From f9857e08c0b4f130f2ae8ace5264e9ba65d9687c Mon Sep 17 00:00:00 2001 From: Alan Saul Date: Fri, 31 May 2013 11:55:32 +0100 Subject: [PATCH] Broken it by getting rid of squeeze, but now working on making it faster using proper vector multiplciation for diagonals --- GPy/examples/laplace_approximations.py | 12 +++-- GPy/likelihoods/Laplace.py | 45 ++++++---------- GPy/likelihoods/likelihood_functions.py | 69 +++++++++++++------------ GPy/models/GP.py | 13 ++++- 4 files changed, 69 insertions(+), 70 deletions(-) diff --git a/GPy/examples/laplace_approximations.py b/GPy/examples/laplace_approximations.py index 203d308d..5103eefb 100644 --- a/GPy/examples/laplace_approximations.py +++ b/GPy/examples/laplace_approximations.py @@ -37,9 +37,10 @@ def timing(): def debug_student_t_noise_approx(): plot = False - real_var = 0.4 + real_var = 0.1 #Start a function, any function X = np.linspace(0.0, 10.0, 100)[:, None] + #X = np.array([0.5])[:, None] Y = np.sin(X) + np.random.randn(*X.shape)*real_var X_full = np.linspace(0.0, 10.0, 500)[:, None] @@ -52,7 +53,7 @@ def debug_student_t_noise_approx(): real_sd = np.sqrt(real_var) print "Real noise: ", real_sd - initial_var_guess = 1 + initial_var_guess = 0.02 #t_rv = t(deg_free, loc=0, scale=real_var) #noise = t_rvrvs(size=Y.shape) #Y += noise @@ -91,12 +92,14 @@ def debug_student_t_noise_approx(): #m.constrain_positive('rbf') #m.constrain_fixed('rbf_v', 1.0898) #m.constrain_fixed('rbf_l', 1.8651) - m.constrain_positive('t_noi') #m.constrain_fixed('t_noise_variance', real_sd) + m.constrain_positive('rbf') + m.constrain_fixed('t_noi', real_sd) + m.ensure_default_constraints() m.update_likelihood_approximation() m.optimize(messages=True) print(m) - return m + #return m #m.optimize('lbfgsb', messages=True, callback=m._update_params_callback) if plot: plt.suptitle('Student-t likelihood') @@ -104,6 +107,7 @@ def debug_student_t_noise_approx(): m.plot() plt.plot(X_full, Y_full) plt.ylim(-2.5, 2.5) + return m #print "Clean student t, ncg" #t_distribution = GPy.likelihoods.likelihood_functions.student_t(deg_free, sigma=edited_real_sd) diff --git a/GPy/likelihoods/Laplace.py b/GPy/likelihoods/Laplace.py index 85af82f9..027f014e 100644 --- a/GPy/likelihoods/Laplace.py +++ b/GPy/likelihoods/Laplace.py @@ -53,7 +53,7 @@ class Laplace(likelihood): def predictive_values(self, mu, var, full_cov): if full_cov: - raise NotImplementedError("Cannot make correlated predictions with an EP likelihood") + raise NotImplementedError("Cannot make correlated predictions with an Laplace likelihood") return self.likelihood_function.predictive_values(mu, var) def _get_params(self): @@ -63,42 +63,28 @@ class Laplace(likelihood): return self.likelihood_function._get_param_names() def _set_params(self, p): - #print "Setting laplace param with: ", p return self.likelihood_function._set_params(p) - def both_gradients(self, dL_d_K_Sigma, dK_dthetaK): - """ - Find the gradients of the marginal likelihood w.r.t both thetaK and thetaL - - dL_dthetaK