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Have most of the likelihood testing working, laplace likelihood parameters need fixing, some of the signs are wrong I believe
This commit is contained in:
Alan Saul
parent
625943ef27
commit
0f263d2ff2
5 changed files with 122 additions and 71 deletions
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@ -32,6 +32,7 @@ class LaplaceInference(object):
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self._mode_finding_tolerance = 1e-7
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self._mode_finding_max_iter = 40
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self.bad_fhat = True
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self._previous_Ki_fhat = None
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def inference(self, kern, X, likelihood, Y, Y_metadata=None):
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"""
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@ -53,14 +54,13 @@ class LaplaceInference(object):
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f_hat, Ki_fhat = self.rasm_mode(K, Y, likelihood, Ki_f_init, Y_metadata=Y_metadata)
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#Compute hessian and other variables at mode
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log_marginal, Ki_W_i, K_Wi_i, dL_dK, woodbury_vector = self.mode_computations(f_hat, Ki_fhat, K, Y, likelihood, Y_metadata)
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log_marginal, woodbury_vector, woodbury_inv, dL_dK, dL_dthetaL = self.mode_computations(f_hat, Ki_fhat, K, Y, likelihood, kern, Y_metadata)
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#likelihood.gradient = self.likelihood_gradients()
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kern.update_gradients_full(dL_dK, X)
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likelihood.update_gradients(np.ones(10))
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likelihood.update_gradients(dL_dthetaL)
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self._previous_Ki_fhat = Ki_fhat.copy()
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return Posterior(woodbury_vector=woodbury_vector, woodbury_inv = K_Wi_i, K=K), log_marginal, {'dL_dK':dL_dK}
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return Posterior(woodbury_vector=woodbury_vector, woodbury_inv=woodbury_inv, K=K), log_marginal, {'dL_dK':dL_dK}
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def rasm_mode(self, K, Y, likelihood, Ki_f_init, Y_metadata=None):
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"""
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@ -134,13 +134,15 @@ class LaplaceInference(object):
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return f, Ki_f
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def mode_computations(self, f_hat, Ki_f, K, Y, likelihood, Y_metadata):
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def mode_computations(self, f_hat, Ki_f, K, Y, likelihood, kern, Y_metadata):
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"""
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At the mode, compute the hessian and effective covariance matrix.
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returns: logZ : approximation to the marginal likelihood
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Cov : the approximation to the covariance matrix
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woodbury_vector : variable required for calculating the approximation to the covariance matrix
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woodbury_inv : variable required for calculating the approximation to the covariance matrix
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dL_dthetaL : array of derivatives (1 x num_kernel_params)
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dL_dthetaL : array of derivatives (1 x num_likelihood_params)
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"""
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#At this point get the hessian matrix (or vector as W is diagonal)
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W = -likelihood.d2logpdf_df2(f_hat, Y, extra_data=Y_metadata)
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@ -154,48 +156,75 @@ class LaplaceInference(object):
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#compute the log marginal
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log_marginal = -0.5*np.dot(Ki_f.flatten(), f_hat.flatten()) + likelihood.logpdf(f_hat, Y, extra_data=Y_metadata) - np.sum(np.log(np.diag(L)))
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#compute dL_dK
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explicit_part = 0.5*(np.dot(Ki_f, Ki_f.T) - K_Wi_i)
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#Implicit
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#Compute vival matrices for derivatives
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dW_df = likelihood.d3logpdf_df3(f_hat, Y, extra_data=Y_metadata) # d3lik_d3fhat
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woodbury_vector = likelihood.dlogpdf_df(f_hat, Y, extra_data=Y_metadata)
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dL_dfhat = 0.5*(np.diag(Ki_W_i)[:, None]*dW_df) #why isn't this -0.5? s2 in R&W p126 line 9.
