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work on likeluhoods and likelihoods tests
This commit is contained in:
James Hensman
parent
5cf792504a
commit
2876e5a07a
11 changed files with 186 additions and 222 deletions
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@ -6,3 +6,4 @@ import regression
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import dimensionality_reduction
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import tutorials
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import stochastic
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import non_gaussian
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@ -36,28 +36,28 @@ def student_t_approx(optimize=True, plot=True):
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edited_real_sd = initial_var_guess
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# Kernel object
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kernel1 = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1])
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kernel2 = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1])
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kernel3 = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1])
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kernel4 = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1])
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kernel1 = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1])
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kernel2 = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1])
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kernel3 = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1])
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kernel4 = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1])
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#Gaussian GP model on clean data
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#m1 = GPy.models.GPRegression(X, Y.copy(), kernel=kernel1)
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## optimize
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#m1['white'].constrain_fixed(1e-5)
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#m1.randomize()
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m1 = GPy.models.GPRegression(X, Y.copy(), kernel=kernel1)
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# optimize
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m1['.*white'].constrain_fixed(1e-5)
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m1.randomize()
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##Gaussian GP model on corrupt data
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#m2 = GPy.models.GPRegression(X, Yc.copy(), kernel=kernel2)
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#m1['white'].constrain_fixed(1e-5)
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#m2.randomize()
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m2 = GPy.models.GPRegression(X, Yc.copy(), kernel=kernel2)
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m1['.*white'].constrain_fixed(1e-5)
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m2.randomize()
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#Student t GP model on clean data
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t_distribution = GPy.likelihoods.StudentT(deg_free=deg_free, sigma2=edited_real_sd)
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laplace_inf = GPy.inference.latent_function_inference.Laplace()
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m3 = GPy.core.GP(X, Y.copy(), kernel3, likelihood=t_distribution, inference_method=laplace_inf)
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m3['t_noise'].constrain_bounded(1e-6, 10.)
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m3['white'].constrain_fixed(1e-5)
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m3['.*t_noise'].constrain_bounded(1e-6, 10.)
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m3['.*white'].constrain_fixed(1e-5)
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m3.randomize()
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debug = True
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print m3
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@ -69,8 +69,8 @@ def student_t_approx(optimize=True, plot=True):
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t_distribution = GPy.likelihoods.StudentT(deg_free=deg_free, sigma2=edited_real_sd)
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laplace_inf = GPy.inference.latent_function_inference.Laplace()
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m4 = GPy.core.GP(X, Yc.copy(), kernel4, likelihood=t_distribution, inference_method=laplace_inf)
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m4['t_noise'].constrain_bounded(1e-6, 10.)
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m4['white'].constrain_fixed(1e-5)
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m4['.*t_noise'].constrain_bounded(1e-6, 10.)
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m4['.*white'].constrain_fixed(1e-5)
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m4.randomize()
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if optimize:
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@ -153,7 +153,7 @@ def boston_example(optimize=True, plot=True):
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#Gaussian GP
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print "Gauss GP"
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mgp = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelgp.copy())
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mgp.constrain_fixed('white', 1e-5)
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mgp.constrain_fixed('.*white', 1e-5)
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mgp['rbf_len'] = rbf_len
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mgp['noise'] = noise
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print mgp
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@ -171,7 +171,7 @@ def boston_example(optimize=True, plot=True):
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g_likelihood = GPy.likelihoods.Laplace(Y_train.copy(), g_distribution)
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mg = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelstu.copy(), likelihood=g_likelihood)
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mg.constrain_positive('noise_variance')
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mg.constrain_fixed('white', 1e-5)
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mg.constrain_fixed('.*white', 1e-5)
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mg['rbf_len'] = rbf_len
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mg['noise'] = noise
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print mg
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@ -189,10 +189,10 @@ def boston_example(optimize=True, plot=True):
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t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=df, sigma2=noise)
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stu_t_likelihood = GPy.likelihoods.Laplace(Y_train.copy(), t_distribution)
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mstu_t = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelstu.copy(), likelihood=stu_t_likelihood)
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mstu_t.constrain_fixed('white', 1e-5)
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mstu_t.constrain_bounded('t_noise', 0.0001, 1000)
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mstu_t.constrain_fixed('.*white', 1e-5)
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mstu_t.constrain_bounded('.*t_noise', 0.0001, 1000)
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mstu_t['rbf_len'] = rbf_len
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mstu_t['t_noise'] = noise
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mstu_t['.*t_noise'] = noise
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print mstu_t
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if optimize:
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mstu_t.optimize(optimizer=optimizer, messages=messages)
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@ -87,13 +87,13 @@ class Laplace(object):
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#define the objective function (to be maximised)
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def obj(Ki_f, f):
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return -0.5*np.dot(Ki_f.flatten(), f.flatten()) + likelihood.logpdf(f, Y, extra_data=Y_metadata)
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return -0.5*np.dot(Ki_f.flatten(), f.flatten()) + likelihood.logpdf(f, Y, Y_metadata=Y_metadata)
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difference = np.inf
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iteration = 0
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while difference > self._mode_finding_tolerance and iteration < self._mode_finding_max_iter:
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W = -likelihood.d2logpdf_df2(f, Y, extra_data=Y_metadata)
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grad = likelihood.dlogpdf_df(f, Y, extra_data=Y_metadata)
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W = -likelihood.d2logpdf_df2(f, Y, Y_metadata=Y_metadata)
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grad = likelihood.dlogpdf_df(f, Y, Y_metadata=Y_metadata)
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W_f = W*f
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@ -143,7 +143,7 @@ class Laplace(object):
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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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W = -likelihood.d2logpdf_df2(f_hat, Y, Y_metadata=Y_metadata)
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K_Wi_i, L, LiW12 = self._compute_B_statistics(K, W, likelihood.log_concave)
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@ -152,11 +152,11 @@ class Laplace(object):
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Ki_W_i = K - C.T.dot(C)
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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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log_marginal = -0.5*np.dot(Ki_f.flatten(), f_hat.flatten()) + likelihood.logpdf(f_hat, Y, Y_metadata=Y_metadata) - np.sum(np.log(np.diag(L)))
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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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dW_df = -likelihood.d3logpdf_df3(f_hat, Y, Y_metadata=Y_metadata) # -d3lik_d3fhat
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woodbury_vector = likelihood.dlogpdf_df(f_hat, Y, Y_metadata=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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#BiK, _ = dpotrs(L, K, lower=1)
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#dL_dfhat = 0.5*np.diag(BiK)[:, None]*dW_df
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@ -180,7 +180,7 @@ class Laplace(object):
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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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dlik_dthetaL, dlik_grad_dthetaL, dlik_hess_dthetaL = likelihood._laplace_gradients(f_hat, Y, Y_metadata=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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@ -95,7 +95,7 @@ class Bernoulli(Likelihood):
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return np.nan
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#raise NotImplementedError
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def pdf_link(self, link_f, y, extra_data=None):
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def pdf_link(self, link_f, y, Y_metadata=None):
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"""
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Likelihood function given link(f)
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@ -106,7 +106,7 @@ class Bernoulli(Likelihood):
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:type link_f: Nx1 array
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:param y: data
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:type y: Nx1 array
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:param extra_data: extra_data not used in bernoulli
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:param Y_metadata: Y_metadata not used in bernoulli
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:returns: likelihood evaluated for this point
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:rtype: float
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@ -118,7 +118,7 @@ class Bernoulli(Likelihood):
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objective = np.where(y, link_f, 1.-link_f)
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return np.exp(np.sum(np.log(objective)))
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def logpdf_link(self, link_f, y, extra_data=None):
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def logpdf_link(self, link_f, y, Y_metadata=None):
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"""
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Log Likelihood function given link(f)
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@ -129,7 +129,7 @@ class Bernoulli(Likelihood):
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:type link_f: Nx1 array
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:param y: data
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:type y: Nx1 array
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:param extra_data: extra_data not used in bernoulli
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:param Y_metadata: Y_metadata not used in bernoulli
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:returns: log likelihood evaluated at points link(f)