differs from that of normal likelihoods as it has additional terms coming from - changes to y_tilde and changes to Sigma_tilde when the kernel parameters are adjusted - - Similar terms arise when finding the gradients with respect to changes in the liklihood - parameters - """ - return (self._Kgradients(dL_d_K_Sigma, dK_dthetaK), self._gradients(dL_d_K_Sigma)) - def _shared_gradients_components(self): #FIXME: Careful of side effects! And make sure W and K are up to date! - Ki, _, _, _ = pdinv(self.K) d3lik_d3fhat = self.likelihood_function.d3lik_d3f(self.data, self.f_hat) - #dL_dfhat = -0.5*np.diag(self.Ki_W_i)*d3lik_d3fhat dL_dfhat = -0.5*(np.diag(self.Ki_W_i)*d3lik_d3fhat)[:, None] Wi_K_i = mdot(self.W_12, self.Bi, self.W_12) #same as rasms R I_KW_i = np.eye(self.N) - np.dot(self.K, Wi_K_i) - return dL_dfhat, Ki, I_KW_i, Wi_K_i + return dL_dfhat, I_KW_i, Wi_K_i - def _Kgradients(self, dL_d_K_Sigma, dK_dthetaK): + def _Kgradients(self, dK_dthetaK): """ Gradients with respect to prior kernel parameters """ - dL_dfhat, Ki, I_KW_i, Wi_K_i = self._shared_gradients_components() + dL_dfhat, I_KW_i, Wi_K_i = self._shared_gradients_components() dlp = self.likelihood_function.dlik_df(self.data, self.f_hat)[:, None] dL_dthetaK = np.zeros(dK_dthetaK.shape) for thetaK_i, dK_dthetaK_i in enumerate(dK_dthetaK): #Explicit - dL_dthetaK[thetaK_i] = 0.5*mdot(self.f_hat.T, Ki, dK_dthetaK_i, Ki, self.f_hat) - 0.5*np.trace(Wi_K_i*dK_dthetaK_i) + f_Ki_dK_dtheta_Ki_f = mdot(self.Ki_f.T, dK_dthetaK_i, self.Ki_f) + dL_dthetaK[thetaK_i] = 0.5*f_Ki_dK_dtheta_Ki_f - 0.5*np.trace(Wi_K_i*dK_dthetaK_i) #Implicit df_hat_dthetaK = mdot(I_KW_i, dK_dthetaK_i, dlp) dL_dthetaK[thetaK_i] += np.dot(dL_dfhat.T, df_hat_dthetaK) @@ -109,11 +95,12 @@ class Laplace(likelihood): """ Gradients with respect to likelihood parameters """ - dL_dfhat, Ki, I_KW_i, Wi_K_i = self._shared_gradients_components() + return np.zeros(1) + #return np.zeros(0) + dL_dfhat, I_KW_i, Wi_K_i = self._shared_gradients_components() dlik_dthetaL, dlik_grad_dthetaL, dlik_hess_dthetaL = self.likelihood_function._gradients(self.data, self.f_hat) num_params = len(dlik_dthetaL) - #Ki_W_i = np.diag(inv(Ki + self.W))[:, None] dL_dthetaL = np.zeros((1, num_params)) # make space for one derivative for each likelihood parameter for thetaL_i in range(num_params): #Explicit @@ -123,7 +110,6 @@ class Laplace(likelihood): dL_dthetaL[thetaL_i] = np.sum(dlik_dthetaL[thetaL_i]) - 0.5*np.dot(np.diag(self.Ki_W_i), dlik_hess_dthetaL[thetaL_i]) #Implicit df_hat_dthetaL = mdot(I_KW_i, self.K, dlik_grad_dthetaL[thetaL_i]) - import ipdb; ipdb.set_trace() ### XXX BREAKPOINT dL_dthetaL[thetaL_i] += np.dot(dL_dfhat.T, df_hat_dthetaL) return np.squeeze(dL_dthetaL) #should be array of length *params-being optimized*, for student t just optimising 1 parameter, this is (1,) @@ -230,10 +216,8 @@ class Laplace(likelihood): self._compute_likelihood_variables() def _compute_likelihood_variables(self): - #At this point get the hessian matrix - #print "Data: ", self.data - #print "fhat: ", self.f_hat - self.W = -np.diag(self.likelihood_function.d2lik_d2f(self.data, self.f_hat, extra_data=self.extra_data)) + #At this point get the hessian matrix (or vector as W is diagonal) + self.W = -self.likelihood_function.d2lik_d2f(self.data, self.f_hat, extra_data=self.extra_data) if not self.likelihood_function.log_concave: self.W[self.W < 0] = 1e-6 # FIXME-HACK: This is a hack since GPy can't handle negative variances which can occur @@ -273,7 +257,8 @@ class Laplace(likelihood): """ #W is diagnoal so its sqrt is just the sqrt of the diagonal elements W_12 = np.sqrt(W) - B = np.eye(K.shape[0]) + np.dot(W_12, np.dot(K, W_12)) + assert np.all(W_12.T*K*W_12 == np.dot(np.diagflat(W_12), np.dot(K, np.diagflat(W_12)))) # FIXME Take this out when you've done multiinput + B = np.eye(K.shape[0]) + W_12.T*K*W_12 L = jitchol(B) return (B, L, W_12) @@ -330,7 +315,7 @@ class Laplace(likelihood): i = 0 while difference > epsilon and i < MAX_ITER and rs < MAX_RESTART: #f_old = f.copy() - W = -np.diag(self.likelihood_function.d2lik_d2f(self.data, f, extra_data=self.extra_data)) + W = -self.likelihood_function.d2lik_d2f(self.data, f, extra_data=self.extra_data) if not self.likelihood_function.log_concave: W[W < 0] = 1e-6 # FIXME-HACK: This is a hack since GPy can't handle negative variances which can occur # If the likelihood is non-log-concave. We wan't to say that there is a negative variance @@ -339,7 +324,7 @@ class Laplace(likelihood): B, L, W_12 = self._compute_B_statistics(K, W) W_f = np.dot(W, f) - grad = self.likelihood_function.dlik_df(self.data, f, extra_data=self.extra_data)[:, None] + grad = self.likelihood_function.dlik_df(self.data, f, extra_data=self.extra_data) #Find K_i_f b = W_f + grad diff --git a/GPy/likelihoods/likelihood_functions.py b/GPy/likelihoods/likelihood_functions.py index c6186137..c3aee835 100644 --- a/GPy/likelihoods/likelihood_functions.py +++ b/GPy/likelihoods/likelihood_functions.py @@ -191,8 +191,8 @@ class student_t(likelihood_function): :returns: float(likelihood evaluated for this point) """ - y = np.squeeze(y) - f = np.squeeze(f) + #y = np.squeeze(y) + #f = np.squeeze(f) assert y.shape == f.shape e = y - f @@ -207,7 +207,7 @@ class student_t(likelihood_function): """ Gradient of the link function at y, given f w.r.t f - $$\frac{dp(y_{i}|f_{i})}{df} = \frac{-(v+1)(f_{i}-y_{i})}{(f_{i}-y_{i})^{2} + \sigma^{2}v}$$ + $$\frac{dp(y_{i}|f_{i})}{df} = \frac{(v+1)(y_{i}-f_{i})}{(y_{i}-f_{i})^{2} + \sigma^{2}v}$$ :y: data :f: latent variables f @@ -215,51 +215,52 @@ class student_t(likelihood_function): :returns: gradient of likelihood evaluated at points """ - y = np.squeeze(y) - f = np.squeeze(f) + #y = np.squeeze(y) + #f = np.squeeze(f) assert y.shape == f.shape e = y - f - grad = -((self.v + 1) * e) / (self.v * (self.sigma**2) + (e**2)) - return np.squeeze(grad) + grad = ((self.v + 1) * e) / (self.v * (self.sigma**2) + (e**2)) + return grad def d2lik_d2f(self, y, f, extra_data=None): """ Hessian at this point (if we are only looking at the link function not the prior) the hessian will be 0 unless i == j i.e. second derivative link_function at y given f f_j w.r.t f and f_j - Will return diagonal of hessian, since every where else it is 0 + Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases + (the distribution for y_{i} depends only on f_{i} not on f_{j!