mirror of
https://github.com/SheffieldML/GPy.git
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Seem to have gradients much closer now
This commit is contained in:
Alan Saul
parent
84f12c1079
commit
6c4866662c
4 changed files with 110 additions and 60 deletions
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@ -36,6 +36,7 @@ def timing():
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print np.mean(the_is)
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def debug_student_t_noise_approx():
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plot = False
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real_var = 0.1
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#Start a function, any function
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X = np.linspace(0.0, 10.0, 30)[:, None]
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@ -57,8 +58,6 @@ def debug_student_t_noise_approx():
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#Y += noise
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plt.close('all')
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plt.figure(1)
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plt.suptitle('Gaussian likelihood')
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# Kernel object
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kernel1 = GPy.kern.rbf(X.shape[1])
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kernel2 = kernel1.copy()
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@ -75,12 +74,14 @@ def debug_student_t_noise_approx():
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m.ensure_default_constraints()
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m.optimize()
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# plot
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plt.subplot(131)
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m.plot()
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plt.plot(X_full, Y_full)
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if plot:
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plt.figure(1)
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plt.suptitle('Gaussian likelihood')
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plt.subplot(131)
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m.plot()
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plt.plot(X_full, Y_full)
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print m
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plt.suptitle('Student-t likelihood')
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edited_real_sd = initial_var_guess #real_sd
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print "Clean student t, rasm"
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@ -91,10 +92,12 @@ def debug_student_t_noise_approx():
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m.update_likelihood_approximation()
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m.optimize()
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print(m)
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plt.subplot(132)
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m.plot()
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plt.plot(X_full, Y_full)
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plt.ylim(-2.5, 2.5)
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if plot:
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plt.suptitle('Student-t likelihood')
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plt.subplot(132)
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m.plot()
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plt.plot(X_full, Y_full)
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plt.ylim(-2.5, 2.5)
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print "Clean student t, ncg"
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t_distribution = GPy.likelihoods.likelihood_functions.student_t(deg_free, sigma=edited_real_sd)
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@ -104,12 +107,13 @@ def debug_student_t_noise_approx():
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m.update_likelihood_approximation()
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m.optimize()
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print(m)
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plt.subplot(133)
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m.plot()
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plt.plot(X_full, Y_full)
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plt.ylim(-2.5, 2.5)
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if plot:
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plt.subplot(133)
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m.plot()
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plt.plot(X_full, Y_full)
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plt.ylim(-2.5, 2.5)
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plt.show()
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#plt.show()
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def student_t_approx():
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"""
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@ -5,8 +5,8 @@ from scipy.linalg import inv, cho_solve, det
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from numpy.linalg import cond
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from likelihood import likelihood
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from ..util.linalg import pdinv, mdot, jitchol, chol_inv, det_ln_diag, pddet
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from scipy.linalg.flapack import dtrtrs
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import pylab as plt
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from scipy.linalg.lapack import dtrtrs
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#import pylab as plt
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class Laplace(likelihood):
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@ -79,9 +79,9 @@ class Laplace(likelihood):
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return (self._Kgradients(dL_d_K_Sigma, dK_dthetaK), self._gradients(dL_d_K_Sigma))
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def _shared_gradients_components(self):
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dL_dytil = -np.dot(self.Y.T, (self.K+self.Sigma_tilde)) #or *0.5?
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dL_dytil = -np.dot(self.Y.T, (self.K+self.Sigma_tilde)) #or *0.5? Shouldn't this be -y*R
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dytil_dfhat = self.Wi__Ki_W # np.dot(self.Sigma_tilde, self.Ki) + np.eye(self.N) # or self.Wi__Ki_W?
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#Ki = inv(self.K)
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#Ki, _, _, _ = pdinv(self.K)
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#dytil_dfhat = np.dot(self.Sigma_tilde, Ki) + np.eye(self.N) # or self.Wi__Ki_W?