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:rtype: float
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"""
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@ -140,7 +140,7 @@ class Bernoulli(Likelihood):
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np.seterr(**state)
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return np.sum(objective)
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def dlogpdf_dlink(self, link_f, y, extra_data=None):
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def dlogpdf_dlink(self, link_f, y, Y_metadata=None):
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"""
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Gradient of the pdf at y, given link(f) w.r.t link(f)
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@ -151,7 +151,7 @@ class Bernoulli(Likelihood):
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:type link_f: Nx1 array
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:param y: data
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:type y: Nx1 array
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:param extra_data: extra_data not used in bernoulli
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:param Y_metadata: Y_metadata not used in bernoulli
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:returns: gradient of log likelihood evaluated at points link(f)
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:rtype: Nx1 array
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"""
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@ -162,7 +162,7 @@ class Bernoulli(Likelihood):
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np.seterr(**state)
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return grad
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def d2logpdf_dlink2(self, link_f, y, extra_data=None):
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def d2logpdf_dlink2(self, link_f, y, Y_metadata=None):
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"""
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Hessian at y, given link_f, w.r.t link_f the hessian will be 0 unless i == j
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i.e. second derivative logpdf at y given link(f_i) link(f_j) w.r.t link(f_i) and link(f_j)
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@ -175,7 +175,7 @@ class Bernoulli(Likelihood):
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:type link_f: Nx1 array
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:param y: data
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:type y: Nx1 array
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:param extra_data: extra_data not used in bernoulli
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:param Y_metadata: Y_metadata not used in bernoulli
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:returns: Diagonal of log hessian matrix (second derivative of log likelihood evaluated at points link(f))
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:rtype: Nx1 array
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@ -190,7 +190,7 @@ class Bernoulli(Likelihood):
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np.seterr(**state)
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return d2logpdf_dlink2
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def d3logpdf_dlink3(self, link_f, y, extra_data=None):
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def d3logpdf_dlink3(self, link_f, y, Y_metadata=None):
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"""
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Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
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@ -201,7 +201,7 @@ class Bernoulli(Likelihood):
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:type link_f: Nx1 array
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:param y: data
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:type y: Nx1 array
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:param extra_data: extra_data not used in bernoulli
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:param Y_metadata: Y_metadata not used in bernoulli
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:returns: third derivative of log likelihood evaluated at points link(f)
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:rtype: Nx1 array
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"""
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@ -18,13 +18,12 @@ class Exponential(Likelihood):
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L(x) = \exp(\lambda) * \lambda**Y_i / Y_i!
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$$
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"""
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def __init__(self,gp_link=None,analytical_mean=False,analytical_variance=False):
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super(Exponential, self).__init__(gp_link,analytical_mean,analytical_variance)
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def __init__(self,gp_link=None):
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if gp_link is None:
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gp_link = link_functions.Log()
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super(Exponential, self).__init__(gp_link, 'ExpLikelihood')
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def _preprocess_values(self,Y):
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return Y
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def pdf_link(self, link_f, y, extra_data=None):
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def pdf_link(self, link_f, y, Y_metadata=None):
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"""
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Likelihood function given link(f)
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@ -35,16 +34,15 @@ class Exponential(Likelihood):
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:type link_f: Nx1 array
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:param y: data
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:type y: Nx1 array
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:param extra_data: extra_data which is not used in exponential distribution
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:param Y_metadata: Y_metadata which is not used in exponential distribution
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:returns: likelihood evaluated for this point
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:rtype: float
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"""
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assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
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log_objective = link_f*np.exp(-y*link_f)
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return np.exp(np.sum(np.log(log_objective)))
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#return np.exp(np.sum(-y/link_f - np.log(link_f) ))
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def logpdf_link(self, link_f, y, extra_data=None):
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def logpdf_link(self, link_f, y, Y_metadata=None):
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"""
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Log Likelihood Function given link(f)
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@ -55,17 +53,16 @@ class Exponential(Likelihood):
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:type link_f: Nx1 array
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:param y: data
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:type y: Nx1 array
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:param extra_data: extra_data which is not used in exponential distribution
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:param Y_metadata: Y_metadata which is not used in exponential distribution
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:returns: likelihood evaluated for this point
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:rtype: float
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"""
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assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
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log_objective = np.log(link_f) - y*link_f
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#logpdf_link = np.sum(-np.log(link_f) - y/link_f)
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return np.sum(log_objective)
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def dlogpdf_dlink(self, link_f, y, extra_data=None):
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def dlogpdf_dlink(self, link_f, y, Y_metadata=None):
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"""
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Gradient of the log likelihood function at y, given link(f) w.r.t link(f)
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@ -76,7 +73,7 @@ class Exponential(Likelihood):
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:type link_f: Nx1 array
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:param y: data
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:type y: Nx1 array
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:param extra_data: extra_data which is not used in exponential distribution
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:param Y_metadata: Y_metadata which is not used in exponential distribution
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:returns: gradient of likelihood evaluated at points
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:rtype: Nx1 array
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@ -86,7 +83,7 @@ class Exponential(Likelihood):
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#grad = y/(link_f**2) - 1./link_f
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return grad
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def d2logpdf_dlink2(self, link_f, y, extra_data=None):
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def d2logpdf_dlink2(self, link_f, y, Y_metadata=None):
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"""
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Hessian at y, given link(f), w.r.t link(f)
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i.e. second derivative logpdf at y given link(f_i) and link(f_j) w.r.t link(f_i) and link(f_j)
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@ -99,7 +96,7 @@ class Exponential(Likelihood):
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:type link_f: Nx1 array
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:param y: data
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:type y: Nx1 array
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:param extra_data: extra_data which is not used in exponential distribution
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:param Y_metadata: Y_metadata which is not used in exponential distribution
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:returns: Diagonal of hessian matrix (second derivative of likelihood evaluated at points f)
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:rtype: Nx1 array
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@ -112,7 +109,7 @@ class Exponential(Likelihood):
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#hess = -2*y/(link_f**3) + 1/(link_f**2)
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return hess
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def d3logpdf_dlink3(self, link_f, y, extra_data=None):
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def d3logpdf_dlink3(self, link_f, y, Y_metadata=None):
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"""
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Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
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@ -123,7 +120,7 @@ class Exponential(Likelihood):
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:type link_f: Nx1 array
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:param y: data
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:type y: Nx1 array
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:param extra_data: extra_data which is not used in exponential distribution
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:param Y_metadata: Y_metadata which is not used in exponential distribution
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:returns: third derivative of likelihood evaluated at points f
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:rtype: Nx1 array
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"""
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@ -132,18 +129,6 @@ class Exponential(Likelihood):
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#d3lik_dlink3 = 6*y/(link_f**4) - 2./(link_f**3)
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return d3lik_dlink3
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def _mean(self,gp):
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"""
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Mass (or density) function
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"""
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return self.gp_link.transf(gp)
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def _variance(self,gp):
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"""
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Mass (or density) function
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"""
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return self.gp_link.transf(gp)**2
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def samples(self, gp):
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"""
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Returns a set of samples of observations based on a given value of the latent variable.