=i} - $$\frac{d^{2}p(y_{i}|f_{i})}{d^{3}f} = \frac{(v+1)((f_{i}-y_{i})^{2} - \sigma^{2}v)}{((f_{i}-y_{i})^{2} + \sigma^{2}v)^{2}}$$ + $$\frac{d^{2}p(y_{i}|f_{i})}{d^{3}f} = \frac{(v+1)((y_{i}-f_{i})^{2} - \sigma^{2}v)}{((y_{i}-f_{i})^{2} + \sigma^{2}v)^{2}}$$ :y: data :f: latent variables f :extra_data: extra_data which is not used in student t distribution :returns: array which is diagonal of covariance matrix (second derivative of likelihood evaluated at points) """ - y = np.squeeze(y) - f = np.squeeze(f) + #y = np.squeeze(y) + #f = np.squeeze(f) assert y.shape == f.shape e = y - f hess = ((self.v + 1)*(e**2 - self.v*(self.sigma**2))) / ((((self.sigma**2)*self.v) + e**2)**2) - return np.squeeze(hess) + return hess def d3lik_d3f(self, y, f, extra_data=None): """ Third order derivative link_function (log-likelihood ) at y given f f_j w.r.t f and f_j - $$\frac{d^{3}p(y_{i}|f_{i})}{d^{3}f} = \frac{-2(v+1)((f_{i} - y_{i})^3 - 3(f_{i} - y_{i}) \sigma^{2} v))}{((f_{i} - y_{i}) + \sigma^{2} v)^3}$$ + $$\frac{d^{3}p(y_{i}|f_{i})}{d^{3}f} = \frac{-2(v+1)((y_{i} - f_{i})^3 - 3(y_{i} - f_{i}) \sigma^{2} v))}{((y_{i} - f_{i}) + \sigma^{2} v)^3}$$ """ - y = np.squeeze(y) - f = np.squeeze(f) + #y = np.squeeze(y) + #f = np.squeeze(f) assert y.shape == f.shape e = y - f - d3lik_d3f = ( -(2*(self.v + 1)*(e**3 - e*3*self.v*(self.sigma**2))) / + d3lik_d3f = ( (2*(self.v + 1)*(-e)*(e**2 - 3*self.v*(self.sigma**2))) / ((e**2 + (self.sigma**2)*self.v)**3) ) - return np.squeeze(d3lik_d3f) + return d3lik_d3f - def link_dstd(self, y, f, extra_data=None): + def lik_dstd(self, y, f, extra_data=None): """ Gradient of the likelihood (lik) w.r.t sigma parameter (standard deviation) @@ -268,48 +269,48 @@ class student_t(likelihood_function): $$\frac{dp(y_{i}|f_{i})}{d\sigma} = -\frac{1}{\sigma} + \frac{(1+v)(y_{i}-f_{i})^2}{\sigma^3 v(1 + \frac{1}{v}(\frac{(y_{i} - f_{i})}{\sigma^2})^2)}$$ """ - y = np.squeeze(y) - f = np.squeeze(f) + #y = np.squeeze(y) + #f = np.squeeze(f) assert y.shape == f.shape e = y - f - dlik_dsigma = ( (1/self.sigma) - - ((1+self.v)*(e**2))/((self.sigma**3)*self.v*(1 + (e**2) / ((self.sigma**2)*self.v) ) ) + dlik_dsigma = ( - (1/self.sigma) + + ((1+self.v)*(e**2))/((self.sigma**3)*self.v*(1 + ((e**2) / ((self.sigma**2)*self.v)) ) ) ) - return np.squeeze(dlik_dsigma) + return dlik_dsigma def dlik_df_dstd(self, y, f, extra_data=None): """ Gradient of the dlik_df w.r.t sigma parameter (standard deviation) - $$\frac{d}{d\sigma}(\frac{dp(y_{i}|f_{i})}{df}) = \frac{2\sigma v(v + 1)(f-y)}{(f-y)^2 + \sigma^2 v)^2}$$ + $$\frac{d}{d\sigma}(\frac{dp(y_{i}|f_{i})}{df}) = \frac{-2\sigma