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Scale factor added to sparse_GP_regression
and sparse_GP_demo ammended to be less annoying (m1)
This commit is contained in:
James Hensman
parent
9f05744374
commit
126b45673b
2 changed files with 61 additions and 52 deletions
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@ -11,8 +11,8 @@ import numpy as np
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import GPy
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np.random.seed(2)
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pb.ion()
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N = 500
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M = 5
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N = 1200
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M = 20
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######################################
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## 1 dimensional example
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@ -27,20 +27,21 @@ noise = GPy.kern.white(1)
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kernel = rbf + noise
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# create simple GP model
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m1 = GPy.models.sparse_GP_regression(X, Y, kernel, M=M)
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m = GPy.models.sparse_GP_regression(X, Y, kernel, M=M)
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# contrain all parameters to be positive
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m1.constrain_positive('(variance|lengthscale|precision)')
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#m1.constrain_positive('(variance|lengthscale)')
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#m1.constrain_fixed('prec',10.)
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m.constrain_positive('(variance|lengthscale|precision)')
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#m.constrain_positive('(variance|lengthscale)')
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#m.constrain_fixed('prec',10.)
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#check gradient FIXME unit test please
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m1.checkgrad()
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m.checkgrad(verbose=1)
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stop
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# optimize and plot
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m1.optimize('tnc', messages = 1)
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m1.plot()
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# print(m1)
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m.optimize('tnc', messages = 1)
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m.plot()
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# print(m)
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######################################
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## 2 dimensional example
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@ -37,7 +37,7 @@ class sparse_GP_regression(GP_regression):
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"""
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def __init__(self,X,Y,kernel=None, X_uncertainty=None, beta=100., Z=None,Zslices=None,M=10,normalize_X=False,normalize_Y=False):
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self.stabilit_multiplier = 1.
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self.scale_factor = 1e1
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self.beta = beta
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if Z is None:
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self.Z = np.random.permutation(X.copy())[:M]
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@ -60,14 +60,6 @@ class sparse_GP_regression(GP_regression):
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if self.has_uncertain_inputs:
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self.X_uncertainty /= np.square(self._Xstd)
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def set_param(self, p):
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self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
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self.beta = p[self.M*self.Q]
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self.kern.set_param(p[self.Z.size + 1:])
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self.beta2 = self.beta**2
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self._compute_kernel_matrices()
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self._computations()
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def _compute_kernel_matrices(self):
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# kernel computations, using BGPLVM notation
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#TODO: slices for psi statistics (easy enough)
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@ -77,35 +69,62 @@ class sparse_GP_regression(GP_regression):
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self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty).sum()
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self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T
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self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty)
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raise NotImplementedError, "scale psi2 (in kern?)"
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else:
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self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices).sum()
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self.psi1 = self.kern.K(self.Z,self.X)
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self.psi2 = np.dot(self.psi1,self.psi1.T)
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#self.psi2 = np.dot(self.psi1,self.psi1.T)
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#self.psi2 = self.psi1.T[:,:,None]*self.psi1.T[:,None,:]
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self.psi1_scaled = self.psi1/self.scale_factor
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#self.psi2_scaled = psi1_scaled.T[:,:,None]*psi1_scaled.T[:,None,:]
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self.psi2_scaled = np.dot(self.psi1_scaled,self.psi1_scaled.T)
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def _computations(self):
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# TODO find routine to multiply triangular matrices
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self.V = self.beta*self.Y
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sf = self.scale_factor
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sf2 = sf**2
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self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
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self.V = (self.beta/self.scale_factor)*self.Y
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self.A = mdot(self.Lmi, self.beta*self.psi2_scaled, self.Lmi.T)
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self.B = np.eye(self.M)/sf2 + self.A
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self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
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self.psi1V = np.dot(self.psi1, self.V)
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self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T)
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self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