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@ -1,11 +1,12 @@
|
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# Copyright (c) 2012, 2013 Ricardo Andrade
|
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# Copyright (c) 2012 - 2014, GPy authors (see AUTHORS.txt).
|
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
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|
||||
|
||||
import numpy as np
|
||||
from scipy import stats,special
|
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import scipy as sp
|
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from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf
|
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from ..util.univariate_Gaussian import std_norm_pdf,std_norm_cdf
|
||||
from ..core.parameterization import Param
|
||||
import link_functions
|
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from likelihood import Likelihood
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|
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|
|
@ -18,14 +19,16 @@ class Gamma(Likelihood):
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\\alpha_{i} = \\beta y_{i}
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||||
|
||||
"""
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||||
def __init__(self,gp_link=None,analytical_mean=False,analytical_variance=False,beta=1.):
|
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self.beta = beta
|
||||
super(Gamma, self).__init__(gp_link,analytical_mean,analytical_variance)
|
||||
def __init__(self,gp_link=None,beta=1.):
|
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if gp_link is None:
|
||||
gp_link = link_functions.Log()
|
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super(Gamma, self).__init__(gp_link, 'Gamma')
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|
||||
def _preprocess_values(self,Y):
|
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return Y
|
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self.beta = Param('beta', beta)
|
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self.add_parameter(self.beta)
|
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self.beta.fix()#TODO: gradients!
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|
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def pdf_link(self, link_f, y, extra_data=None):
|
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def pdf_link(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Likelihood function given link(f)
|
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|
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|
|
@ -37,7 +40,7 @@ class Gamma(Likelihood):
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|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in poisson distribution
|
||||
:param Y_metadata: Y_metadata which is not used in poisson distribution
|
||||
:returns: likelihood evaluated for this point
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||||
:rtype: float
|
||||
"""
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|
|
@ -47,7 +50,7 @@ class Gamma(Likelihood):
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objective = (y**(alpha - 1.) * np.exp(-self.beta*y) * self.beta**alpha)/ special.gamma(alpha)
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return np.exp(np.sum(np.log(objective)))
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|
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def logpdf_link(self, link_f, y, extra_data=None):
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def logpdf_link(self, link_f, y, Y_metadata=None):
|
||||
"""
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||||
Log Likelihood Function given link(f)
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|
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@ -59,7 +62,7 @@ class Gamma(Likelihood):
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:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in poisson distribution
|
||||
:param Y_metadata: Y_metadata which is not used in poisson distribution
|
||||
:returns: likelihood evaluated for this point
|
||||
:rtype: float
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@ -71,7 +74,7 @@ class Gamma(Likelihood):
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log_objective = alpha*np.log(self.beta) - np.log(special.gamma(alpha)) + (alpha - 1)*np.log(y) - self.beta*y
|
||||
return np.sum(log_objective)
|
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|
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def dlogpdf_dlink(self, link_f, y, extra_data=None):
|
||||
def dlogpdf_dlink(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Gradient of the log likelihood function at y, given link(f) w.r.t link(f)
|
||||
|
||||
|
|
@ -83,7 +86,7 @@ class Gamma(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in gamma distribution
|
||||
:param Y_metadata: Y_metadata which is not used in gamma distribution
|
||||
:returns: gradient of likelihood evaluated at points
|
||||
:rtype: Nx1 array
|
||||
|
||||
|
|
@ -94,7 +97,7 @@ class Gamma(Likelihood):
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#return -self.gp_link.dtransf_df(gp)*self.beta*np.log(obs) + special.psi(self.gp_link.transf(gp)*self.beta) * self.gp_link.dtransf_df(gp)*self.beta
|
||||
return grad
|
||||
|
||||
def d2logpdf_dlink2(self, link_f, y, extra_data=None):
|
||||
def d2logpdf_dlink2(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Hessian at y, given link(f), w.r.t link(f)
|
||||
i.e. second derivative logpdf at y given link(f_i) and link(f_j) w.r.t link(f_i) and link(f_j)
|
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|
|
@ -108,7 +111,7 @@ class Gamma(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in gamma distribution
|
||||
:param Y_metadata: Y_metadata which is not used in gamma distribution
|
||||
:returns: Diagonal of hessian matrix (second derivative of likelihood evaluated at points f)
|
||||
:rtype: Nx1 array
|
||||
|
||||
|
|
@ -122,7 +125,7 @@ class Gamma(Likelihood):
|
|||