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#implicit_part = np.dot(woodbury_vector, dL_dfhat.T).dot(np.eye(Y.shape[0]) - np.dot(K, K_Wi_i))
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BiK, _ = dpotrs(L, K, lower=1)
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#BiK, _ = dpotrs(L, K, lower=1)
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#dL_dfhat = 0.5*np.diag(BiK)[:, None]*dW_df
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implicit_part = np.dot(woodbury_vector, dL_dfhat.T).dot(np.eye(Y.shape[0]) - np.dot(K, K_Wi_i))
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I_KW_i = np.eye(Y.shape[0]) - np.dot(K, K_Wi_i)
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dL_dK = explicit_part + implicit_part
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return log_marginal, Ki_W_i, K_Wi_i, dL_dK, woodbury_vector
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def likelihood_gradients(self):
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"""
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Gradients with respect to likelihood parameters (dL_dthetaL)
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:rtype: array of derivatives (1 x num_likelihood_params)
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"""
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dL_dfhat, I_KW_i = self._shared_gradients_components()
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dlik_dthetaL, dlik_grad_dthetaL, dlik_hess_dthetaL = likelihood._laplace_gradients(self.f_hat, self.data, extra_data=self.extra_data)
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num_params = len(self._get_param_names())
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# make space for one derivative for each likelihood parameter
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dL_dthetaL = np.zeros(num_params)
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for thetaL_i in range(num_params):
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####################
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#compute dL_dK#
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####################
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if kern.size > 0 and not kern.is_fixed:
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#Explicit
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dL_dthetaL_exp = ( np.sum(dlik_dthetaL[:, thetaL_i])
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#- 0.5*np.trace(mdot(self.Ki_W_i, (self.K, np.diagflat(dlik_hess_dthetaL[thetaL_i]))))
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+ np.dot(0.5*np.diag(self.Ki_W_i)[:,None].T, dlik_hess_dthetaL[:, thetaL_i])
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)
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explicit_part = 0.5*(np.dot(Ki_f, Ki_f.T) - K_Wi_i)
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#Implicit
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dfhat_dthetaL = mdot(I_KW_i, self.K, dlik_grad_dthetaL[:, thetaL_i])
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dL_dthetaL_imp = np.dot(dL_dfhat, dfhat_dthetaL)
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dL_dthetaL[thetaL_i] = dL_dthetaL_exp + dL_dthetaL_imp
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implicit_part = np.dot(woodbury_vector, dL_dfhat.T).dot(I_KW_i)
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return dL_dthetaL
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dL_dK = explicit_part + implicit_part
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else:
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dL_dK = np.zeros(likelihood.size)
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####################
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#compute dL_dthetaL#
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####################
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if likelihood.size > 0 and not likelihood.is_fixed:
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dlik_dthetaL, dlik_grad_dthetaL, dlik_hess_dthetaL = likelihood._laplace_gradients(f_hat, Y, extra_data=Y_metadata)
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num_params = likelihood.size
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# make space for one derivative for each likelihood parameter
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dL_dthetaL = np.zeros(num_params)
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for thetaL_i in range(num_params):
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#Explicit
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dL_dthetaL_exp = ( + np.sum(dlik_dthetaL[thetaL_i])
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+ 0.5*np.sum(np.diag(Ki_W_i).flatten()*dlik_hess_dthetaL[:, thetaL_i].flatten())
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#- 0.5*np.trace(np.diag(Ki_W_i)[:,None]*dlik_hess_dthetaL[:, thetaL_i])
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#+ 0.5*np.trace(np.dot(I_KW_i, K)*dlik_hess_dthetaL[:, thetaL_i])
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)
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#Implicit
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dfhat_dthetaL = mdot(I_KW_i, K, dlik_grad_dthetaL[:, thetaL_i])
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#dfhat_dthetaL = mdot(Wi_K_i, dlik_grad_dthetaL[:, thetaL_i])
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dL_dthetaL_imp = np.dot(dL_dfhat.T, dfhat_dthetaL)
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#import pylab as pb
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#pb.figure(1)
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#pb.matshow(Ki_W_i)
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#pb.title('I_KW_i approx')
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#pb.colorbar()
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#pb.figure(2)
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#pb.matshow(np.linalg.inv(np.dot(np.eye(Y.shape[0]) + np.sqrt(W).T*K*np.sqrt(W), K)))
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#pb.title('I_KW_i')
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#pb.colorbar()
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#print likelihood
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#pb.show()
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#import ipdb; ipdb.set_trace() # XXX BREAKPOINT
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dL_dthetaL[thetaL_i] = dL_dthetaL_exp + dL_dthetaL_imp
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else:
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dL_dthetaL = np.zeros(likelihood.size)
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return log_marginal, woodbury_vector, K_Wi_i, dL_dK, dL_dthetaL
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#def likelihood_gradients(self, f_hat, K, Y, Ki_W_i, dL_dfhat, I_KW_i, likelihood, Y_metadata):
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#"""
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#Gradients with respect to likelihood parameters (dL_dthetaL)
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#:rtype: array of derivatives (1 x num_likelihood_params)
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#"""
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def _compute_B_statistics(self, K, W, log_concave):
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"""
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