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RBF (both ARD and non-ARD) kernels working nicely with psi statistics

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This commit is contained in:
Nicolo Fusi 2013-01-30 16:27:45 +00:00
parent be5b775729
commit 8a5f075ef0
3 changed files with 47 additions and 29 deletions
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10
GPy/examples/BGPLVM_demo.py
View file

@ -7,17 +7,17 @@ import GPy
np.random.seed(123344) np.random.seed(123344)
N = 10 N = 10
M = 3 M = 5
Q = 2 Q = 3
D = 3 D = 4
#generate GPLVM-like data #generate GPLVM-like data
X = np.random.rand(N, Q) X = np.random.rand(N, Q)
k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001) k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
K = k.K(X) K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,D).T Y = np.random.multivariate_normal(np.zeros(N),K,D).T
k = GPy.kern.rbf(Q) + GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001) # k = GPy.kern.rbf(Q) + GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001)
# k = GPy.kern.rbf_ARD(Q) + GPy.kern.white(Q, 0.00001) k = GPy.kern.rbf(Q, ARD = False) + GPy.kern.white(Q, 0.00001)
m = GPy.models.Bayesian_GPLVM(Y, Q, kernel = k, M=M) m = GPy.models.Bayesian_GPLVM(Y, Q, kernel = k, M=M)
m.constrain_positive('(rbf|bias|noise|white|S)') m.constrain_positive('(rbf|bias|noise|white|S)')
# m.constrain_fixed('S', 1) # m.constrain_fixed('S', 1)