#return -self.gp_link.d2transf_df2(gp)*self.beta*np.log(obs) + special.polygamma(1,self.gp_link.transf(gp)*self.beta)*(self.gp_link.dtransf_df(gp)*self.beta)**2 + special.psi(self.gp_link.transf(gp)*self.beta)*self.gp_link.d2transf_df2(gp)*self.beta
|
||||
return hess
|
||||
|
||||
def d3logpdf_dlink3(self, link_f, y, extra_data=None):
|
||||
def d3logpdf_dlink3(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
|
||||
|
||||
|
|
@ -134,22 +137,10 @@ class Gamma(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in gamma distribution
|
||||
:param Y_metadata: Y_metadata which is not used in gamma distribution
|
||||
:returns: third derivative of likelihood evaluated at points f
|
||||
:rtype: Nx1 array
|
||||
"""
|
||||
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
|
||||
d3lik_dlink3 = -special.polygamma(2, self.beta*link_f)*(self.beta**3)
|
||||
return d3lik_dlink3
|
||||
|
||||
def _mean(self,gp):
|
||||
"""
|
||||
Mass (or density) function
|
||||
"""
|
||||
return self.gp_link.transf(gp)
|
||||
|
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def _variance(self,gp):
|
||||
"""
|
||||
Mass (or density) function
|
||||
"""
|
||||
return self.gp_link.transf(gp)/self.beta
|
||||
|
|
|
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|
|
@ -93,7 +93,7 @@ class Gaussian(Likelihood):
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|||
def predictive_variance(self, mu, sigma, predictive_mean=None):
|
||||
return self.variance + sigma**2
|
||||
|
||||
def pdf_link(self, link_f, y, extra_data=None):
|
||||
def pdf_link(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Likelihood function given link(f)
|
||||
|
||||
|
|
@ -104,14 +104,14 @@ class Gaussian(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data not used in gaussian
|
||||
:param Y_metadata: Y_metadata not used in gaussian
|
||||
:returns: likelihood evaluated for this point
|
||||
:rtype: float
|
||||
"""
|
||||
#Assumes no covariance, exp, sum, log for numerical stability
|
||||
return np.exp(np.sum(np.log(stats.norm.pdf(y, link_f, np.sqrt(self.variance)))))
|
||||
|
||||
def logpdf_link(self, link_f, y, extra_data=None):
|
||||
def logpdf_link(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Log likelihood function given link(f)
|
||||
|
||||
|
|
@ -122,7 +122,7 @@ class Gaussian(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data not used in gaussian
|
||||
:param Y_metadata: Y_metadata not used in gaussian
|
||||
:returns: log likelihood evaluated for this point
|
||||
:rtype: float
|
||||
"""
|
||||
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|
@ -132,7 +132,7 @@ class Gaussian(Likelihood):
|
|||
|
||||
return -0.5*(np.sum((y-link_f)**2/self.variance) + ln_det_cov + N*np.log(2.*np.pi))
|
||||
|
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def dlogpdf_dlink(self, link_f, y, extra_data=None):
|
||||
def dlogpdf_dlink(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Gradient of the pdf at y, given link(f) w.r.t link(f)
|
||||
|
||||
|
|
@ -143,7 +143,7 @@ class Gaussian(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data not used in gaussian
|
||||
:param Y_metadata: Y_metadata not used in gaussian
|
||||
:returns: gradient of log likelihood evaluated at points link(f)
|
||||
:rtype: Nx1 array
|
||||
"""
|
||||
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|
@ -152,7 +152,7 @@ class Gaussian(Likelihood):
|
|||
grad = s2_i*y - s2_i*link_f
|
||||
return grad
|
||||
|
||||
def d2logpdf_dlink2(self, link_f, y, extra_data=None):
|
||||
def d2logpdf_dlink2(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Hessian at y, given link_f, w.r.t link_f.
|
||||
i.e. second derivative logpdf at y given link(f_i) link(f_j) w.r.t link(f_i) and link(f_j)
|
||||
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|
@ -166,7 +166,7 @@ class Gaussian(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data not used in gaussian
|
||||
:param Y_metadata: Y_metadata not used in gaussian
|
||||
:returns: Diagonal of log hessian matrix (second derivative of log likelihood evaluated at points link(f))
|
||||
:rtype: Nx1 array
|
||||
|
||||
|
|
@ -179,7 +179,7 @@ class Gaussian(Likelihood):
|
|||
hess = -(1.0/self.variance)*np.ones((N, 1))
|
||||
return hess
|
||||
|
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def d3logpdf_dlink3(self, link_f, y, extra_data=None):
|
||||
def d3logpdf_dlink3(self, link_f, y, Y_metadata=None):
|
||||
"""
|
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Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
|
||||
|
||||
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@ -190,7 +190,7 @@ class Gaussian(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data not used in gaussian
|
||||
:param Y_metadata: Y_metadata not used in gaussian
|
||||
:returns: third derivative of log likelihood evaluated at points link(f)
|
||||
:rtype: Nx1 array
|
||||
"""
|
||||
|
|
@ -199,7 +199,7 @@ class Gaussian(Likelihood):
|
|||
d3logpdf_dlink3 = np.zeros((N,1))
|
||||
return d3logpdf_dlink3
|
||||
|
||||
def dlogpdf_link_dvar(self, link_f, y, extra_data=None):
|
||||
def dlogpdf_link_dvar(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Gradient of the log-likelihood function at y given link(f), w.r.t variance parameter (noise_variance)
|
||||
|
||||
|
|
@ -210,7 +210,7 @@ class Gaussian(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data not used in gaussian
|
||||
:param Y_metadata: Y_metadata not used in gaussian
|
||||
:returns: derivative of log likelihood evaluated at points link(f) w.r.t variance parameter
|
||||
:rtype: float
|
||||
"""
|
||||
|
|
@ -221,7 +221,7 @@ class Gaussian(Likelihood):
|
|||
dlik_dsigma = -0.5*N/self.variance + 0.5*s_4*np.sum(np.square(e))
|
||||
return np.sum(dlik_dsigma) # Sure about this sum?
|
||||
|
||||
def dlogpdf_dlink_dvar(self, link_f, y, extra_data=None):
|
||||
def dlogpdf_dlink_dvar(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Derivative of the dlogpdf_dlink w.r.t variance parameter (noise_variance)
|
||||
|
||||
|
|
