower = self.predict(Xnew)
|
||||
pb.plot(mu[:,0], mu[:,1],'k',linewidth=1.5)
|
||||
|
||||
def plot_latent(self, *args, **kwargs):
|
||||
return util.plot_latent.plot_latent(self, *args, **kwargs)
|
||||
|
|
@ -1,41 +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 GP_classification(GP):
|
||||
"""
|
||||
Gaussian Process classification
|
||||
|
||||
This is a thin wrapper around the models.GP class, with a set of sensible defalts
|
||||
|
||||
:param X: input observations
|
||||
:param Y: observed values
|
||||
:param likelihood: a GPy likelihood, defaults to binomial with probit link_function
|
||||
:param kernel: a GPy kernel, defaults to rbf
|
||||
: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
|
||||
|
||||
.. Note:: Multiple independent outputs are allowed using columns of Y
|
||||
|
||||
"""
|
||||
|
||||
def __init__(self,X,Y=None,likelihood=None,kernel=None,normalize_X=False,normalize_Y=False):
|
||||
if kernel is None:
|
||||
kernel = kern.rbf(X.shape[1])
|
||||
|
||||
if likelihood is None:
|
||||
distribution = likelihoods.likelihood_functions.binomial()
|
||||
likelihood = likelihoods.EP(Y, distribution)
|
||||
elif Y is not None:
|
||||
if not all(Y.flatten() == likelihood.data.flatten()):
|
||||
raise Warning, 'likelihood.data and Y are different.'
|
||||
|
||||
GP.__init__(self, X, likelihood, kernel, normalize_X=normalize_X)
|
||||
self._set_params(self._get_params())
|
||||
|
|
@ -1,35 +0,0 @@
|
|||
# Copyright (c) 2012, James Hensman
|
||||
# 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 GP_regression(GP):
|
||||
"""
|
||||
Gaussian Process model for regression
|
||||
|
||||
This is a thin wrapper around the models.GP class, with a set of sensible defalts
|
||||
|
||||
:param X: input observations
|
||||
:param Y: observed values
|
||||
:param kernel: a GPy kernel, defaults to rbf
|
||||
: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
|
||||
|
||||
.. Note:: Multiple independent outputs are allowed using columns of Y
|
||||
|
||||
"""
|
||||
|
||||
def __init__(self,X,Y,kernel=None,normalize_X=False,normalize_Y=False):
|
||||
if kernel is None:
|
||||
kernel = kern.rbf(X.shape[1])
|
||||
|
||||
likelihood = likelihoods.Gaussian(Y,normalize=normalize_Y)
|
||||
|
||||
GP.__init__(self, X, likelihood, kernel, normalize_X=normalize_X)
|
||||
self._set_params(self._get_params())
|
||||
|
|
@ -2,14 +2,12 @@
|
|||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
||||
|
||||
|
||||
from GP_regression import GP_regression
|
||||
from GP_classification import GP_classification
|
||||
from sparse_GP_regression import sparse_GP_regression
|
||||
from sparse_GP_classification import sparse_GP_classification
|
||||
from GPLVM import GPLVM
|
||||
from warped_GP import warpedGP
|
||||
from sparse_GPLVM import sparse_GPLVM
|
||||
from Bayesian_GPLVM import Bayesian_GPLVM
|
||||
from gp_regression import GPRegression
|
||||
from sparse_gp_regression import SparseGPRegression
|
||||
from gplvm import GPLVM
|
||||
from warped_gp import WarpedGP
|
||||
from bayesian_gplvm import BayesianGPLVM
|
||||
from mrd import MRD
|
||||
from generalized_FITC import generalized_FITC
|
||||
from FITC import FITC
|
||||
from generalized_fitc import GeneralizedFITC
|
||||
from fitc import FITC
|
||||
|
||||
|
|
|
|||
|
|
@ -1,221 +0,0 @@
|
|||
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
|
||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
||||
|
||||
import numpy as np
|
||||
import pylab as pb
|
||||
from ..util.linalg import mdot, jitchol, chol_inv, pdinv, trace_dot
|
||||
from ..util.plot import gpplot
|
||||
from .. import kern
|
||||
from scipy import stats, linalg
|
||||
from ..core import sparse_GP
|
||||
|
||||
def backsub_both_sides(L,X):
|
||||
""" Return L^-T * X * L^-1, assumuing X is symmetrical and L is lower cholesky"""
|
||||
tmp,_ = linalg.lapack.flapack.dtrtrs(L,np.asfortranarray(X),lower=1,trans=1)
|
||||
return linalg.lapack.flapack.dtrtrs(L,np.asfortranarray(tmp.T),lower=1,trans=1)[0].T
|
||||
|
||||
|
||||
class generalized_FITC(sparse_GP):
|
||||
"""
|
||||
Naish-Guzman, A. and Holden, S. (2008) implemantation of EP with FITC.