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return dL_dytil, dytil_dfhat
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@ -95,9 +95,8 @@ class Laplace(likelihood):
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"""
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dL_dytil, dytil_dfhat = self._shared_gradients_components()
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d3phi_d3fhat = self.likelihood_function.d3link(self.data, self.f_hat, self.extra_data)
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dSigma_dfhat = -np.dot(self.Sigma_tilde, np.dot(d3phi_d3fhat, self.Sigma_tilde))
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#dSigma_dfhat = -np.dot(self.Sigma_tilde, np.dot(d3phi_d3fhat, self.Sigma_tilde))
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print "Computing K gradients"
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print "dytil_dfhat: ", np.mean(dytil_dfhat)
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@ -107,7 +106,8 @@ class Laplace(likelihood):
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#plt.imshow(A)
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#plt.show()
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I_KW_i, _, _, _ = pdinv(A) #FIXME: WHY SO MUCH JITTER?!
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#I_KW_i, _, _, _ = pdinv(A) #FIXME: WHY SO MUCH JITTER?!
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I_KW_i = self.Bi # could use self.B_chol??
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#FIXME: Careful dK_dthetaK is not the derivative with respect to the marginal just prior K!
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#Derivative for each f dimension, for each of K's hyper parameters
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@ -117,25 +117,44 @@ class Laplace(likelihood):
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dfhat_dthetaK[:, ind_j] = np.dot(I_KW_i, np.dot(thetaj, grad))
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dytil_dthetaK = np.dot(dytil_dfhat, dfhat_dthetaK) # should be (D,thetaK)
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#FIXME: Careful dL_dK = dL_d_K_Sigma
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#FIXME: Careful the -D*0.5 in dL_d_K_sigma might need to be -0.5?
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dL_dSigma = dL_d_K_Sigma
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#d3phi_d3fhat = self.likelihood_function.d3link(self.data, self.f_hat, self.extra_data)
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#explicit #implicit
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dSigmai_dthetaK = 0 + np.dot(d3phi_d3fhat, dfhat_dthetaK)
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dSigma_dthetaK = np.zeros((self.f_hat.shape[0], self.f_hat.shape[0], dK_dthetaK.shape[0]))
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for ind_j, dSigmai_dthetaj in enumerate(dSigmai_dthetaK):
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dSigma_dthetaK[:, :, ind_j] = -np.dot(self.Sigma_tilde, dSigmai_dthetaj*self.Sigma_tilde)
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print "dL_dytil: ", np.mean(dL_dytil)
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print "dytil_dthetaK: ", np.mean(dytil_dthetaK)
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#dSigmai_dthetaK = 0 + np.dot(d3phi_d3fhat, dfhat_dthetaK)
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#dSigma_dthetaK = np.zeros((self.f_hat.shape[0], self.f_hat.shape[0], dK_dthetaK.shape[0]))
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d3likelihood_d3fhat = self.likelihood_function.d3link(self.data, self.f_hat, self.extra_data)
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Wi = np.diagonal(self.Sigma_tilde) #Convenience
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dSigma_dthetaK_explicit = 0
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#Can just hadamard product as diagonal matricies multiplied are just multiplying elements
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dWi_dfhat = np.diagflat(-1*Wi*(-1*d3likelihood_d3fhat)*Wi)
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#dSigma_dthetaK_implicit = -np.sum(np.dot(dWi_dfhat, dfhat_dthetaK), axis=0)
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dSigma_dthetaK_implicit = np.dot(dWi_dfhat, dfhat_dthetaK)
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dSigma_dthetaK = dSigma_dthetaK_explicit + dSigma_dthetaK_implicit
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#dSigma_dthetaK = 0 + np.dot(, dfhat_dthetaK)
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#for ind_j, dSigmai_dthetaj in enumerate(dSigmai_dthetaK):
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#dSigma_dthetaK_explicit = 0
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#dSigma_dthetaK_implicit = -np.dot(Wi, dW_dfhat
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#dSigma_dthetaK[:, :, ind_j] = -np.dot(self.Sigma_tilde, dSigmai_dthetaj*self.Sigma_tilde)
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#FIXME: Won't handle multi dimensional data
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dL_dthetaK_via_ytil = np.sum(np.dot(dL_dytil, dytil_dthetaK), axis=0)