@ -232,7 +232,7 @@ class Gaussian(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data not used in gaussian
|
||||
:param Y_metadata: Y_metadata not used in gaussian
|
||||
:returns: derivative of log likelihood evaluated at points link(f) w.r.t variance parameter
|
||||
:rtype: Nx1 array
|
||||
"""
|
||||
|
|
@ -241,7 +241,7 @@ class Gaussian(Likelihood):
|
|||
dlik_grad_dsigma = -s_4*y + s_4*link_f
|
||||
return dlik_grad_dsigma
|
||||
|
||||
def d2logpdf_dlink2_dvar(self, link_f, y, extra_data=None):
|
||||
def d2logpdf_dlink2_dvar(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Gradient of the hessian (d2logpdf_dlink2) w.r.t variance parameter (noise_variance)
|
||||
|
||||
|
|
@ -252,7 +252,7 @@ class Gaussian(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data not used in gaussian
|
||||
:param Y_metadata: Y_metadata not used in gaussian
|
||||
:returns: derivative of log hessian evaluated at points link(f_i) and link(f_j) w.r.t variance parameter
|
||||
:rtype: Nx1 array
|
||||
"""
|
||||
|
|
@ -262,16 +262,16 @@ class Gaussian(Likelihood):
|
|||
d2logpdf_dlink2_dvar = np.ones((N,1))*s_4
|
||||
return d2logpdf_dlink2_dvar
|
||||
|
||||
def dlogpdf_link_dtheta(self, f, y, extra_data=None):
|
||||
dlogpdf_dvar = self.dlogpdf_link_dvar(f, y, extra_data=extra_data)
|
||||
def dlogpdf_link_dtheta(self, f, y, Y_metadata=None):
|
||||
dlogpdf_dvar = self.dlogpdf_link_dvar(f, y, Y_metadata=Y_metadata)
|
||||
return np.asarray([[dlogpdf_dvar]])
|
||||
|
||||
def dlogpdf_dlink_dtheta(self, f, y, extra_data=None):
|
||||
dlogpdf_dlink_dvar = self.dlogpdf_dlink_dvar(f, y, extra_data=extra_data)
|
||||
def dlogpdf_dlink_dtheta(self, f, y, Y_metadata=None):
|
||||
dlogpdf_dlink_dvar = self.dlogpdf_dlink_dvar(f, y, Y_metadata=Y_metadata)
|
||||
return dlogpdf_dlink_dvar
|
||||
|
||||
def d2logpdf_dlink2_dtheta(self, f, y, extra_data=None):
|
||||
d2logpdf_dlink2_dvar = self.d2logpdf_dlink2_dvar(f, y, extra_data=extra_data)
|
||||
def d2logpdf_dlink2_dtheta(self, f, y, Y_metadata=None):
|
||||
d2logpdf_dlink2_dvar = self.d2logpdf_dlink2_dvar(f, y, Y_metadata=Y_metadata)
|
||||
return d2logpdf_dlink2_dvar
|
||||
|
||||
def _mean(self, gp):
|
||||
|
|
|
|||
|
|
@ -174,31 +174,31 @@ class Likelihood(Parameterized):
|
|||
# V(Y_star) = E( V(Y_star|f_star) ) + V( E(Y_star|f_star) )
|
||||
return exp_var + var_exp
|
||||
|
||||
def pdf_link(self, link_f, y, extra_data=None):
|
||||
def pdf_link(self, link_f, y, Y_metadata=None):
|
||||
raise NotImplementedError
|
||||
|
||||
def logpdf_link(self, link_f, y, extra_data=None):
|
||||
def logpdf_link(self, link_f, y, Y_metadata=None):
|
||||
raise NotImplementedError
|
||||
|
||||
def dlogpdf_dlink(self, link_f, y, extra_data=None):
|
||||
def dlogpdf_dlink(self, link_f, y, Y_metadata=None):
|
||||
raise NotImplementedError
|
||||
|
||||
def d2logpdf_dlink2(self, link_f, y, extra_data=None):
|
||||
def d2logpdf_dlink2(self, link_f, y, Y_metadata=None):
|
||||
raise NotImplementedError
|
||||
|
||||
def d3logpdf_dlink3(self, link_f, y, extra_data=None):
|
||||
def d3logpdf_dlink3(self, link_f, y, Y_metadata=None):
|
||||
raise NotImplementedError
|
||||
|
||||
def dlogpdf_link_dtheta(self, link_f, y, extra_data=None):
|
||||
def dlogpdf_link_dtheta(self, link_f, y, Y_metadata=None):
|
||||
raise NotImplementedError
|
||||
|
||||
def dlogpdf_dlink_dtheta(self, link_f, y, extra_data=None):
|
||||
def dlogpdf_dlink_dtheta(self, link_f, y, Y_metadata=None):
|
||||
raise NotImplementedError
|
||||
|
||||
def d2logpdf_dlink2_dtheta(self, link_f, y, extra_data=None):
|
||||
def d2logpdf_dlink2_dtheta(self, link_f, y, Y_metadata=None):
|
||||
raise NotImplementedError
|
||||
|
||||
def pdf(self, f, y, extra_data=None):
|
||||
def pdf(self, f, y, Y_metadata=None):
|
||||
"""
|
||||
Evaluates the link function link(f) then computes the likelihood (pdf) using it
|
||||
|
||||
|
|
@ -209,14 +209,14 @@ class Likelihood(Parameterized):
|
|||
:type f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in student t distribution - not used
|
||||
:param Y_metadata: Y_metadata which is not used in student t distribution - not used
|
||||
:returns: likelihood evaluated for this point
|
||||
:rtype: float
|
||||
"""
|
||||
link_f = self.gp_link.transf(f)
|
||||
return self.pdf_link(link_f, y, extra_data=extra_data)
|
||||
return self.pdf_link(link_f, y, Y_metadata=Y_metadata)
|
||||
|
||||
def logpdf(self, f, y, extra_data=None):
|
||||
def logpdf(self, f, y, Y_metadata=None):
|
||||
"""
|
||||
Evaluates the link function link(f) then computes the log likelihood (log pdf) using it
|
||||
|
||||
|
|
@ -227,14 +227,14 @@ class Likelihood(Parameterized):
|
|||
:type f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in student t distribution - not used
|
||||
:param Y_metadata: Y_metadata which is not used in student t distribution - not used
|
||||
:returns: log likelihood evaluated for this point
|
||||
:rtype: float
|
||||
"""
|
||||
link_f = self.gp_link.transf(f)
|
||||
return self.logpdf_link(link_f, y, extra_data=extra_data)
|
||||
return self.logpdf_link(link_f, y, Y_metadata=Y_metadata)
|
||||
|
||||
def dlogpdf_df(self, f, y, extra_data=None):
|
||||
def dlogpdf_df(self, f, y, Y_metadata=None):
|
||||
"""
|
||||
Evaluates the link function link(f) then computes the derivative of log likelihood using it
|
||||
Uses the Faa di Bruno's formula for the chain rule
|
||||
|
|
@ -246,16 +246,16 @@ class Likelihood(Parameterized):
|
|||
:type f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in student t distribution - not used
|
||||
:param Y_metadata: Y_metadata which is not used in student t distribution - not used
|
||||
:returns: derivative of log likelihood evaluated for this point
|
||||
:rtype: 1xN array
|
||||
"""
|
||||
link_f = self.gp_link.transf(f)
|
||||
dlogpdf_dlink = self.dlogpdf_dlink(link_f, y, extra_data=extra_data)
|
||||
dlogpdf_dlink = self.dlogpdf_dlink(link_f, y, Y_metadata=Y_metadata)
|
||||
dlink_df = self.gp_link.dtransf_df(f)
|
||||
return chain_1(dlogpdf_dlink, dlink_df)
|
||||
|
||||
def d2logpdf_df2(self, f, y, extra_data=None):
|
||||
