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Merge branch 'master' of github.com:SheffieldML/GPy
This commit is contained in:
Nicolo Fusi
commit
da51f69ec3
15 changed files with 167 additions and 101 deletions
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@ -11,45 +11,21 @@ from ..util.linalg import pdinv,mdot,jitchol
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from ..util.plot import gpplot
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from .. import kern
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class EP:
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def __init__(self,covariance,likelihood,Kmn=None,Knn_diag=None,epsilon=1e-3,powerep=[1.,1.]):
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"""
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Expectation Propagation
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class EP_base:
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"""
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Expectation Propagation.
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Arguments
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---------
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X : input observations
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likelihood : Output's likelihood (likelihood class)
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kernel : a GPy kernel (kern class)
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inducing : Either an array specifying the inducing points location or a sacalar defining their number. None value for using a non-sparse model is used.
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powerep : Power-EP parameters (eta,delta) - 2x1 numpy array (floats)
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epsilon : Convergence criterion, maximum squared difference allowed between mean updates to stop iterations (float)
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"""
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This is just the base class for expectation propagation. We'll extend it for full and sparse EP.
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"""
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def __init__(self,likelihood,epsilon=1e-3,powerep=[1.,1.]):
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self.likelihood = likelihood
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assert covariance.shape[0] == covariance.shape[1]
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if Kmn is not None:
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self.Kmm = covariance
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self.Kmn = Kmn
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self.M = self.Kmn.shape[0]
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self.N = self.Kmn.shape[1]
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assert self.M < self.N, 'The number of inducing inputs must be smaller than the number of observations'
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else:
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self.K = covariance
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self.N = self.K.shape[0]
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if Knn_diag is not None:
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self.Knn_diag = Knn_diag
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assert len(Knn_diag) == self.N, 'Knn_diagonal has size different from N'
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self.epsilon = epsilon
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self.eta, self.delta = powerep
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self.jitter = 1e-12
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"""
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Initial values - Likelihood approximation parameters:
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p(y|f) = t(f|tau_tilde,v_tilde)
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"""
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self.tau_tilde = np.zeros(self.N)
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self.v_tilde = np.zeros(self.N)
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#Initial values - Likelihood approximation parameters:
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#p(y|f) = t(f|tau_tilde,v_tilde)
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self.restart_EP()
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def restart_EP(self):
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"""
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@ -59,8 +35,23 @@ class EP:
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self.v_tilde = np.zeros(self.N)
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self.mu = np.zeros(self.N)
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class Full(EP):
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def fit_EP(self):
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class Full(EP_base):
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"""
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:param likelihood: Output's likelihood (e.g. probit)
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:type likelihood: GPy.inference.likelihood instance
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:param K: prior covariance matrix
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:type K: np.ndarray (N x N)
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:param likelihood: Output's likelihood (e.g. probit)
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:type likelihood: GPy.inference.likelihood instance
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:param epsilon: Convergence criterion, maximum squared difference allowed between mean updates to stop iterations (float)
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:param powerep: Power-EP parameters (eta,delta) - 2x1 numpy array (floats)
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"""
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def __init__(self,K,likelihood,*args,**kwargs):
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assert K.shape[0] == K.shape[1]
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self.K = K
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self.N = self.K.shape[0]
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EP_base.__init__(self,likelihood,*args,**kwargs)
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def fit_EP(self,messages=False):
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"""
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The expectation-propagation algorithm.
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For nomenclature see Rasmussen & Williams 2006 (pag. 52-60)
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@ -78,15 +69,16 @@ class Full(EP):
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sigma_ = 1./tau_
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mu_ = v_/tau_
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"""
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self.tau_ = np.empty(self.N,dtype=float)
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self.v_ = np.empty(self.N,dtype=float)
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self.tau_ = np.empty(self.N,dtype=np.float64)
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self.v_ = np.empty(self.N,dtype=np.float64)
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#Initial values - Marginal moments
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z = np.empty(self.N,dtype=float)
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self.Z_hat = np.empty(self.N,dtype=float)
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phi = np.empty(self.N,dtype=float)
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mu_hat = np.empty(self.N,dtype=float)
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sigma2_hat = np.empty(self.N,dtype=float)
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z = np.empty(self.N,dtype=np.float64)
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self.Z_hat = np.empty(self.N,dtype=np.float64)
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phi = np.empty(self.N,dtype=np.float64)
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mu_hat = np.empty(self.N,dtype=np.float64)
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sigma2_hat = np.empty(self.N,dtype=np.float64)
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#Approximation
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epsilon_np1 = self.epsilon + 1.
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@ -95,8 +87,7 @@ class Full(EP):
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self.np1 = [self.tau_tilde.copy()]
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self.np2 = [self.v_tilde.copy()]
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while epsilon_np1 > self.epsilon or epsilon_np2 > self.epsilon:
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update_order = np.arange(self.N)
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random.shuffle(update_order)
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update_order = np.random.permutation(self.N)
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for i in update_order:
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#Cavity distribution parameters
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self.tau_[i] = 1./self.Sigma[i,i] - self.eta*self.tau_tilde[i]
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@ -120,14 +111,35 @@ class Full(EP):
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V,info = linalg.flapack.dtrtrs(L,Sroot_tilde_K,lower=1)
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self.Sigma = self.K - np.dot(V.T,V)
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self.mu = np.dot(self.Sigma,self.v_tilde)
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epsilon_np1 = sum((self.tau_tilde-self.np1[-1])**2)/self.N
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epsilon_np2 = sum((self.v_tilde-self.np2[-1])**2)/self.N
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epsilon_np1 = np.mean(self.tau_tilde-self.np1[-1]**2)
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epsilon_np2 = np.mean(self.v_tilde-self.np2[-1]**2)
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self.np1.append(self.tau_tilde.copy())
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self.np2.append(self.v_tilde.copy())
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if messages:
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print "EP iteration %i, epsiolon %d"%(self.iterations,epsilon_np1)
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self.np2.append(self.v_tilde.copy())
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class FITC(EP_base):
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"""
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:param likelihood: Output's likelihood (e.g. probit)
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:type likelihood: GPy.inference.likelihood instance
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:param Knn_diag: The diagonal elements of Knn is a 1D vector
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:param Kmn: The 'cross' variance between inducing inputs and data
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:param Kmm: the covariance matrix of the inducing inputs
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:param likelihood: Output's likelihood (e.g. probit)
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:type likelihood: GPy.inference.likelihood instance
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:param epsilon: Convergence criterion, maximum squared difference allowed between mean updates to stop iterations (float)
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:param powerep: Power-EP parameters (eta,delta) - 2x1 numpy array (floats)
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"""
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def __init__(self,likelihood,Knn_diag,Kmn,Kmm,*args,**kwargs):
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self.Knn_diag = Knn_diag
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self.Kmn = Kmn
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self.Kmm = Kmm
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self.M = self.Kmn.shape[0]
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self.N = self.Kmn.shape[1]
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assert self.M <= self.N, 'The number of inducing inputs must be smaller than the number of observations'
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assert len(Knn_diag) == self.N, 'Knn_diagonal has size different from N'
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EP_base.__init__(self,likelihood,*args,**kwargs)
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class FITC(EP):
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def fit_EP(self):
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"""
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The expectation-propagation algorithm with sparse pseudo-input.
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@ -166,15 +178,15 @@ class FITC(EP):
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sigma_ = 1./tau_
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mu_ = v_/tau_
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"""
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self.tau_ = np.empty(self.N,dtype=float)
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self.v_ = np.empty(self.N,dtype=float)
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self.tau_ = np.empty(self.N,dtype=np.float64)
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self.v_ = np.empty(self.N,dtype=np.float64)
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#Initial values - Marginal moments
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z = np.empty(self.N,dtype=float)
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self.Z_hat = np.empty(self.N,dtype=float)
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phi = np.empty(self.N,dtype=float)
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mu_hat = np.empty(self.N,dtype=float)
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sigma2_hat = np.empty(self.N,dtype=float)
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z = np.empty(self.N,dtype=np.float64)
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self.Z_hat = np.empty(self.N,dtype=np.float64)
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phi = np.empty(self.N,dtype=np.float64)
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mu_hat = np.empty(self.N,dtype=np.float64)
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sigma2_hat = np.empty(self.N,dtype=np.float64)
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#Approximation
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epsilon_np1 = 1
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