64
GPy/kern/rbf.py
View file

@ -38,7 +38,7 @@ class rbf(kernpart):
if lengthscale is not None: if lengthscale is not None:
assert lengthscale.shape == (1,) assert lengthscale.shape == (1,)
else: else:
lengthscale = np.ones(1) lengthscale = np.ones(1)
else: else:
self.Nparam = self.D + 1 self.Nparam = self.D + 1
self.name = 'rbf_ARD' self.name = 'rbf_ARD'
@ -47,7 +47,7 @@ class rbf(kernpart):
else: else:
lengthscale = np.ones(self.D) lengthscale = np.ones(self.D)
self._set_params(np.hstack((variance,lengthscale))) self._set_params(np.hstack((variance,lengthscale)))
#initialize cache #initialize cache
self._Z, self._mu, self._S = np.empty(shape=(3,1)) self._Z, self._mu, self._S = np.empty(shape=(3,1))
@ -69,7 +69,7 @@ class rbf(kernpart):
if self.Nparam == 2: if self.Nparam == 2:
return ['variance','lengthscale'] return ['variance','lengthscale']
else: else:
return ['variance']+['lengthscale_%i'%i for i in range(self.lengthscale.size)] return ['variance']+['lengthscale_%i'%i for i in range(self.lengthscale.size)]
def K(self,X,X2,target): def K(self,X,X2,target):
if X2 is None: if X2 is None:
@ -103,17 +103,10 @@ class rbf(kernpart):
def dKdiag_dX(self,partial,X,target): def dKdiag_dX(self,partial,X,target):
pass pass
def _K_computations(self,X,X2):
if not (np.all(X==self._X) and np.all(X2==self._X2)): #---------------------------------------#
self._X = X # PSI statistics #
self._X2 = X2 #---------------------------------------#
if X2 is None: X2 = X
self._K_dist = X[:,None,:]-X2[None,:,:] # this can be computationally heavy
self._params = np.empty(shape=(1,0)) #ensure the next section gets called
if not np.all(self._params == self._get_params()):
self._params == self._get_params()
self._K_dist2 = np.square(self._K_dist/self.lengthscale)
self._K_dvar = np.exp(-0.5*self._K_dist2.sum(-1))
def psi0(self,Z,mu,S,target): def psi0(self,Z,mu,S,target):
target += self.variance target += self.variance
@ -133,7 +126,11 @@ class rbf(kernpart):
denom_deriv = S[:,None,:]/(self.lengthscale**3+self.lengthscale*S[:,None,:]) denom_deriv = S[:,None,:]/(self.lengthscale**3+self.lengthscale*S[:,None,:])
d_length = self._psi1[:,:,None]*(self.lengthscale*np.square(self._psi1_dist/(self.lengthscale2+S[:,None,:])) + denom_deriv) d_length = self._psi1[:,:,None]*(self.lengthscale*np.square(self._psi1_dist/(self.lengthscale2+S[:,None,:])) + denom_deriv)
target[0] += np.sum(partial*self._psi1/self.variance) target[0] += np.sum(partial*self._psi1/self.variance)
target[1] += np.sum(d_length*partial[:,:,None]) dpsi1_dlength = d_length*partial[:,:,None]
if not self.ARD:
target[1] += dpsi1_dlength.sum()
else:
target[1:] += dpsi1_dlength.sum(0).sum(0)
def dpsi1_dZ(self,partial,Z,mu,S,target): def dpsi1_dZ(self,partial,Z,mu,S,target):
self._psi_computations(Z,mu,S) self._psi_computations(Z,mu,S)
@ -149,30 +146,52 @@ class rbf(kernpart):
def psi2(self,Z,mu,S,target): def psi2(self,Z,mu,S,target):
self._psi_computations(Z,mu,S) self._psi_computations(Z,mu,S)
target += self._psi2.sum(0) #TODO: psi2 should be NxMxM (for het. noise) target += self._psi2
def dpsi2_dtheta(self,partial,Z,mu,S,target): def dpsi2_dtheta(self,partial,Z,mu,S,target):
"""Shape N,M,M,Ntheta""" """Shape N,M,M,Ntheta"""
self._psi_computations(Z,mu,S) self._psi_computations(Z,mu,S)
d_var = np.sum(2.*self._psi2/self.variance,0) d_var = 2.*self._psi2/self.variance
d_length = self._psi2[:,:,:,None]*(0.5*self._psi2_Zdist_sq*self._psi2_denom + 2.*self._psi2_mudist_sq + 2.*S[:,None,None,:]/self.lengthscale2)/(self.lengthscale*self._psi2_denom) d_length = self._psi2[:,:,:,None]*(0.5*self._psi2_Zdist_sq*self._psi2_denom + 2.*self._psi2_mudist_sq + 2.*S[:,None,None,:]/self.lengthscale2)/(self.lengthscale*self._psi2_denom)
d_length = d_length.sum(0) d_length = d_length.sum(0)
target[0] += np.sum(partial*d_var) target[0] += np.sum(partial*d_var)
target[1] += np.sum(d_length*partial[:,:,None]) dpsi2_dlength = d_length*partial[:,:,:,None]
if not self.ARD:
target[1] += dpsi2_dlength.sum()
else:
target[1:] += dpsi2_dlength.sum(0).sum(0).sum(0)
def dpsi2_dZ(self,partial,Z,mu,S,target): def dpsi2_dZ(self,partial,Z,mu,S,target):
self._psi_computations(Z,mu,S) self._psi_computations(Z,mu,S)
term1 = 0.5*self._psi2_Zdist/self.lengthscale2 # M, M, Q term1 = 0.5*self._psi2_Zdist/self.lengthscale2 # M, M, Q
term2 = self._psi2_mudist/self._psi2_denom/self.lengthscale2 # N, M, M, Q term2 = self._psi2_mudist/self._psi2_denom/self.lengthscale2 # N, M, M, Q
dZ = self._psi2[:,:,:,None] * (term1[None] + term2) dZ = self._psi2[:,:,:,None] * (term1[None] + term2)
target += (partial[None,:,:,None]*dZ).sum(0).sum(0) target += (partial[:,:,:,None]*dZ).sum(0).sum(0) # <----------------- TODO not sure about the first ':' here, should be a None (WAS a none in the debug branch)
def dpsi2_dmuS(self,partial,Z,mu,S,target_mu,target_S): def dpsi2_dmuS(self,partial,Z,mu,S,target_mu,target_S):
"""Think N,M,M,Q """ """Think N,M,M,Q """
self._psi_computations(Z,mu,S) self._psi_computations(Z,mu,S)
tmp = self._psi2[:,:,:,None]/self.lengthscale2/self._psi2_denom tmp = self._psi2[:,:,:,None]/self.lengthscale2/self._psi2_denom
target_mu += (partial[None,:,:,None]*-tmp*2.*self._psi2_mudist).sum(1).sum(1) target_mu += (partial[:,:,:,None]*-tmp*2.*self._psi2_mudist).sum(1).sum(1)
target_S += (partial[None,:,:,None]*tmp*(2.*self._psi2_mudist_sq-1)).sum(1).sum(1) target_S += (partial[:,:,:,None]*tmp*(2.*self._psi2_mudist_sq-1)).sum(1).sum(1)
#---------------------------------------#
# Precomputations #
#---------------------------------------#
def _K_computations(self,X,X2):
if not (np.all(X==self._X) and np.all(X2==self._X2)):
self._X = X
self._X2 = X2
if X2 is None: X2 = X
self._K_dist = X[:,None,:]-X2[None,:,:] # this can be computationally heavy
self._params = np.empty(shape=(1,0)) #ensure the next section gets called
if not np.all(self._params == self._get_params()):
self._params == self._get_params()
self._K_dist2 = np.square(self._K_dist/self.lengthscale)
self._K_dvar = np.exp(-0.5*self._K_dist2.sum(-1))
def _psi_computations(self,Z,mu,S): def _psi_computations(self,Z,mu,S):
#here are the "statistics" for psi1 and psi2 #here are the "statistics" for psi1 and psi2
@ -202,4 +221,3 @@ class rbf(kernpart):
self._psi2 = np.square(self.variance)*np.exp(self._psi2_exponent) # N,M,M self._psi2 = np.square(self.variance)*np.exp(self._psi2_exponent) # N,M,M
self._Z, self._mu, self._S = Z, mu,S self._Z, self._mu, self._S = Z, mu,S

2
GPy/models/BGPLVM.py
View file

@ -58,5 +58,5 @@ class Bayesian_GPLVM(sparse_GP_regression, GPLVM):
return np.hstack((dL_dmu.flatten(), dL_dS.flatten())) return np.hstack((dL_dmu.flatten(), dL_dS.flatten()))
def _log_likelihood_gradients(self): def _log_likelihood_gradients(self):
return np.hstack((self.dL_dmuS().flatten(), sparse_GP_regression.log_likelihood_gradients(self))) return np.hstack((self.dL_dmuS().flatten(), sparse_GP_regression._log_likelihood_gradients(self)))