def d2logpdf_df2(self, f, y, Y_metadata=None):
|
||||
"""
|
||||
Evaluates the link function link(f) then computes the second derivative of log likelihood using it
|
||||
Uses the Faa di Bruno's formula for the chain rule
|
||||
|
|
@ -267,18 +267,18 @@ class Likelihood(Parameterized):
|
|||
:type f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in student t distribution - not used
|
||||
:param Y_metadata: Y_metadata which is not used in student t distribution - not used
|
||||
:returns: second derivative of log likelihood evaluated for this point (diagonal only)
|
||||
:rtype: 1xN array
|
||||
"""
|
||||
link_f = self.gp_link.transf(f)
|
||||
d2logpdf_dlink2 = self.d2logpdf_dlink2(link_f, y, extra_data=extra_data)
|
||||
d2logpdf_dlink2 = self.d2logpdf_dlink2(link_f, y, Y_metadata=Y_metadata)
|
||||
dlink_df = self.gp_link.dtransf_df(f)
|
||||
dlogpdf_dlink = self.dlogpdf_dlink(link_f, y, extra_data=extra_data)
|
||||
dlogpdf_dlink = self.dlogpdf_dlink(link_f, y, Y_metadata=Y_metadata)
|
||||
d2link_df2 = self.gp_link.d2transf_df2(f)
|
||||
return chain_2(d2logpdf_dlink2, dlink_df, dlogpdf_dlink, d2link_df2)
|
||||
|
||||
def d3logpdf_df3(self, f, y, extra_data=None):
|
||||
def d3logpdf_df3(self, f, y, Y_metadata=None):
|
||||
"""
|
||||
Evaluates the link function link(f) then computes the third derivative of log likelihood using it
|
||||
Uses the Faa di Bruno's formula for the chain rule
|
||||
|
|
@ -290,44 +290,44 @@ class Likelihood(Parameterized):
|
|||
:type f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in student t distribution - not used
|
||||
:param Y_metadata: Y_metadata which is not used in student t distribution - not used
|
||||
:returns: third derivative of log likelihood evaluated for this point
|
||||
:rtype: float
|
||||
"""
|
||||
link_f = self.gp_link.transf(f)
|
||||
d3logpdf_dlink3 = self.d3logpdf_dlink3(link_f, y, extra_data=extra_data)
|
||||
d3logpdf_dlink3 = self.d3logpdf_dlink3(link_f, y, Y_metadata=Y_metadata)
|
||||
dlink_df = self.gp_link.dtransf_df(f)
|
||||
d2logpdf_dlink2 = self.d2logpdf_dlink2(link_f, y, extra_data=extra_data)
|
||||
d2logpdf_dlink2 = self.d2logpdf_dlink2(link_f, y, Y_metadata=Y_metadata)
|
||||
d2link_df2 = self.gp_link.d2transf_df2(f)
|
||||
dlogpdf_dlink = self.dlogpdf_dlink(link_f, y, extra_data=extra_data)
|
||||
dlogpdf_dlink = self.dlogpdf_dlink(link_f, y, Y_metadata=Y_metadata)
|
||||
d3link_df3 = self.gp_link.d3transf_df3(f)
|
||||
return chain_3(d3logpdf_dlink3, dlink_df, d2logpdf_dlink2, d2link_df2, dlogpdf_dlink, d3link_df3)
|
||||
|
||||
def dlogpdf_dtheta(self, f, y, extra_data=None):
|
||||
def dlogpdf_dtheta(self, f, y, Y_metadata=None):
|
||||
"""
|
||||
TODO: Doc strings
|
||||
"""
|
||||
if self.size > 0:
|
||||
link_f = self.gp_link.transf(f)
|
||||
return self.dlogpdf_link_dtheta(link_f, y, extra_data=extra_data)
|
||||
return self.dlogpdf_link_dtheta(link_f, y, Y_metadata=Y_metadata)
|
||||
else:
|
||||
#Is no parameters so return an empty array for its derivatives
|
||||
return np.zeros([1, 0])
|
||||
|
||||
def dlogpdf_df_dtheta(self, f, y, extra_data=None):
|
||||
def dlogpdf_df_dtheta(self, f, y, Y_metadata=None):
|
||||
"""
|
||||
TODO: Doc strings
|
||||
"""
|
||||
if self.size > 0:
|
||||
link_f = self.gp_link.transf(f)
|
||||
dlink_df = self.gp_link.dtransf_df(f)
|
||||
dlogpdf_dlink_dtheta = self.dlogpdf_dlink_dtheta(link_f, y, extra_data=extra_data)
|
||||
dlogpdf_dlink_dtheta = self.dlogpdf_dlink_dtheta(link_f, y, Y_metadata=Y_metadata)
|
||||
return chain_1(dlogpdf_dlink_dtheta, dlink_df)
|
||||
else:
|
||||
#Is no parameters so return an empty array for its derivatives
|
||||
return np.zeros([f.shape[0], 0])
|
||||
|
||||
def d2logpdf_df2_dtheta(self, f, y, extra_data=None):
|
||||
def d2logpdf_df2_dtheta(self, f, y, Y_metadata=None):
|
||||
"""
|
||||
TODO: Doc strings
|
||||
"""
|
||||
|
|
@ -335,17 +335,17 @@ class Likelihood(Parameterized):
|
|||
link_f = self.gp_link.transf(f)
|
||||
dlink_df = self.gp_link.dtransf_df(f)
|
||||
d2link_df2 = self.gp_link.d2transf_df2(f)
|
||||
d2logpdf_dlink2_dtheta = self.d2logpdf_dlink2_dtheta(link_f, y, extra_data=extra_data)
|
||||
dlogpdf_dlink_dtheta = self.dlogpdf_dlink_dtheta(link_f, y, extra_data=extra_data)
|
||||
d2logpdf_dlink2_dtheta = self.d2logpdf_dlink2_dtheta(link_f, y, Y_metadata=Y_metadata)
|
||||
dlogpdf_dlink_dtheta = self.dlogpdf_dlink_dtheta(link_f, y, Y_metadata=Y_metadata)
|
||||
return chain_2(d2logpdf_dlink2_dtheta, dlink_df, dlogpdf_dlink_dtheta, d2link_df2)
|
||||
else:
|
||||
#Is no parameters so return an empty array for its derivatives
|
||||
return np.zeros([f.shape[0], 0])
|
||||
|
||||
def _laplace_gradients(self, f, y, extra_data=None):
|
||||
dlogpdf_dtheta = self.dlogpdf_dtheta(f, y, extra_data=extra_data)
|
||||
dlogpdf_df_dtheta = self.dlogpdf_df_dtheta(f, y, extra_data=extra_data)
|
||||
d2logpdf_df2_dtheta = self.d2logpdf_df2_dtheta(f, y, extra_data=extra_data)
|
||||
def _laplace_gradients(self, f, y, Y_metadata=None):
|
||||
dlogpdf_dtheta = self.dlogpdf_dtheta(f, y, Y_metadata=Y_metadata)
|
||||
dlogpdf_df_dtheta = self.dlogpdf_df_dtheta(f, y, Y_metadata=Y_metadata)
|
||||
d2logpdf_df2_dtheta = self.d2logpdf_df2_dtheta(f, y, Y_metadata=Y_metadata)
|
||||
|
||||
#Parameters are stacked vertically. Must be listed in same order as 'get_param_names'
|
||||
# ensure we have gradients for every parameter we want to optimize
|
||||
|
|
|
|||
|
|
@ -28,7 +28,7 @@ class Poisson(Likelihood):
|
|||
def _preprocess_values(self,Y):
|
||||
return Y
|
||||
|
||||
def pdf_link(self, link_f, y, extra_data=None):
|
||||
def pdf_link(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Likelihood function given link(f)
|
||||
|
||||
|
|
@ -39,14 +39,14 @@ class Poisson(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in poisson distribution
|
||||
:param Y_metadata: Y_metadata which is not used in poisson distribution
|
||||
:returns: likelihood evaluated for this point
|
||||
:rtype: float
|
||||
"""
|
||||
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
|
||||
return np.prod(stats.poisson.pmf(y,link_f))
|