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dL_dthetaK_via_Sigma = np.sum(np.dot(dL_dSigma, dSigma_dthetaK), axis=(0,1))
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dL_dthetaK_via_Sigma = np.sum(np.dot(dL_dSigma, dSigma_dthetaK), axis=0)
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dL_dthetaK_implicit = dL_dthetaK_via_ytil + dL_dthetaK_via_Sigma
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#dL_dthetaK_implicit = np.dot(dL_dytil.T, dytil_dthetaK.T)
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import ipdb; ipdb.set_trace() # XXX BREAKPOINT
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#print "\n"
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#print "dL_dytil: ", np.mean(dL_dytil)
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#print "dytil_dthetaK: ", np.mean(dytil_dthetaK)
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#print "dL_dthetaK_via_ytil: ", dL_dthetaK_via_ytil
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#print "\n"
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#print "dL_dSigma: ", np.mean(dL_dSigma)
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#print "dSigma_dthetaK: ", np.mean(dSigma_dthetaK)
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#print "dL_dthetaK_via_Sigma: ", dL_dthetaK_via_Sigma
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#print "\n"
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#print "dL_dthetaK_implicit: ", dL_dthetaK_implicit
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#import ipdb; ipdb.set_trace() # XXX BREAKPOINT
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return np.squeeze(dL_dthetaK_implicit)
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def _gradients(self, partial):
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@ -159,27 +178,51 @@ class Laplace(likelihood):
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dW_dthetaX = d_dthetaX[d2phi_d2fhat]
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d2phi_d2fhat = Hessian function of likelihood
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partial = dL_dK
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partial = dL_d_K_Sigma
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"""
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dL_dytil, dytil_dfhat = self._shared_gradients_components()
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dfhat_dthetaL, dSigmai_dthetaL = self.likelihood_function._gradients(self.data, self.f_hat, self.extra_data) #FIXME: Shouldn't this have a implicit component aswell?
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#dfhat_dthetaL, dSigmai_dthetaL = self.likelihood_function._gradients(self.data, self.f_hat, self.extra_data) #FIXME: Shouldn't this have a implicit component aswell?
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dlikelihood_dthetaL_explicit, d2likelihood_dthetaL = self.likelihood_function._gradients(self.data, self.f_hat, self.extra_data) #FIXME: Shouldn't this have a implicit component aswell?
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dlikelihood_dfhat = self.likelihood_function.link_hess(self.data, self.f_hat, self.extra_data)
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dfhat_dthetaL_cyclic = 0 #what is this? how can dfhat_dthetaL be used in the value of itself?
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dlikelihood_dthetaL_implicit = np.dot(dlikelihood_dfhat, dfhat_dthetaL_cyclic) # may need a sum over f
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dfhat_dthetaL = np.dot(self.K, (dlikelihood_dthetaL_explicit + dlikelihood_dthetaL_implicit)[:, None])
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dytil_dthetaL = np.dot(dytil_dfhat, dfhat_dthetaL)
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#FIXME: Careful the -D*0.5 in dL_d_K_sigma might need to be -0.5?
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dL_dSigma = partial #Is actually but can't rename it because of naming convention... dL_d_K_Sigma
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Wi = np.diagonal(self.Sigma_tilde) #Convenience
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#-1 as we are looking at W which is -1*d2log p(y|f)
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#Can just hadamard product as diagonal matricies multiplied are just multiplying elements
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dSigma_dthetaL_explicit = np.diagflat(-(Wi*(-1*d2likelihood_dthetaL)*Wi))
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d3likelihood_d3fhat = self.likelihood_function.d3link(self.data, self.f_hat, self.extra_data)
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dWi_dfhat = np.diagflat(-1*Wi*(-1*d3likelihood_d3fhat)*Wi)
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dSigma_dthetaL_implicit = np.dot(dWi_dfhat, dfhat_dthetaL_cyclic)
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dSigma_dthetaL = dSigma_dthetaL_explicit + dSigma_dthetaL_implicit
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#dSigmai_dthetaL = self.likelihood_function._gradients(self.data, self.f_hat, self.extra_data) #FIXME: Shouldn't this have a implicit component aswell?
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#Derivative for each f dimension, for each of K's hyper parameters
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dSigma_dthetaL = np.empty((self.N, len(self.likelihood_function._get_param_names())))
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for ind_l, dSigmai_dtheta_l in enumerate(dSigmai_dthetaL.T):
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dSigma_dthetaL[:, ind_l] = -mdot(self.Sigma_tilde,
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dSigmai_dtheta_l, # Careful, shouldn't this be (N, 1)?
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self.Sigma_tilde
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)
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#dSigma_dthetaL = np.empty((self.N, len(self.likelihood_function._get_param_names())))
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#for ind_l, dSigmai_dtheta_l in enumerate(dSigmai_dthetaL.T):
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#dSigma_dthetaL[:, ind_l] = -mdot(self.Sigma_tilde,
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#dSigmai_dtheta_l, # Careful, shouldn't this be (N, 1)?
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#self.Sigma_tilde
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#)
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#TODO: This is Wi*A*Wi, can be more numerically stable with a trick
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#dSigma_dthetaL = -mdot(self.Sigma_tilde, dSigmai_dthetaL, self.Sigma_tilde)
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dL_dSigma = partial # partial is dL_dK but K here is K+Sigma_tilde.... which is fine in this case
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#dytil_dthetaL = dytil_dfhat*dfhat_dthetaL
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dytil_dthetaL = np.dot(dytil_dfhat, dfhat_dthetaL)
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dL_dthetaL = 0 + np.dot(dL_dytil, dytil_dthetaL)# + np.dot(dL_dSigma, dSigma_dthetaL)
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#dytil_dthetaL = np.dot(dytil_dfhat, dfhat_dthetaL)
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#dL_dthetaL = 0 + np.dot(dL_dytil, dytil_dthetaL)# + np.dot(dL_dSigma, dSigma_dthetaL)
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dL_dthetaL_via_ytil = np.sum(np.dot(dL_dytil, dytil_dthetaL), axis=0)
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dL_dthetaL_via_Sigma = np.sum(np.dot(dL_dSigma, dSigma_dthetaL), axis=0)
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dL_dthetaL = dL_dthetaL_via_ytil + dL_dthetaL_via_Sigma
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return np.squeeze(dL_dthetaL) #should be array of length *params-being optimized*, for student t just optimising 1 parameter, this is (1,)
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def _compute_GP_variables(self):
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@ -248,17 +248,16 @@ class student_t(likelihood_function):
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"""
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Third order derivative link_function (log-likelihood ) at y given f f_j w.r.t f and f_j
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$$\frac{-2(v+1)((f-y)^{3} - 3\sigma^{2}v(f-y))}{((f-y)^{2} + \sigma^{2}v)^{3}}$$
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$$\frac{2(v+1)((y-f)^{3} - 3\sigma^{2}v(y-f))}{((y-f)^{2} + \sigma^{2}v)^{3}}$$
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"""
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y = np.squeeze(y)
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f = np.squeeze(f)
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assert y.shape == f.shape
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#NB f-y not y-f
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e = f - y
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d3link_d3f = ( (-2*(self.v + 1)*(e**3 - 3*(self.sigma**2)*self.v*e))
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e = y - f
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d3link_d3f = ( (2*(self.v + 1)*(e**3 - 3*(self.sigma**2)*self.v*e))
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/ ((e**2 + (self.sigma**2)*self.v)**3)
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)
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return d3link_d3f
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return np.squeeze(d3link_d3f)
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def link_hess_grad_std(self, y, f, extra_data=None):
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"""
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@ -270,10 +269,10 @@ class student_t(likelihood_function):
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f = np.squeeze(f)
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assert y.shape == f.shape
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e = y - f
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hess_grad_sigma = ( (2*self.sigma*(self.v + 1)*((self.sigma**2)*self.v - 3*(e**2)))