|
||||
|
||||
:param X: inputs
|
||||
:type X: np.ndarray (N x input_dim)
|
||||
:param likelihood: a likelihood instance, containing the observed data
|
||||
:type likelihood: GPy.likelihood.(Gaussian | EP)
|
||||
:param kernel : the kernel/covariance function. See link kernels
|
||||
:type kernel: a GPy kernel
|
||||
:param X_variance: The variance in the measurements of X (Gaussian variance)
|
||||
:type X_variance: np.ndarray (N x input_dim) | None
|
||||
:param Z: inducing inputs (optional, see note)
|
||||
:type Z: np.ndarray (M x input_dim) | None
|
||||
:param M : Number of inducing points (optional, default 10. Ignored if Z is not None)
|
||||
:type M: int
|
||||
: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, likelihood, kernel, Z, X_variance=None, normalize_X=False):
|
||||
self.Z = Z
|
||||
self.M = self.Z.shape[0]
|
||||
self.true_precision = likelihood.precision
|
||||
|
||||
super(generalized_FITC, self).__init__(X, likelihood, kernel=kernel, Z=self.Z, X_variance=X_variance, normalize_X=normalize_X)
|
||||
self._set_params(self._get_params())
|
||||
|
||||
def _set_params(self, p):
|
||||
self.Z = p[:self.M*self.input_dim].reshape(self.M, self.input_dim)
|
||||
self.kern._set_params(p[self.Z.size:self.Z.size+self.kern.Nparam])
|
||||
self.likelihood._set_params(p[self.Z.size+self.kern.Nparam:])
|
||||
self._compute_kernel_matrices()
|
||||
self._computations()
|
||||
self._FITC_computations()
|
||||
|
||||
def update_likelihood_approximation(self):
|
||||
"""
|
||||
Approximates a non-gaussian likelihood using Expectation Propagation
|
||||
|
||||
For a Gaussian (or direct: TODO) likelihood, no iteration is required:
|
||||
this function does nothing
|
||||
|
||||
Diag(Knn - Qnn) is added to the noise term to use the tools already implemented in sparse_GP.
|
||||
The true precison is now 'true_precision' not 'precision'.
|
||||
"""
|
||||
if self.has_uncertain_inputs:
|
||||
raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
|
||||
else:
|
||||
self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
|
||||
self.true_precision = self.likelihood.precision # Save the true precision
|
||||
self.likelihood.precision = self.true_precision/(1. + self.true_precision*self.Diag0[:,None]) # Add the diagonal element of the FITC approximation
|
||||
self._set_params(self._get_params()) # update the GP
|
||||
|
||||
def _FITC_computations(self):
|
||||
"""
|
||||
FITC approximation doesn't have the correction term in the log-likelihood bound,
|
||||
but adds a diagonal term to the covariance matrix: diag(Knn - Qnn).
|
||||
This function:
|
||||
- computes the FITC diagonal term
|
||||
- removes the extra terms computed in the sparse_GP approximation
|
||||
- computes the likelihood gradients wrt the true precision.
