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328 lines
12 KiB
Python
328 lines
12 KiB
Python
'''
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Created on 10 Apr 2013
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@author: Max Zwiessele
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'''
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from GPy.core import model
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from GPy.models.Bayesian_GPLVM import Bayesian_GPLVM
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from GPy.models.sparse_GP import sparse_GP
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from GPy.util.linalg import PCA
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from scipy import linalg
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import numpy
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import itertools
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import pylab
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class MRD(model):
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"""
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Do MRD on given Datasets in Ylist.
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All Ys in Ylist are in [N x Dn], where Dn can be different per Yn,
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N must be shared across datasets though.
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:param Ylist...: observed datasets
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:type Ylist: [np.ndarray]
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:param names: names for different gplvm models
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:type names: [str]
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:param Q: latent dimensionality (will raise
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:type Q: int
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:param initx: initialisation method for the latent space
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:type initx: 'PCA'|'random'
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:param initz: initialisation method for inducing inputs
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:type initz: 'permute'|'random'
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:param X:
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Initial latent space
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:param X_variance:
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Initial latent space variance
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:param init: [PCA|random]
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initialization method to use
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:param M:
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number of inducing inputs to use
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:param Z:
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initial inducing inputs
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:param kernel:
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kernel to use
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"""
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def __init__(self, *Ylist, **kwargs):
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if kwargs.has_key("_debug"):
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self._debug = kwargs['_debug']
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del kwargs['_debug']
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else:
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self._debug = False
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if kwargs.has_key("names"):
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self.names = kwargs['names']
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del kwargs['names']
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else:
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self.names = ["{}".format(i + 1) for i in range(len(Ylist))]
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if kwargs.has_key('kernel'):
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kernel = kwargs['kernel']
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k = lambda: kernel.copy()
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del kwargs['kernel']
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else:
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k = lambda: None
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if kwargs.has_key('initx'):
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initx = kwargs['initx']
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del kwargs['initx']
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else:
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initx = "PCA"
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if kwargs.has_key('initz'):
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initz = kwargs['initz']
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del kwargs['initz']
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else:
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initz = "permute"
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try:
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self.Q = kwargs["Q"]
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except KeyError:
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raise ValueError("Need Q for MRD")
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try:
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self.M = kwargs["M"]
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del kwargs["M"]
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except KeyError:
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self.M = 10
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self._init = True
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X = self._init_X(initx, Ylist)
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Z = self._init_Z(initz, X)
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self.bgplvms = [Bayesian_GPLVM(Y, kernel=k(), X=X, Z=Z, M=self.M, **kwargs) for Y in Ylist]
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del self._init
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self.gref = self.bgplvms[0]
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nparams = numpy.array([0] + [sparse_GP._get_params(g).size - g.Z.size for g in self.bgplvms])
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self.nparams = nparams.cumsum()
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self.N = self.gref.N
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self.NQ = self.N * self.Q
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self.MQ = self.M * self.Q
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model.__init__(self) # @UndefinedVariable
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@property
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def X(self):
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return self.gref.X
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@X.setter
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def X(self, X):
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try:
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self.propagate_param(X=X)
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except AttributeError:
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if not self._init:
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raise AttributeError("bgplvm list not initialized")
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@property
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def Z(self):
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return self.gref.Z
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@Z.setter
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def Z(self, Z):
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try:
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self.propagate_param(Z=Z)
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except AttributeError:
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if not self._init:
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raise AttributeError("bgplvm list not initialized")
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@property
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def X_variance(self):
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return self.gref.X_variance
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@X_variance.setter
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def X_variance(self, X_var):
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try:
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self.propagate_param(X_variance=X_var)
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except AttributeError:
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if not self._init:
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raise AttributeError("bgplvm list not initialized")
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@property
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def Ylist(self):
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return [g.likelihood.Y for g in self.bgplvms]
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@Ylist.setter
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def Ylist(self, Ylist):
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for g, Y in itertools.izip(self.bgplvms, Ylist):
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g.likelihood.Y = Y
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@property
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def auto_scale_factor(self):
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"""
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set auto_scale_factor for all gplvms
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:param b: auto_scale_factor
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:type b:
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"""
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return self.gref.auto_scale_factor
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@auto_scale_factor.setter
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def auto_scale_factor(self, b):
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self.propagate_param(auto_scale_factor=b)
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def propagate_param(self, **kwargs):
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for key, val in kwargs.iteritems():
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for g in self.bgplvms:
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g.__setattr__(key, val)
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def randomize(self, initx='concat', initz='permute', *args, **kw):
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super(MRD, self).randomize(*args, **kw)
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self._init_X(initx, self.Ylist)
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self._init_Z(initz, self.X)
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def _get_param_names(self):
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# X_names = sum([['X_%i_%i' % (n, q) for q in range(self.Q)] for n in range(self.N)], [])
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# S_names = sum([['X_variance_%i_%i' % (n, q) for q in range(self.Q)] for n in range(self.N)], [])
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n1 = self.gref._get_param_names()
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n1var = n1[:self.NQ * 2 + self.MQ]
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map_names = lambda ns, name: map(lambda x: "{1}_{0}".format(*x),
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itertools.izip(ns,
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itertools.repeat(name)))
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return list(itertools.chain(n1var, *(map_names(\
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sparse_GP._get_param_names(g)[self.MQ:], n) \
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for g, n in zip(self.bgplvms, self.names))))
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def _get_params(self):
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"""
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return parameter list containing private and shared parameters as follows:
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=================================================================
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| mu | S | Z || theta1 | theta2 | .. | thetaN |
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=================================================================
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"""
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X = self.gref.X.ravel()
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X_var = self.gref.X_variance.ravel()
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Z = self.gref.Z.ravel()
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if self._debug:
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for g in self.bgplvms:
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assert numpy.allclose(g.X.ravel(), X)
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assert numpy.allclose(g.X_variance.ravel(), X_var)
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assert numpy.allclose(g.Z.ravel(), Z)
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thetas = [sparse_GP._get_params(g)[g.Z.size:] for g in self.bgplvms]
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params = numpy.hstack([X, X_var, Z, numpy.hstack(thetas)])
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return params
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# def _set_var_params(self, g, X, X_var, Z):
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# g.X = X.reshape(self.N, self.Q)
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# g.X_variance = X_var.reshape(self.N, self.Q)
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# g.Z = Z.reshape(self.M, self.Q)
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#
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# def _set_kern_params(self, g, p):
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# g.kern._set_params(p[:g.kern.Nparam])
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# g.likelihood._set_params(p[g.kern.Nparam:])
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def _set_params(self, x):
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start = 0; end = self.NQ
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X = x[start:end]
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start = end; end += start
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X_var = x[start:end]
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start = end; end += self.MQ
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Z = x[start:end]
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thetas = x[end:]
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if self._debug:
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for g in self.bgplvms:
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assert numpy.allclose(g.X, self.gref.X)
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assert numpy.allclose(g.X_variance, self.gref.X_variance)
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assert numpy.allclose(g.Z, self.gref.Z)
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# set params for all:
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for g, s, e in itertools.izip(self.bgplvms, self.nparams, self.nparams[1:]):
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g._set_params(numpy.hstack([X, X_var, Z, thetas[s:e]]))
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# self._set_var_params(g, X, X_var, Z)
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# self._set_kern_params(g, thetas[s:e].copy())
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# g._compute_kernel_matrices()
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# if self.auto_scale_factor:
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# g.scale_factor = numpy.sqrt(g.psi2.sum(0).mean() * g.likelihood.precision)
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# # self.scale_factor = numpy.sqrt(self.psi2.sum(0).mean() * self.likelihood.precision)
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# g._computations()
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def log_likelihood(self):
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ll = -self.gref.KL_divergence()
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for g in self.bgplvms:
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ll += sparse_GP.log_likelihood(g)
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return ll
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def _log_likelihood_gradients(self):
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dLdmu, dLdS = reduce(lambda a, b: [a[0] + b[0], a[1] + b[1]], (g.dL_dmuS() for g in self.bgplvms))
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dKLmu, dKLdS = self.gref.dKL_dmuS()
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dLdmu -= dKLmu
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dLdS -= dKLdS
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dLdmuS = numpy.hstack((dLdmu.flatten(), dLdS.flatten())).flatten()
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dldzt1 = reduce(lambda a, b: a + b, (sparse_GP._log_likelihood_gradients(g)[:self.MQ] for g in self.bgplvms))
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return numpy.hstack((dLdmuS,
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dldzt1,
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numpy.hstack([numpy.hstack([g.dL_dtheta(),
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g.likelihood._gradients(\
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partial=g.partial_for_likelihood)]) \
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for g in self.bgplvms])))
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def _init_X(self, init='PCA', Ylist=None):
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if Ylist is None:
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Ylist = self.Ylist
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if init in "PCA_single":
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X = numpy.zeros((Ylist[0].shape[0], self.Q))
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for qs, Y in itertools.izip(numpy.array_split(numpy.arange(self.Q), len(Ylist)), Ylist):
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X[:, qs] = PCA(Y, len(qs))[0]
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elif init in "PCA_concat":
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X = PCA(numpy.hstack(Ylist), self.Q)[0]
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else: # init == 'random':
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X = numpy.random.randn(Ylist[0].shape[0], self.Q)
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self.X = X
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return X
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def _init_Z(self, init="permute", X=None):
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if X is None:
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X = self.X
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if init in "permute":
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Z = numpy.random.permutation(X.copy())[:self.M]
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elif init in "random":
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Z = numpy.random.randn(self.M, self.Q) * X.var()
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self.Z = Z
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return Z
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def _handle_plotting(self, fig_num, axes, plotf):
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if axes is None:
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fig = pylab.figure(num=fig_num, figsize=(4 * len(self.bgplvms), 3 * len(self.bgplvms)))
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for i, g in enumerate(self.bgplvms):
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if axes is None:
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ax = fig.add_subplot(1, len(self.bgplvms), i + 1)
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else:
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ax = axes[i]
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plotf(i, g, ax)
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pylab.draw()
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if axes is None:
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fig.tight_layout()
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return fig
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else:
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return pylab.gcf()
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def plot_X(self, fig_num="MRD Predictions", axes=None):
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fig = self._handle_plotting(fig_num, axes, lambda i, g, ax: ax.imshow(g.X))
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return fig
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def plot_predict(self, fig_num="MRD Predictions", axes=None):
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fig = self._handle_plotting(fig_num, axes, lambda i, g, ax: ax.imshow(g.predict(g.X)[0]))
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return fig
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def plot_scales(self, fig_num="MRD Scales", axes=None, *args, **kwargs):
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fig = self._handle_plotting(fig_num, axes, lambda i, g, ax: g.kern.plot_ARD(ax=ax, *args, **kwargs))
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return fig
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def plot_latent(self, fig_num="MRD Latent Spaces", axes=None, *args, **kwargs):
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fig = self._handle_plotting(fig_num, axes, lambda i, g, ax: g.plot_latent(ax=ax, *args, **kwargs))
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return fig
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def _debug_plot(self):
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self.plot_X_1d()
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fig = pylab.figure("MRD DEBUG PLOT", figsize=(4 * len(self.bgplvms), 9))
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fig.clf()
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axes = [fig.add_subplot(3, len(self.bgplvms), i + 1) for i in range(len(self.bgplvms))]
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self.plot_X(axes=axes)
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axes = [fig.add_subplot(3, len(self.bgplvms), i + len(self.bgplvms) + 1) for i in range(len(self.bgplvms))]
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self.plot_latent(axes=axes)
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axes = [fig.add_subplot(3, len(self.bgplvms), i + 2 * len(self.bgplvms) + 1) for i in range(len(self.bgplvms))]
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self.plot_scales(axes=axes)
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pylab.draw()
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fig.tight_layout()
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def _debug_optimize(self, opt='scg', maxiters=5000, itersteps=10):
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iters = 0
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optstep = lambda: self.optimize(opt, messages=1, max_f_eval=itersteps)
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self._debug_plot()
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raw_input("enter to start debug")
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while iters < maxiters:
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optstep()
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self._debug_plot()
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iters += itersteps
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