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hess_grad_sigma = ( (2*self.sigma*self.v*(self.v + 1)*((self.sigma**2)*self.v - 3*(e**2)))
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/ ((e**2 + (self.sigma**2)*self.v)**3)
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)
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return hess_grad_sigma
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return np.squeeze(hess_grad_sigma)
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def link_grad_std(self, y, f, extra_data=None):
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"""
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@ -288,11 +287,11 @@ class student_t(likelihood_function):
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grad_sigma = ( (-2*self.sigma*self.v*(self.v + 1)*e)
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/ ((self.v*(self.sigma**2) + e**2)**2)
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)
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return grad_sigma
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return np.squeeze(grad_sigma)
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def _gradients(self, y, f, extra_data=None):
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return [self.link_grad_std(y, f, extra_data=extra_data)[:, None],
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self.link_hess_grad_std(y, f, extra_data=extra_data)[:, None]] # list as we might learn many parameters
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return [self.link_grad_std(y, f, extra_data=extra_data),
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self.link_hess_grad_std(y, f, extra_data=extra_data)] # list as we might learn many parameters
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def predictive_values(self, mu, var):
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"""
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@ -125,19 +125,23 @@ class GP(model):
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if isinstance(self.likelihood, Laplace):
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dL_dthetaK_explicit = dL_dthetaK
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#Need to pass in a matrix of ones to get access to raw dK_dthetaK values without being chained
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fake_dL_dKs = np.ones(self.dL_dK.shape)
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fake_dL_dKs = np.eye(self.dL_dK.shape[0])
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dK_dthetaK = self.kern.dK_dtheta(dL_dK=fake_dL_dKs, X=self.X)
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dL_dthetaK_implicit = self.likelihood._Kgradients(self.dL_dK, dK_dthetaK)
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#We need the dL_dK where K is equal to the prior K, not K+Sigma as is the case now
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dL_dthetaK_implicit = self.likelihood._Kgradients(dL_d_K_Sigma=self.dL_dK, dK_dthetaK=dK_dthetaK)
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dL_dthetaK = dL_dthetaK_explicit + dL_dthetaK_implicit
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print "dL_dthetaK_explicit: {dldkx} dL_dthetaK_implicit: {dldki} dL_dthetaK: {dldk}".format(dldkx=dL_dthetaK_explicit, dldki=dL_dthetaK_implicit, dldk=dL_dthetaK)
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#print "dL_dthetaK_explicit: {dldkx} dL_dthetaK_implicit: {dldki} dL_dthetaK: {dldk}".format(dldkx=dL_dthetaK_explicit, dldki=dL_dthetaK_implicit, dldk=dL_dthetaK)
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dL_dthetaL = self.likelihood._gradients(partial=self.dL_dK)
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else:
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print "dL_dthetaK: ", dL_dthetaK
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dL_dthetaL = self.likelihood._gradients(partial=np.diag(self.dL_dK))
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print "dL_dthetaL: ", dL_dthetaL
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print "Stacked dL_dthetaK, dL_dthetaL: ", np.hstack((dL_dthetaK, dL_dthetaL))
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import ipdb; ipdb.set_trace() ### XXX BREAKPOINT
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else:
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#print "dL_dthetaK: ", dL_dthetaK
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dL_dthetaL = self.likelihood._gradients(partial=np.diag(self.dL_dK))
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print "Stacked dL_dthetaK, dL_dthetaL: ", np.hstack((dL_dthetaK, dL_dthetaL))
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#print "dL_dthetaL: ", dL_dthetaL
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return np.hstack((dL_dthetaK, dL_dthetaL))
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#return np.hstack((self.kern.dK_dtheta(dL_dK=self.dL_dK, X=self.X), self.likelihood._gradients(partial=np.diag(self.dL_dK))))
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|
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Reference in a new issue