|
||||
"""
|
||||
#NOTE the true precison is now 'true_precision' not 'precision'
|
||||
if self.likelihood.is_heteroscedastic:
|
||||
|
||||
# Compute generalized FITC's diagonal term of the covariance
|
||||
self.Lmi,info = linalg.lapack.flapack.dtrtrs(self.Lm,np.eye(self.M),lower=1)
|
||||
Lmipsi1 = np.dot(self.Lmi,self.psi1)
|
||||
self.Qnn = np.dot(Lmipsi1.T,Lmipsi1)
|
||||
#self.Kmmi, Lm, Lmi, Kmm_logdet = pdinv(self.Kmm)
|
||||
#self.Qnn = mdot(self.psi1.T,self.Kmmi,self.psi1)
|
||||
#a = kj
|
||||
self.Diag0 = self.psi0 - np.diag(self.Qnn)
|
||||
Iplus_Dprod_i = 1./(1.+ self.Diag0 * self.true_precision.flatten())
|
||||
self.Diag = self.Diag0 * Iplus_Dprod_i
|
||||
|
||||
self.P = Iplus_Dprod_i[:,None] * self.psi1.T
|
||||
self.RPT0 = np.dot(self.Lmi,self.psi1)
|
||||
self.L = np.linalg.cholesky(np.eye(self.M) + np.dot(self.RPT0,((1. - Iplus_Dprod_i)/self.Diag0)[:,None]*self.RPT0.T))
|
||||
self.R,info = linalg.flapack.dtrtrs(self.L,self.Lmi,lower=1)
|
||||
self.RPT = np.dot(self.R,self.P.T)
|
||||
self.Sigma = np.diag(self.Diag) + np.dot(self.RPT.T,self.RPT)
|
||||
self.w = self.Diag * self.likelihood.v_tilde
|
||||
self.Gamma = np.dot(self.R.T, np.dot(self.RPT,self.likelihood.v_tilde))
|
||||
self.mu = self.w + np.dot(self.P,self.Gamma)
|
||||
|
||||
# Remove extra term from dL_dpsi1
|
||||
self.dL_dpsi1 -= mdot(self.Lmi.T,Lmipsi1*self.likelihood.precision.flatten().reshape(1,self.N))
|
||||
#self.Kmmi, Lm, Lmi, Kmm_logdet = pdinv(self.Kmm)
|
||||
#self.dL_dpsi1 -= mdot(self.Kmmi,self.psi1*self.likelihood.precision.flatten().reshape(1,self.N)) #dB
|
||||
|
||||
#########333333
|
||||
#self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
|
||||
#########333333
|
||||
|
||||
|
||||
|
||||
else:
|
||||
raise NotImplementedError, "homoscedastic fitc not implemented"
|
||||
# Remove extra term from dL_dpsi1
|
||||
#self.dL_dpsi1 += -mdot(self.Kmmi,self.psi1*self.likelihood.precision) #dB
|
||||
|
||||
sf = self.scale_factor
|
||||
sf2 = sf**2
|
||||
|
||||
# Remove extra term from dL_dKmm
|
||||
self.dL_dKmm += 0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi)*sf2 # dB
|
||||
self.dL_dpsi0 = None
|
||||
|
||||
#the partial derivative vector for the likelihood
|
||||
if self.likelihood.Nparams == 0:
|
||||
self.partial_for_likelihood = None
|
||||
elif self.likelihood.is_heteroscedastic:
|
||||
raise NotImplementedError, "heteroscedastic derivates not implemented"
|
||||
else:
|
||||
raise NotImplementedError, "homoscedastic derivatives not implemented"
|
||||
#likelihood is not heterscedatic
|
||||
#self.partial_for_likelihood = - 0.5 * self.N*self.D*self.likelihood.precision + 0.5 * np.sum(np.square(self.likelihood.Y))*self.likelihood.precision**2
|
||||
#self.partial_for_likelihood += 0.5 * self.D * trace_dot(self.Bi,self.A)*self.likelihood.precision
|
||||
#self.partial_for_likelihood += self.likelihood.precision*(0.5*trace_dot(self.psi2_beta_scaled,self.E*sf2) - np.trace(self.Cpsi1VVpsi1))
|
||||
#TODO partial derivative vector for the likelihood not implemented
|
||||
|
||||
def dL_dtheta(self):
|
||||
"""
|
||||
Compute and return the derivative of the log marginal likelihood wrt the parameters of the kernel
|
||||
"""
|
||||
dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm,self.Z)
|
||||
if self.has_uncertain_inputs:
|
||||
raise NotImplementedError, "heteroscedatic derivates not implemented"
|
||||
else:
|
||||
#NOTE in sparse_GP this would include the gradient wrt psi0
|
||||
dL_dtheta += self.kern.dK_dtheta(self.dL_dpsi1,self.Z,self.X)
|
||||
return dL_dtheta
|
||||
|
||||
|
||||
def log_likelihood(self):
|
||||
""" Compute the (lower bound on the) log marginal likelihood """
|
||||
sf2 = self.scale_factor**2
|
||||
if self.likelihood.is_heteroscedastic:
|
||||
A = -0.5*self.N*self.D*np.log(2.*np.pi) +0.5*np.sum(np.log(self.likelihood.precision)) -0.5*np.sum(self.V*self.likelihood.Y)
|
||||
else:
|
||||
A = -0.5*self.N*self.D*(np.log(2.*np.pi) + np.log(self.likelihood._variance)) -0.5*self.likelihood.precision*self.likelihood.trYYT
|
||||
C = -self.D * (np.sum(np.log(np.diag(self.LB))) + 0.5*self.M*np.log(sf2))
|
||||
#C = -0.5*self.D * (self.B_logdet + self.M*np.log(sf2))
|
||||
D = 0.5*np.sum(np.square(self._LBi_Lmi_psi1V))
|
||||
#self.Cpsi1VVpsi1 = np.dot(self.Cpsi1V,self.psi1V.T)
|
||||
#D_ = 0.5*np.trace(self.Cpsi1VVpsi1)
|
||||
return A+C+D
|
||||
|
||||
def _raw_predict(self, Xnew, which_parts, full_cov=False):
|
||||
if self.likelihood.is_heteroscedastic:
|
||||
"""
|
||||
Make a prediction for the generalized FITC model
|
||||
|
||||
Arguments
|
||||
---------
|
||||
X : Input prediction data - Nx1 numpy array (floats)
|
||||
"""
|
||||
# q(u|f) = N(u| R0i*mu_u*f, R0i*C*R0i.T)
|
||||
|
||||
# Ci = I + (RPT0)Di(RPT0).T
|
||||
# C = I - [RPT0] * (D+[RPT0].T*[RPT0])^-1*[RPT0].T
|
||||
# = I - [RPT0] * (D + self.Qnn)^-1 * [RPT0].T
|
||||
# = I - [RPT0] * (U*U.T)^-1 * [RPT0].T
|
||||
# = I - V.T * V
|
||||
U = np.linalg.cholesky(np.diag(self.Diag0) + self.Qnn)
|
||||
V,info = linalg.flapack.dtrtrs(U,self.RPT0.T,lower=1)
|
||||
C = np.eye(self.M) - np.dot(V.T,V)
|
||||
mu_u = np.dot(C,self.RPT0)*(1./self.Diag0[None,:])
|
||||
#self.C = C
|
||||
#self.RPT0 = np.dot(self.R0,self.Knm.T) P0.T
|
||||
#self.mu_u = mu_u
|
||||
#self.U = U
|
||||
# q(u|y) = N(u| R0i*mu_H,R0i*Sigma_H*R0i.T)
|
||||
mu_H = np.dot(mu_u,self.mu)
|
||||
self.mu_H = mu_H
|
||||
Sigma_H = C + np.dot(mu_u,np.dot(self.Sigma,mu_u.T))
|
||||
# q(f_star|y) = N(f_star|mu_star,sigma2_star)
|
||||
Kx = self.kern.K(self.Z, Xnew, which_parts=which_parts)
|
||||
KR0T = np.dot(Kx.T,self.Lmi.T)
|
||||
mu_star = np.dot(KR0T,mu_H)
|
||||
if full_cov:
|
||||
Kxx = self.kern.K(Xnew,which_parts=which_parts)
|
||||
var = Kxx + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.M),KR0T.T))
|
||||
else:
|
||||
Kxx = self.kern.Kdiag(Xnew,which_parts=which_parts)
|
||||
Kxx_ = self.kern.K(Xnew,which_parts=which_parts) # TODO: RA, is this line needed?
|
||||
var_ = Kxx_ + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.M),KR0T.T)) # TODO: RA, is this line needed?