||||
|
||||
def logpdf_link(self, link_f, y, extra_data=None):
|
||||
def logpdf_link(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Log Likelihood Function given link(f)
|
||||
|
||||
|
|
@ -57,7 +57,7 @@ class Poisson(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in poisson distribution
|
||||
:param Y_metadata: Y_metadata which is not used in poisson distribution
|
||||
:returns: likelihood evaluated for this point
|
||||
:rtype: float
|
||||
|
||||
|
|
@ -65,7 +65,7 @@ class Poisson(Likelihood):
|
|||
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
|
||||
return np.sum(-link_f + y*np.log(link_f) - special.gammaln(y+1))
|
||||
|
||||
def dlogpdf_dlink(self, link_f, y, extra_data=None):
|
||||
def dlogpdf_dlink(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Gradient of the log likelihood function at y, given link(f) w.r.t link(f)
|
||||
|
||||
|
|
@ -76,7 +76,7 @@ class Poisson(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in poisson distribution
|
||||
:param Y_metadata: Y_metadata which is not used in poisson distribution
|
||||
:returns: gradient of likelihood evaluated at points
|
||||
:rtype: Nx1 array
|
||||
|
||||
|
|
@ -84,7 +84,7 @@ class Poisson(Likelihood):
|
|||
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
|
||||
return y/link_f - 1
|
||||
|
||||
def d2logpdf_dlink2(self, link_f, y, extra_data=None):
|
||||
def d2logpdf_dlink2(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Hessian at y, given link(f), w.r.t link(f)
|
||||
i.e. second derivative logpdf at y given link(f_i) and link(f_j) w.r.t link(f_i) and link(f_j)
|
||||
|
|
@ -97,7 +97,7 @@ class Poisson(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in poisson distribution
|
||||
:param Y_metadata: Y_metadata which is not used in poisson distribution
|
||||
:returns: Diagonal of hessian matrix (second derivative of likelihood evaluated at points f)
|
||||
:rtype: Nx1 array
|
||||
|
||||
|
|
@ -112,7 +112,7 @@ class Poisson(Likelihood):
|
|||
#transf = self.gp_link.transf(gp)
|
||||
#return obs * ((self.gp_link.dtransf_df(gp)/transf)**2 - d2_df/transf) + d2_df
|
||||
|
||||
def d3logpdf_dlink3(self, link_f, y, extra_data=None):
|
||||
def d3logpdf_dlink3(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
|
||||
|
||||
|
|
@ -123,7 +123,7 @@ class Poisson(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in poisson distribution
|
||||
:param Y_metadata: Y_metadata which is not used in poisson distribution
|
||||
:returns: third derivative of likelihood evaluated at points f
|
||||
:rtype: Nx1 array
|
||||
"""
|
||||
|
|
@ -131,18 +131,6 @@ class Poisson(Likelihood):
|
|||
d3lik_dlink3 = 2*y/(link_f)**3
|
||||
return d3lik_dlink3
|
||||
|
||||
def _mean(self,gp):
|
||||
"""
|
||||
Mass (or density) function
|
||||
"""
|
||||
return self.gp_link.transf(gp)
|
||||
|
||||
def _variance(self,gp):
|
||||
"""
|
||||
Mass (or density) function
|
||||
"""
|
||||
return self.gp_link.transf(gp)
|
||||
|
||||
def samples(self, gp):
|
||||
"""
|
||||
Returns a set of samples of observations based on a given value of the latent variable.
|
||||
|
|
|
|||
|
|
@ -37,15 +37,15 @@ class StudentT(Likelihood):
|
|||
def parameters_changed(self):
|
||||
self.variance = (self.v / float(self.v - 2)) * self.sigma2
|
||||
|
||||
def update_gradients(self, partial):
|
||||
def update_gradients(self, derivatives):
|
||||
"""
|
||||
Pull out the gradients, be careful as the order must match the order
|
||||
in which the parameters are added
|
||||
"""
|
||||
self.sigma2.gradient = partial[0]
|
||||
self.v.gradient = partial[1]
|
||||
self.sigma2.gradient = derivatives[0]
|
||||
self.v.gradient = derivatives[1]
|
||||
|
||||
def pdf_link(self, link_f, y, extra_data=None):
|
||||
def pdf_link(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Likelihood function given link(f)
|
||||
|
||||
|
|
@ -56,7 +56,7 @@ class StudentT(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in student t distribution
|
||||
:param Y_metadata: Y_metadata which is not used in student t distribution
|
||||
:returns: likelihood evaluated for this point
|
||||
:rtype: float
|
||||
"""
|
||||
|
|
@ -69,7 +69,7 @@ class StudentT(Likelihood):
|
|||
)
|
||||
return np.prod(objective)
|
||||
|
||||
def logpdf_link(self, link_f, y, extra_data=None):
|
||||
def logpdf_link(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Log Likelihood Function given link(f)
|
||||
|
||||
|
|
@ -80,7 +80,7 @@ class StudentT(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in student t distribution
|
||||
:param Y_metadata: Y_metadata which is not used in student t distribution
|
||||
:returns: likelihood evaluated for this point
|
||||
:rtype: float
|
||||
|
||||
|
|
@ -98,7 +98,7 @@ class StudentT(Likelihood):
|
|||
)
|
||||
return np.sum(objective)
|
||||
|
||||
def dlogpdf_dlink(self, link_f, y, extra_data=None):
|
||||
def dlogpdf_dlink(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Gradient of the log likelihood function at y, given link(f) w.r.t link(f)
|
||||
|
||||
|
|
@ -109,7 +109,7 @@ class StudentT(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in student t distribution
|
||||
:param Y_metadata: Y_metadata which is not used in student t distribution
|
||||
:returns: gradient of likelihood evaluated at points
|
||||
:rtype: Nx1 array
|
||||
|
||||
|
|
@ -119,7 +119,7 @@ class StudentT(Likelihood):
|
|||
grad = ((self.v + 1) * e) / (self.v * self.sigma2 + (e**2))
|
||||
return grad
|
||||
|
||||
def d2logpdf_dlink2(self, link_f, y, extra_data=None):
|
||||
def d2logpdf_dlink2(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Hessian at y, given link(f), w.r.t link(f)
|
||||
i.e. second derivative logpdf at y given link(f_i) and link(f_j) w.r.t link(f_i) and link(f_j)
|
||||
|
|
@ -132,7 +132,7 @@ class StudentT(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in student t distribution
|
||||
:param Y_metadata: Y_metadata which is not used in student t distribution
|
||||
:returns: Diagonal of hessian matrix (second derivative of likelihood evaluated at points f)
|
||||
:rtype: Nx1 array