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self.A = mdot(self.Lmi, self.beta*self.psi2, self.Lmi.T)
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self.B = np.eye(self.M)*self.stabilit_multiplier + self.A
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self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
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self.LLambdai = np.dot(self.LBi, self.Lmi)
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self.trace_K = self.psi0 - np.trace(self.A)/self.beta
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self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi)
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self.C = mdot(self.LLambdai, self.psi1V)
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self.G = mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T)
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self.C = mdot(self.Lmi.T, self.Bi, self.Lmi)
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self.E = mdot(self.C, self.psi1VVpsi1/sf2, self.C.T)
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# Compute dL_dpsi
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self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N)
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self.dL_dpsi1 = mdot(self.LLambdai.T,self.C,self.V.T)
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self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
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self.dL_dpsi1 = mdot(self.V, self.psi1V.T,self.C).T
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self.dL_dpsi2 = 0.5 * self.beta * self.D * self.Kmmi # dB
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self.dL_dpsi2 += - 0.5 * self.beta/sf2 * self.D * self.C # dC
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self.dL_dpsi2 += - 0.5 * self.beta * self.E # dD
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# Compute dL_dKmm
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self.dL_dKmm = -0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi) # dB
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self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - 2.*self.beta*mdot(self.LBL_inv, self.psi2, self.Kmmi) + self.Kmmi) # dC
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self.dL_dKmm += np.dot(np.dot(self.G,self.beta*self.psi2) - np.dot(self.LBL_inv, self.psi1VVpsi1), self.Kmmi) + 0.5*self.G # dE
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self.dL_dKmm = -0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi)*sf2 # dB
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self.dL_dKmm += -0.5 * self.D * (- self.C/sf2 - 2.*self.beta*mdot(self.C, self.psi2_scaled, self.Kmmi) + self.Kmmi) # dC
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self.dL_dKmm += np.dot(np.dot(self.E*sf2, self.beta*self.psi2_scaled) - np.dot(self.C, self.psi1VVpsi1), self.Kmmi) + 0.5*self.E # dD
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def log_likelihood(self):
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""" Compute the (lower bound on the) log marginal likelihood """
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sf2 = self.scale_factor**2
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A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta)) -0.5*self.beta*self.trYYT
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B = -0.5*self.D*(self.beta*self.psi0-np.trace(self.A)*sf2)
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C = -0.5*self.D * (self.B_logdet + self.M*np.log(sf2))
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D = +0.5*np.sum(self.psi1VVpsi1 * self.C)
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return A+B+C+D
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def set_param(self, p):
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self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
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self.beta = p[self.M*self.Q]
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self.kern.set_param(p[self.Z.size + 1:])
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self.beta2 = self.beta**2
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self._compute_kernel_matrices()
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self._computations()
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def get_param(self):
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return np.hstack([self.Z.flatten(),self.beta,self.kern.extract_param()])
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@ -113,30 +132,19 @@ class sparse_GP_regression(GP_regression):
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def get_param_names(self):
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return sum([['iip_%i_%i'%(i,j) for i in range(self.Z.shape[0])] for j in range(self.Z.shape[1])],[]) + ['noise_precision']+self.kern.extract_param_names()
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def log_likelihood(self):
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"""
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Compute the (lower bound on the) log marginal likelihood
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"""
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A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta))
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B = -0.5*self.beta*self.D*self.trace_K
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C = -0.5*self.D * self.B_logdet
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D = -0.5*self.beta*self.trYYT
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E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv)
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return A+B+C+D+E
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def dL_dbeta(self):
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"""
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Compute the gradient of the log likelihood wrt beta.
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"""
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#TODO: suport heteroscedatic noise
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dA_dbeta = 0.5 * self.N*self.D/self.beta
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dB_dbeta = - 0.5 * self.D * self.trace_K
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sf2 = self.scale_factor**2
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dA_dbeta = 0.5 * self.N*self.D/self.beta - 0.5 * self.trYYT
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dB_dbeta = - 0.5 * self.D * self.psi0 - np.trace(self.A)/self.beta*sf2
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dC_dbeta = - 0.5 * self.D * np.sum(self.Bi*self.A)/self.beta
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dD_dbeta = - 0.5 * self.trYYT
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tmp = mdot(self.LBi.T, self.LLambdai, self.psi1V)
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dE_dbeta = (np.sum(np.square(self.C)) - 0.5 * np.sum(self.A * np.dot(tmp, tmp.T)))/self.beta
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tmp = mdot(self.Bi, self.Lmi, self.psi1V)
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dD_dbeta = (np.sum(np.square(self.C)) - 0.5 * np.sum(self.A * np.dot(tmp, tmp.T)))/self.beta
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return np.squeeze(dA_dbeta + dB_dbeta + dC_dbeta + dD_dbeta + dE_dbeta)
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return np.squeeze(dA_dbeta + dB_dbeta + dC_dbeta + dD_dbeta)
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def dL_dtheta(self):
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"""
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