|
||||
var = (Kxx + np.sum(KR0T.T*np.dot(Sigma_H - np.eye(self.M),KR0T.T),0))[:,None]
|
||||
return mu_star[:,None],var
|
||||
else:
|
||||
raise NotImplementedError, "homoscedastic fitc not implemented"
|
||||
"""
|
||||
Kx = self.kern.K(self.Z, Xnew)
|
||||
mu = mdot(Kx.T, self.C/self.scale_factor, self.psi1V)
|
||||
if full_cov:
|
||||
Kxx = self.kern.K(Xnew)
|
||||
var = Kxx - mdot(Kx.T, (self.Kmmi - self.C/self.scale_factor**2), Kx) #NOTE this won't work for plotting
|
||||
else:
|
||||
Kxx = self.kern.Kdiag(Xnew)
|
||||
var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.C/self.scale_factor**2, Kx),0)
|
||||
return mu,var[:,None]
|
||||
"""
|
||||
|
|
@ -4,14 +4,13 @@ Created on 10 Apr 2013
|
|||
@author: Max Zwiessele
|
||||
'''
|
||||
from GPy.core import model
|
||||
from GPy.models.Bayesian_GPLVM import Bayesian_GPLVM
|
||||
from GPy.core import sparse_GP
|
||||
from GPy.core import SparseGP
|
||||
from GPy.util.linalg import PCA
|
||||
from scipy import linalg
|
||||
import numpy
|
||||
import itertools
|
||||
import pylab
|
||||
from GPy.kern.kern import kern
|
||||
from GPy.models.bayesian_gplvm import BayesianGPLVM
|
||||
|
||||
class MRD(model):
|
||||
"""
|
||||
|
|
@ -38,7 +37,7 @@ class MRD(model):
|
|||
*concat: PCA on concatenated outputs
|
||||
*single: PCA on each output
|
||||
*random: random
|
||||
:param M:
|
||||
:param num_inducing:
|
||||
number of inducing inputs to use
|
||||
:param Z:
|
||||
initial inducing inputs
|
||||
|
|
@ -62,22 +61,22 @@ class MRD(model):
|
|||
assert not ('kernel' in kw), "pass kernels through `kernels` argument"
|
||||
|
||||
self.input_dim = input_dim
|
||||
self.M = M
|
||||
self.num_inducing = M
|
||||
self._debug = _debug
|
||||
|
||||
self._init = True
|
||||
X = self._init_X(initx, likelihood_or_Y_list)
|
||||
Z = self._init_Z(initz, X)
|
||||
self.bgplvms = [Bayesian_GPLVM(l, input_dim=input_dim, kernel=k, X=X, Z=Z, M=self.M, **kw) for l, k in zip(likelihood_or_Y_list, kernels)]
|
||||
self.bgplvms = [BayesianGPLVM(l, input_dim=input_dim, kernel=k, X=X, Z=Z, M=self.num_inducing, **kw) for l, k in zip(likelihood_or_Y_list, kernels)]
|
||||
del self._init
|
||||
|
||||
self.gref = self.bgplvms[0]
|
||||
nparams = numpy.array([0] + [sparse_GP._get_params(g).size - g.Z.size for g in self.bgplvms])
|
||||
nparams = numpy.array([0] + [SparseGP._get_params(g).size - g.Z.size for g in self.bgplvms])
|
||||
self.nparams = nparams.cumsum()
|
||||
|
||||
self.N = self.gref.N
|
||||
self.NQ = self.N * self.input_dim
|
||||
self.MQ = self.M * self.input_dim
|
||||
self.MQ = self.num_inducing * self.input_dim
|
||||
|
||||
model.__init__(self) # @UndefinedVariable
|
||||
self._set_params(self._get_params())
|
||||
|
|
@ -151,7 +150,7 @@ class MRD(model):
|
|||
itertools.izip(ns,
|
||||
itertools.repeat(name)))
|
||||
return list(itertools.chain(n1var, *(map_names(\
|
||||
sparse_GP._get_param_names(g)[self.MQ:], n) \
|
||||
SparseGP._get_param_names(g)[self.MQ:], n) \
|
||||
for g, n in zip(self.bgplvms, self.names))))
|
||||
|
||||
def _get_params(self):
|
||||
|
|
@ -165,14 +164,14 @@ class MRD(model):
|
|||
X = self.gref.X.ravel()
|
||||
X_var = self.gref.X_variance.ravel()
|
||||
Z = self.gref.Z.ravel()
|
||||
thetas = [sparse_GP._get_params(g)[g.Z.size:] for g in self.bgplvms]
|
||||
thetas = [SparseGP._get_params(g)[g.Z.size:] for g in self.bgplvms]
|
||||
params = numpy.hstack([X, X_var, Z, numpy.hstack(thetas)])
|
||||
return params
|
||||
|
||||
# def _set_var_params(self, g, X, X_var, Z):
|
||||
# g.X = X.reshape(self.N, self.input_dim)
|
||||
# g.X_variance = X_var.reshape(self.N, self.input_dim)
|
||||
# g.Z = Z.reshape(self.M, self.input_dim)
|
||||
# g.Z = Z.reshape(self.num_inducing, self.input_dim)
|
||||
#
|
||||
# def _set_kern_params(self, g, p):
|
||||
# g.kern._set_params(p[:g.kern.Nparam])
|
||||
|
|
@ -206,7 +205,7 @@ class MRD(model):
|
|||
def log_likelihood(self):
|
||||
ll = -self.gref.KL_divergence()
|
||||
for g in self.bgplvms:
|
||||
ll += sparse_GP.log_likelihood(g)
|
||||
ll += SparseGP.log_likelihood(g)
|
||||
return ll
|
||||
|
||||
def _log_likelihood_gradients(self):
|
||||
|
|
@ -215,7 +214,7 @@ class MRD(model):
|
|||
dLdmu -= dKLmu
|
||||
dLdS -= dKLdS
|
||||
dLdmuS = numpy.hstack((dLdmu.flatten(), dLdS.flatten())).flatten()
|
||||
dldzt1 = reduce(lambda a, b: a + b, (sparse_GP._log_likelihood_gradients(g)[:self.MQ] for g in self.bgplvms))
|
||||
dldzt1 = reduce(lambda a, b: a + b, (SparseGP._log_likelihood_gradients(g)[:self.MQ] for g in self.bgplvms))
|
||||
|
||||
return numpy.hstack((dLdmuS,
|
||||
dldzt1,
|
||||
|
|
@ -250,9 +249,9 @@ class MRD(model):
|
|||
if X is None:
|
||||
X = self.X
|
||||
if init in "permute":
|
||||
Z = numpy.random.permutation(X.copy())[:self.M]
|
||||
Z = numpy.random.permutation(X.copy())[:self.num_inducing]
|
||||
elif init in "random":
|
||||
Z = numpy.random.randn(self.M, self.input_dim) * X.var()
|
||||
Z = numpy.random.randn(self.num_inducing, self.input_dim) * X.var()
|
||||
self.Z = Z
|
||||
return Z
|
||||
|
||||
|
|
|
|||
|
|
@ -1,61 +0,0 @@
|
|||
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
|
||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
||||
|
||||
|
||||
import numpy as np
|
||||
import pylab as pb
|
||||
import sys, pdb
|
||||
# from .. import kern
|
||||
# from ..core import model
|
||||
# from ..util.linalg import pdinv, PCA
|
||||
from GPLVM import GPLVM
|
||||
from sparse_GP_regression import sparse_GP_regression
|
||||
|
||||
class sparse_GPLVM(sparse_GP_regression, GPLVM):
|
||||
"""
|
||||
Sparse Gaussian Process Latent Variable Model
|
||||
|
||||
:param Y: observed data
|
||||
:type Y: np.ndarray
|
||||
:param input_dim: latent dimensionality
|
||||
:type input_dim: int
|
||||
:param init: initialisation method for the latent space
|
||||
:type init: 'PCA'|'random'
|
||||
|
||||
"""
|
||||
def __init__(self, Y, input_dim, kernel=None, init='PCA', M=10):
|
||||
X = self.initialise_latent(init, input_dim, Y)
|
||||
sparse_GP_regression.__init__(self, X, Y, kernel=kernel,M=M)
|
||||
|
||||
def _get_param_names(self):
|
||||
return (sum([['X_%i_%i'%(n,q) for q in range(self.input_dim)] for n in range(self.N)],[])
|
||||
+ sparse_GP_regression._get_param_names(self))
|
||||
|
||||
def _get_params(self):
|
||||
return np.hstack((self.X.flatten(), sparse_GP_regression._get_params(self)))
|
||||
|
||||
def _set_params(self,x):
|
||||
self.X = x[:self.X.size].reshape(self.N,self.input_dim).copy()
|
||||
sparse_GP_regression._set_params(self, x[self.X.size:])
|
||||
|
||||
def log_likelihood(self):
|
||||
return sparse_GP_regression.log_likelihood(self)
|
||||
|
||||
def dL_dX(self):
|
||||
dL_dX = self.kern.dKdiag_dX(self.dL_dpsi0,self.X)
|
||||
dL_dX += self.kern.dK_dX(self.dL_dpsi1.T,self.X,self.Z)
|
||||
|
||||
return dL_dX
|
||||
|
||||
def _log_likelihood_gradients(self):
|
||||
return np.hstack((self.dL_dX().flatten(), sparse_GP_regression._log_likelihood_gradients(self)))
|
||||
|
||||
def plot(self):
|
||||
GPLVM.plot(self)
|
||||
#passing Z without a small amout of jitter will induce the white kernel where we don;t want it!
|
||||
mu, var, upper, lower = sparse_GP_regression.predict(self, self.Z+np.random.randn(*self.Z.shape)*0.0001)
|
||||
pb.plot(mu[:, 0] , mu[:, 1], 'ko')
|
||||
|
||||
def plot_latent(self, *args, **kwargs):
|
||||
input_1, input_2 = GPLVM.plot_latent(*args, **kwargs)
|
||||
pb.plot(m.Z[:, input_1], m.Z[:, input_2], '^w')
|
||||
|
|
@ -1,50 +0,0 @@
|
|||
# Copyright (c) 2013, Ricardo Andrade
|
||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
||||
|
||||
|
||||
import numpy as np
|
||||
from ..core import sparse_GP
|
||||
from .. import likelihoods
|
||||
from .. import kern
|
||||
from ..likelihoods import likelihood
|
||||
from GP_regression import GP_regression
|
||||
|
||||
class sparse_GP_classification(sparse_GP):
|
||||
"""
|
||||
sparse Gaussian Process model for classification
|
||||
|
||||
This is a thin wrapper around the sparse_GP class, with a set of sensible defalts
|
||||
|
||||
:param X: input observations
|
||||
:param Y: observed values
|
||||
:param likelihood: a GPy likelihood, defaults to binomial with probit link_function
|
||||
: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=None, likelihood=None, kernel=None, normalize_X=False, normalize_Y=False, Z=None, M=10):
|
||||
if kernel is None:
|
||||
kernel = kern.rbf(X.shape[1]) + kern.white(X.shape[1],1e-3)
|
||||
|
||||
if likelihood is None:
|
||||
distribution = likelihoods.likelihood_functions.binomial()
|
||||
likelihood = likelihoods.EP(Y, distribution)
|
||||
elif Y is not None:
|
||||
if not all(Y.flatten() == likelihood.data.flatten()):
|
||||
raise Warning, 'likelihood.data and Y are different.'
|
||||
|
||||
if Z is None:
|
||||
i = np.random.permutation(X.shape[0])[:M]
|
||||
Z = X[i].copy()
|
||||
else:
|
||||
assert Z.shape[1]==X.shape[1]
|
||||
|
||||
sparse_GP.__init__(self, X, likelihood, kernel, Z=Z, normalize_X=normalize_X)
|
||||
self._set_params(self._get_params())
|
||||
|
|
@ -1,47 +0,0 @@
|
|||
# Copyright (c) 2012, James Hensman
|
||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
||||
|
||||
|
||||
import numpy as np
|
||||
from ..core import sparse_GP
|
||||
from .. import likelihoods
|
||||
from .. import kern
|
||||
from ..likelihoods import likelihood
|
||||
from GP_regression import GP_regression
|
||||
|
||||
class sparse_GP_regression(sparse_GP):
|
||||
"""
|
||||
Gaussian Process model for regression
|
||||
|
||||
This is a thin wrapper around the sparse_GP 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, normalize_X=False, normalize_Y=False, Z=None, M=10, X_variance=None):
|
||||
#kern defaults to rbf (plus white for stability)
|
||||
if kernel is None:
|
||||
kernel = kern.rbf(X.shape[1]) + 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])[:M]
|
||||
Z = X[i].copy()
|
||||
else:
|
||||
assert Z.shape[1]==X.shape[1]
|
||||
|
||||
#likelihood defaults to Gaussian
|
||||
likelihood = likelihoods.Gaussian(Y,normalize=normalize_Y)
|
||||
|
||||
sparse_GP.__init__(self, X, likelihood, kernel, Z=Z, normalize_X=normalize_X, X_variance=X_variance)
|
||||
self._set_params(self._get_params())
|
||||
|
|
@ -1,93 +0,0 @@
|
|||
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
|
||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
||||
|
||||
|
||||
import numpy as np
|
||||
from .. import kern
|
||||
from ..core import model
|
||||
from ..util.linalg import pdinv
|
||||
from ..util.plot import gpplot
|
||||
from ..util.warping_functions import *
|
||||
from GP_regression import GP_regression
|
||||
from ..core import GP
|
||||
from .. import likelihoods
|
||||
from .. import kern
|
||||
|
||||
class warpedGP(GP):
|
||||
def __init__(self, X, Y, kernel=None, warping_function = None, warping_terms = 3, normalize_X=False, normalize_Y=False):
|
||||
|
||||
if kernel is None:
|
||||
kernel = kern.rbf(X.shape[1])
|
||||
|
||||
if warping_function == None:
|
||||
self.warping_function = TanhWarpingFunction_d(warping_terms)
|
||||
self.warping_params = (np.random.randn(self.warping_function.n_terms*3+1,) * 1)
|
||||
|
||||
Y = self._scale_data(Y)
|
||||
self.has_uncertain_inputs = False
|
||||
self.Y_untransformed = Y.copy()
|
||||
self.predict_in_warped_space = False
|
||||
likelihood = likelihoods.Gaussian(self.transform_data(), normalize=normalize_Y)
|
||||
|
||||
GP.__init__(self, X, likelihood, kernel, normalize_X=normalize_X)
|
||||
self._set_params(self._get_params())
|
||||
|
||||
def _scale_data(self, Y):
|
||||
self._Ymax = Y.max()
|
||||
self._Ymin = Y.min()
|
||||
return (Y-self._Ymin)/(self._Ymax-self._Ymin) - 0.5
|
||||
|
||||
def _unscale_data(self, Y):
|
||||
return (Y + 0.5)*(self._Ymax - self._Ymin) + self._Ymin
|
||||
|
||||
def _set_params(self, x):
|
||||
self.warping_params = x[:self.warping_function.num_parameters]
|
||||
Y = self.transform_data()
|
||||
self.likelihood.set_data(Y)
|
||||
GP._set_params(self, x[self.warping_function.num_parameters:].copy())
|
||||
|
||||
def _get_params(self):
|
||||
return np.hstack((self.warping_params.flatten().copy(), GP._get_params(self).copy()))
|
||||
|
||||
def _get_param_names(self):
|
||||
warping_names = self.warping_function._get_param_names()
|
||||
param_names = GP._get_param_names(self)
|
||||
return warping_names + param_names
|
||||
|
||||
def transform_data(self):
|
||||
Y = self.warping_function.f(self.Y_untransformed.copy(), self.warping_params).copy()
|
||||
return Y
|
||||
|
||||
def log_likelihood(self):
|
||||
ll = GP.log_likelihood(self)
|
||||
jacobian = self.warping_function.fgrad_y(self.Y_untransformed, self.warping_params)
|
||||
return ll + np.log(jacobian).sum()
|
||||
|
||||
def _log_likelihood_gradients(self):
|
||||
ll_grads = GP._log_likelihood_gradients(self)
|
||||
alpha = np.dot(self.Ki, self.likelihood.Y.flatten())
|
||||
warping_grads = self.warping_function_gradients(alpha)
|
||||
|
||||
warping_grads = np.append(warping_grads[:,:-1].flatten(), warping_grads[0,-1])
|
||||
return np.hstack((warping_grads.flatten(), ll_grads.flatten()))
|
||||
|
||||
def warping_function_gradients(self, Kiy):
|
||||
grad_y = self.warping_function.fgrad_y(self.Y_untransformed, self.warping_params)
|
||||
grad_y_psi, grad_psi = self.warping_function.fgrad_y_psi(self.Y_untransformed, self.warping_params,
|
||||
return_covar_chain = True)
|
||||
djac_dpsi = ((1.0/grad_y[:,:, None, None])*grad_y_psi).sum(axis=0).sum(axis=0)
|
||||
dquad_dpsi = (Kiy[:,None,None,None] * grad_psi).sum(axis=0).sum(axis=0)
|
||||
|
||||
return -dquad_dpsi + djac_dpsi
|
||||
|
||||
def plot_warping(self):
|
||||
self.warping_function.plot(self.warping_params, self.Y_untransformed.min(), self.Y_untransformed.max())
|
||||
|
||||
def _raw_predict(self, *args, **kwargs):
|
||||
mu, var = GP._raw_predict(self, *args, **kwargs)
|
||||
|
||||
if self.predict_in_warped_space:
|
||||
mu = self.warping_function.f_inv(mu, self.warping_params)
|
||||
var = self.warping_function.f_inv(var, self.warping_params)
|
||||
mu = self._unscale_data(mu)
|
||||
return mu, var
|
||||
Loading…
Add table
Add a link
Reference in a new issue