v(v + 1)(y_{i}-f_{i})}{(y_{i}-f_{i})^2 + \sigma^2 v)^2}$$ """ - y = np.squeeze(y) - f = np.squeeze(f) + #y = np.squeeze(y) + #f = np.squeeze(f) assert y.shape == f.shape e = y - f - dlik_grad_dsigma = ((2*self.sigma*self.v*(self.v + 1)*e) + dlik_grad_dsigma = ((-2*self.sigma*self.v*(self.v + 1)*e) / ((self.v*(self.sigma**2) + e**2)**2) ) - return np.squeeze(dlik_grad_dsigma) + return dlik_grad_dsigma def d2lik_d2f_dstd(self, y, f, extra_data=None): """ Gradient of the hessian (d2lik_d2f) w.r.t sigma parameter (standard deviation) - $$\frac{d}{d\sigma}(\frac{d^{2}p(y_{i}|f_{i})}{d^{2}f}) = \frac{(v + 1)((f-y)^2 - \sigma^2 v)}{((f-y)^2 + \sigma^2 v)}$$ + $$\frac{d}{d\sigma}(\frac{d^{2}p(y_{i}|f_{i})}{d^{2}f}) = \frac{2\sigma v(v + 1)(\sigma^2 v - 3(y-f)^2)}{((y-f)^2 + \sigma^2 v)^3}$$ """ - y = np.squeeze(y) - f = np.squeeze(f) + #y = np.squeeze(y) + #f = np.squeeze(f) assert y.shape == f.shape e = y - f - dlik_hess_dsigma = ( ((self.v + 1)*(e**2 - (self.sigma**2)*self.v)) / - ((e**2 + (self.sigma**2)*self.v)**2) + dlik_hess_dsigma = ( (2*self.sigma*self.v*(self.v + 1)*((self.sigma**2)*self.v - 3*(e**2))) / + ((e**2 + (self.sigma**2)*self.v)**3) ) return dlik_hess_dsigma def _gradients(self, y, f, extra_data=None): #must be listed in same order as 'get_param_names' - derivs = ([self.link_dstd(y, f, extra_data=extra_data)], + derivs = ([self.lik_dstd(y, f, extra_data=extra_data)], [self.dlik_df_dstd(y, f, extra_data=extra_data)], [self.d2lik_d2f_dstd(y, f, extra_data=extra_data)] ) # lists as we might learn many parameters diff --git a/GPy/models/GP.py b/GPy/models/GP.py index 9ce83a5a..0f3dcb58 100644 --- a/GPy/models/GP.py +++ b/GPy/models/GP.py @@ -142,13 +142,22 @@ class GP(model): Note, we use the chain rule: dL_dtheta = dL_dK * d_K_dtheta """ dL_dthetaK = self.kern.dK_dtheta(dL_dK=self.dL_dK, X=self.X) + print "dL_dthetaK before: ",dL_dthetaK if isinstance(self.likelihood, Laplace): + #Reapproximate incase it hasnt been done... + if isinstance(self.likelihood, Laplace): + self.likelihood.fit_full(self.kern.K(self.X)) + self.likelihood._set_params(self.likelihood._get_params()) + #Need to pass in a matrix of ones to get access to raw dK_dthetaK values without being chained fake_dL_dKs = np.ones(self.dL_dK.shape) #FIXME: Check this is right... + #fake_dL_dKs = np.eye(self.dL_dK.shape[0]) #FIXME: Check this is right... dK_dthetaK = self.kern.dK_dtheta(dL_dK=fake_dL_dKs, X=self.X) + #THIS SHOULD NOT BE (1,num_k_params) matrix it should be (N,N,num_k_params) - dL_dthetaK = self.likelihood._Kgradients(dL_d_K_Sigma=self.dL_dK, dK_dthetaK=dK_dthetaK) - dL_dthetaL = self.likelihood._gradients(partial=np.diag(self.dL_dK)) + dL_dthetaK = self.likelihood._Kgradients(dK_dthetaK=dK_dthetaK) + dL_dthetaL = 0 # self.likelihood._gradients(partial=np.diag(self.dL_dK)) + print "dL_dthetaK after: ",dL_dthetaK #print "Stacked dL_dthetaK, dL_dthetaL: ", np.hstack((dL_dthetaK, dL_dthetaL)) else: dL_dthetaL = self.likelihood._gradients(partial=np.diag(self.dL_dK))