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Added a debug examples
This commit is contained in:
Alan Saul
parent
f95666a8f9
commit
a52c20f470
3 changed files with 104 additions and 9 deletions
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@ -35,12 +35,86 @@ def timing():
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print the_is
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print np.mean(the_is)
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def debug_student_t_noise_approx():
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real_var = 0.2
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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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Y = np.sin(X) + np.random.randn(*X.shape)*real_var
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X_full = np.linspace(0.0, 10.0, 500)[:, None]
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Y_full = np.sin(X_full)
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#Y = Y/Y.max()
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#Add student t random noise to datapoints
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deg_free = 10000
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real_sd = np.sqrt(real_var)
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print "Real noise: ", real_sd
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initial_var_guess = 0.01
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#t_rv = t(deg_free, loc=0, scale=real_var)
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#noise = t_rvrvs(size=Y.shape)
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#Y += noise
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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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kernel3 = kernel1.copy()
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kernel4 = kernel1.copy()
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kernel5 = kernel1.copy()
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kernel6 = kernel1.copy()
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print "Clean Gaussian"
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#A GP should completely break down due to the points as they get a lot of weight
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# create simple GP model
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m = GPy.models.GP_regression(X, Y, kernel=kernel1)
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# optimize
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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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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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t_distribution = GPy.likelihoods.likelihood_functions.student_t(deg_free, sigma=edited_real_sd)
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stu_t_likelihood = GPy.likelihoods.Laplace(Y.copy(), t_distribution, rasm=True)
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m = GPy.models.GP(X, stu_t_likelihood, kernel6)
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m.ensure_default_constraints()
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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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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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stu_t_likelihood = GPy.likelihoods.Laplace(Y, t_distribution, rasm=False)
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m = GPy.models.GP(X, stu_t_likelihood, kernel3)
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m.ensure_default_constraints()
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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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plt.show()
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def student_t_approx():
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"""
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Example of regressing with a student t likelihood
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"""
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real_var = 0.1
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real_var = 0.2
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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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Y = np.sin(X) + np.random.randn(*X.shape)*real_var
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@ -58,8 +132,11 @@ def student_t_approx():
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#Yc = Yc/Yc.max()
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#Add student t random noise to datapoints
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deg_free = 10
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deg_free = 1000000000000
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real_sd = np.sqrt(real_var)
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print "Real noise: ", real_sd
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initial_var_guess = 0.01
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#t_rv = t(deg_free, loc=0, scale=real_var)
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#noise = t_rvrvs(size=Y.shape)
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#Y += noise
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@ -73,6 +150,7 @@ def student_t_approx():
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#print corrupted_indices
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#noise = t_rv.rvs(size=(len(corrupted_indices), 1))
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#Y[corrupted_indices] += noise
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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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@ -108,7 +186,7 @@ def student_t_approx():
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plt.figure(2)
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plt.suptitle('Student-t likelihood')
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edited_real_sd = real_sd
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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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t_distribution = GPy.likelihoods.likelihood_functions.student_t(deg_free, sigma=edited_real_sd)
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@ -5,7 +5,7 @@ from scipy.linalg import inv, cho_solve, det
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from numpy.linalg import cond
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from GPy.likelihoods.likelihood import likelihood
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from GPy.util.linalg import pdinv, mdot, jitchol, chol_inv, det_ln_diag, pddet
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from scipy.linalg.lapack import dtrtrs
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from scipy.linalg.flapack import dtrtrs
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import pylab as plt
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@ -63,6 +63,7 @@ class Laplace(likelihood):
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return self.likelihood_function._get_param_names()
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def _set_params(self, p):
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print "Setting noise sd: ", p
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return self.likelihood_function._set_params(p)
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def both_gradients(self, dL_d_K_Sigma, dK_dthetaK):
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@ -79,7 +80,9 @@ class Laplace(likelihood):
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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))
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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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#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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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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def _Kgradients(self, dL_d_K_Sigma, dK_dthetaK):
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@ -93,19 +96,26 @@ class Laplace(likelihood):
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dL_dytil, dytil_dfhat = self._shared_gradients_components()
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print "Computing K gradients"
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print "dytil_dfhat: ", np.mean(dytil_dfhat)
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I = np.eye(self.N)
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C = np.dot(self.K, self.W)
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A = I + C
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#plt.imshow(A)
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#plt.show()
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ki, _, _, _ = pdinv(self.K)
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I_KW_i, _, _, _ = pdinv(A)
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#FIXME: K ISNT SYMMETRIC SO NEITHER IS A AND IT MAKES IT NON-PD!
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#ki, _, _, _ = pdinv(self.K)
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#I_KW_i, _, _, _ = pdinv(A)
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I_KW_i = inv(A)
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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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dfhat_dthetaK = np.zeros((self.f_hat.shape[0], dK_dthetaK.shape[0]))
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grad = self.likelihood_function.link_grad(self.data, self.f_hat, self.extra_data)
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for ind_j, thetaj in enumerate(dK_dthetaK):
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dfhat_dthetaK[:, ind_j] = mdot(I_KW_i, thetaj, self.likelihood_function.link_grad(self.data, self.f_hat, self.extra_data))
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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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@ -116,8 +126,11 @@ class Laplace(likelihood):
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dSigmai_dthetaK = 0 #+ np.sum(d3phi_d3fhat*dfhat_dthetaK) #FIXME: CAREFUL OF THIS SUM! SHOULD SUM OVER FHAT NOT THETAS
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dSigma_dthetaK = -mdot(self.Sigma_tilde, dSigmai_dthetaK, 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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dL_dthetaK_implicit = np.sum(np.dot(dL_dytil, dytil_dthetaK), axis=0)# + np.dot(dL_dSigma, dSigma_dthetaK)
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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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return np.squeeze(dL_dthetaK_implicit)
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def _gradients(self, partial):
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@ -116,7 +116,6 @@ class GP(model):
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"""
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return -0.5 * self.D * self.K_logdet + self._model_fit_term() + self.likelihood.Z
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def _log_likelihood_gradients(self):
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"""
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The gradient of all parameters.
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@ -132,9 +131,14 @@ class GP(model):
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dL_dthetaK_implicit = self.likelihood._Kgradients(self.dL_dK, 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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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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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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