|
||||
|
||||
|
|
@ -145,7 +145,7 @@ class StudentT(Likelihood):
|
|||
hess = ((self.v + 1)*(e**2 - self.v*self.sigma2)) / ((self.sigma2*self.v + e**2)**2)
|
||||
return hess
|
||||
|
||||
def d3logpdf_dlink3(self, link_f, y, extra_data=None):
|
||||
def d3logpdf_dlink3(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
|
||||
|
||||
|
|
@ -156,7 +156,7 @@ class StudentT(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in student t distribution
|
||||
:param Y_metadata: Y_metadata which is not used in student t distribution
|
||||
:returns: third derivative of likelihood evaluated at points f
|
||||
:rtype: Nx1 array
|
||||
"""
|
||||
|
|
@ -167,7 +167,7 @@ class StudentT(Likelihood):
|
|||
)
|
||||
return d3lik_dlink3
|
||||
|
||||
def dlogpdf_link_dvar(self, link_f, y, extra_data=None):
|
||||
def dlogpdf_link_dvar(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Gradient of the log-likelihood function at y given f, w.r.t variance parameter (t_noise)
|
||||
|
||||
|
|
@ -178,7 +178,7 @@ class StudentT(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in student t distribution
|
||||
:param Y_metadata: Y_metadata which is not used in student t distribution
|
||||
:returns: derivative of likelihood evaluated at points f w.r.t variance parameter
|
||||
:rtype: float
|
||||
"""
|
||||
|
|
@ -187,7 +187,7 @@ class StudentT(Likelihood):
|
|||
dlogpdf_dvar = self.v*(e**2 - self.sigma2)/(2*self.sigma2*(self.sigma2*self.v + e**2))
|
||||
return np.sum(dlogpdf_dvar)
|
||||
|
||||
def dlogpdf_dlink_dvar(self, link_f, y, extra_data=None):
|
||||
def dlogpdf_dlink_dvar(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Derivative of the dlogpdf_dlink w.r.t variance parameter (t_noise)
|
||||
|
||||
|
|
@ -198,7 +198,7 @@ class StudentT(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in student t distribution
|
||||
:param Y_metadata: Y_metadata which is not used in student t distribution
|
||||
:returns: derivative of likelihood evaluated at points f w.r.t variance parameter
|
||||
:rtype: Nx1 array
|
||||
"""
|
||||
|
|
@ -207,7 +207,7 @@ class StudentT(Likelihood):
|
|||
dlogpdf_dlink_dvar = (self.v*(self.v+1)*(-e))/((self.sigma2*self.v + e**2)**2)
|
||||
return dlogpdf_dlink_dvar
|
||||
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def d2logpdf_dlink2_dvar(self, link_f, y, extra_data=None):
|
||||
def d2logpdf_dlink2_dvar(self, link_f, y, Y_metadata=None):
|
||||
"""
|
||||
Gradient of the hessian (d2logpdf_dlink2) w.r.t variance parameter (t_noise)
|
||||
|
||||
|
|
@ -218,7 +218,7 @@ class StudentT(Likelihood):
|
|||
:type link_f: Nx1 array
|
||||
:param y: data
|
||||
:type y: Nx1 array
|
||||
:param extra_data: extra_data which is not used in student t distribution
|
||||
:param Y_metadata: Y_metadata which is not used in student t distribution
|
||||
:returns: derivative of hessian evaluated at points f and f_j w.r.t variance parameter
|
||||
:rtype: Nx1 array
|
||||
"""
|
||||
|
|
@ -229,18 +229,18 @@ class StudentT(Likelihood):
|
|||
)
|
||||
return d2logpdf_dlink2_dvar
|
||||
|
||||
def dlogpdf_link_dtheta(self, f, y, extra_data=None):
|
||||
dlogpdf_dvar = self.dlogpdf_link_dvar(f, y, extra_data=extra_data)
|
||||
def dlogpdf_link_dtheta(self, f, y, Y_metadata=None):
|
||||
dlogpdf_dvar = self.dlogpdf_link_dvar(f, y, Y_metadata=Y_metadata)
|
||||
dlogpdf_dv = np.zeros_like(dlogpdf_dvar) #FIXME: Not done yet
|
||||
return np.hstack((dlogpdf_dvar, dlogpdf_dv))
|
||||
|
||||
def dlogpdf_dlink_dtheta(self, f, y, extra_data=None):
|
||||
dlogpdf_dlink_dvar = self.dlogpdf_dlink_dvar(f, y, extra_data=extra_data)
|
||||
def dlogpdf_dlink_dtheta(self, f, y, Y_metadata=None):
|
||||
dlogpdf_dlink_dvar = self.dlogpdf_dlink_dvar(f, y, Y_metadata=Y_metadata)
|
||||
dlogpdf_dlink_dv = np.zeros_like(dlogpdf_dlink_dvar) #FIXME: Not done yet
|
||||
return np.hstack((dlogpdf_dlink_dvar, dlogpdf_dlink_dv))
|
||||
|
||||
def d2logpdf_dlink2_dtheta(self, f, y, extra_data=None):
|
||||
d2logpdf_dlink2_dvar = self.d2logpdf_dlink2_dvar(f, y, extra_data=extra_data)
|
||||
def d2logpdf_dlink2_dtheta(self, f, y, Y_metadata=None):
|
||||
d2logpdf_dlink2_dvar = self.d2logpdf_dlink2_dvar(f, y, Y_metadata=Y_metadata)
|
||||
d2logpdf_dlink2_dv = np.zeros_like(d2logpdf_dlink2_dvar) #FIXME: Not done yet
|
||||
return np.hstack((d2logpdf_dlink2_dvar, d2logpdf_dlink2_dv))
|
||||
|
||||
|
|
@ -268,7 +268,6 @@ class StudentT(Likelihood):
|
|||
"""
|
||||
Compute mean of the prediction
|
||||
"""
|
||||
#FIXME: Not correct
|
||||
return mu
|
||||
|
||||
def samples(self, gp):
|
||||
|
|
|
|||
|
|
@ -255,25 +255,25 @@ class TestNoiseModels(object):
|
|||
"Y": self.binary_Y,
|
||||
"ep": False # FIXME: Should be True when we have it working again
|
||||
},
|
||||
#"Exponential_default": {
|
||||
#"model": GPy.likelihoods.exponential(),
|
||||
#"link_f_constraints": [constrain_positive],
|
||||
#"Y": self.positive_Y,
|
||||
#"laplace": True,
|
||||
#},
|
||||
#"Poisson_default": {
|
||||
#"model": GPy.likelihoods.poisson(),
|
||||
#"link_f_constraints": [constrain_positive],
|
||||
#"Y": self.integer_Y,
|
||||
#"laplace": True,
|
||||
#"ep": False #Should work though...
|
||||
#},
|
||||
#"Gamma_default": {
|
||||
#"model": GPy.likelihoods.gamma(),
|
||||
#"link_f_constraints": [constrain_positive],
|
||||
#"Y": self.positive_Y,
|
||||
#"laplace": True
|
||||
#}
|
||||
"Exponential_default": {
|
||||
"model": GPy.likelihoods.Exponential(),
|
||||
"link_f_constraints": [constrain_positive],
|
||||
"Y": self.positive_Y,
|
||||
"laplace": True,
|
||||
},
|
||||
"Poisson_default": {
|
||||
"model": GPy.likelihoods.Poisson(),
|
||||
"link_f_constraints": [constrain_positive],
|
||||
"Y": self.integer_Y,
|
||||
"laplace": True,
|
||||
"ep": False #Should work though...
|
||||
},
|
||||
"Gamma_default": {
|
||||
"model": GPy.likelihoods.Gamma(),
|
||||
"link_f_constraints": [constrain_positive],
|
||||
"Y": self.positive_Y,
|
||||
"laplace": True
|
||||
}
|
||||
}
|
||||
|
||||
for name, attributes in noise_models.iteritems():
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue