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Adding gradients, shapes starting to make sense
This commit is contained in:
Alan Saul
parent
1420aa532c
commit
267a8e427c
4 changed files with 60 additions and 29 deletions
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@ -1,11 +1,12 @@
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import numpy as np
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import scipy as sp
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import GPy
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from scipy.linalg import cholesky, eig, inv, cho_solve, det
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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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import pylab as plt
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class Laplace(likelihood):
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@ -62,7 +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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return self.likelihood_function._set_params()
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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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"""
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@ -77,8 +78,8 @@ 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.K+self.Sigma_tilde), self.Y)
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dytil_dfhat = np.dot(self.Sigma_tilde, self.Ki) + np.eye(self.N) # or self.Wi__Ki_W?
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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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return dL_dytil, dytil_dfhat
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def _Kgradients(self, dL_d_K_Sigma, dK_dthetaK):
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@ -91,12 +92,18 @@ class Laplace(likelihood):
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"""
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dL_dytil, dytil_dfhat = self._shared_gradients_components()
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I_KW_i, _, _, _ = pdinv(np.eye(self.N) + np.dot(self.K, self.W))
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A = np.eye(self.N) + np.dot(self.K, self.W)
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plt.imshow(A)
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plt.show()
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I_KW_i, _, _, _ = pdinv(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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dfhat_dthetaK = I_KW_i*dK_dthetaK*self.likelihood_function.link_grad(self.data, self.f_hat, self.extra_data)
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dytil_dthetaK = dytil_dfhat*dfhat_dthetaK
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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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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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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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@ -105,8 +112,9 @@ 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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dL_dthetaK_implicit = dL_dytil*dytil_dthetaK + dL_dSigma*dSigma_dthetaK
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return dL_dthetaK_implicit
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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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return np.squeeze(dL_dthetaK_implicit)
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def _gradients(self, partial):
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"""
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@ -132,16 +140,25 @@ class Laplace(likelihood):
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partial = dL_dK
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"""
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dL_dytil, dytil_dfhat = self._shared_gradients_components()
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dfhat_dthetaL = self.likelihood_function.df_dtheta()
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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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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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dSigma_dthetaL = -mdot(self.Sigma_tilde, dSigmai_dthetaL, self.Sigma_tilde)
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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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#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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dL_dthetaL = 0 + dL_dytil*dytil_dthetaL + dL_dSigma*dSigma_dthetaL
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return dL_dthetaL
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#return np.zeros(0) # TODO: Laplace likelihood might want to take some parameters...
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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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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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"""
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@ -335,7 +352,7 @@ class Laplace(likelihood):
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rs = 0
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i = 0
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while difference > epsilon and i < MAX_ITER and rs < MAX_RESTART:
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f_old = f.copy()
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#f_old = f.copy()
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W = -np.diag(self.likelihood_function.link_hess(self.data, f, extra_data=self.extra_data))
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if not self.likelihood_function.log_concave:
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W[W < 0] = 1e-6 # FIXME-HACK: This is a hack since GPy can't handle negative variances which can occur
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@ -159,10 +159,10 @@ class student_t(likelihood_function):
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d2ln p(yi|fi)_d2fifj
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"""
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def __init__(self, deg_free, sigma=2):
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super(student_t, self).__init__()
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self.v = deg_free
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self.sigma = sigma
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self.log_concave = False
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#super(student_t, self).__init__()
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def _get_params(self):
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return np.asarray(self.sigma)
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@ -258,9 +258,9 @@ class student_t(likelihood_function):
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)
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return d3link_d3f
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def link_hess_grad_sigma(self, y, f, extra_data=None):
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def link_hess_grad_std(self, y, f, extra_data=None):
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"""
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Gradient of the hessian w.r.t sigma parameter
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Gradient of the hessian w.r.t sigma parameter (standard deviation)
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$$\frac{2\sigma v(v+1)(\sigma^{2}v - 3(f-y)^2)}{((f-y)^{2} + \sigma^{2}v)^{3}}
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"""
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@ -273,8 +273,24 @@ class student_t(likelihood_function):
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)
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return hess_grad_sigma
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def link_grad_std(self, y, f, extra_data=None):
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"""
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Gradient of the likelihood w.r.t sigma parameter (standard deviation)
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$$\frac{-2\sigma(v+1)(y-f)}{(v\sigma^{2} + (y-f)^{2})^{2}}$$
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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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e = y - f
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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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def _gradients(self, y, f, extra_data=None):
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return [self.link_hess_grad_sigma] # list as we might learn many parameters
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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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def predictive_values(self, mu, var):
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"""
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@ -372,9 +388,7 @@ class weibull_survival(likelihood_function):
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def __init__(self, shape, scale):
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self.shape = shape
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self.scale = scale
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#FIXME: This should be in the superclass
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self.log_concave = True
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self.log_concave = True # Or false?
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def link_function(self, y, f, extra_data=None):
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"""
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@ -128,17 +128,17 @@ class GP(model):
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For the likelihood parameters, pass in alpha = K^-1 y
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"""
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dL_dthetaK = self.kern.dK_dtheta(dL_dK=self.dL_dK, X=self.X, slices1=self.Xslices, slices2=self.Xslices)
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if isinstance(self.likelihood, Laplace):
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dL_dthetaK_explicit = self.kern.dK_dtheta(dL_dK=self.dL_dK, X=self.X, slices1=self.Xslices, slices2=self.Xslices)
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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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dK_dthetaK = self.kern.dK_dtheta(dL_dK=fake_dL_dKs, X=self.X, slices1=self.Xslices, slices2=self.Xslices)
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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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dL_dthetaL = self.likelihood._gradients(partial=np.diag(self.dL_dK))
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dL_dthetaL = self.likelihood._gradients(partial=self.dL_dK)
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else:
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dL_dthetaK = self.kern.dK_dtheta(dL_dK=self.dL_dK, X=self.X, slices1=self.Xslices, slices2=self.Xslices)
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dL_dthetaL = self.likelihood._gradients(partial=np.diag(self.dL_dK))
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return np.hstack((dL_dthetaK, dL_dthetaL))
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@ -25,7 +25,7 @@ def pddet(A):
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"""
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Determinant of a positive definite matrix
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"""
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L = cholesky(A)
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L = jitchol(A)
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logdetA = 2*sum(np.log(np.diag(L)))
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return logdetA
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