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Started adding gaussian sanity checker
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Alan Saul
parent
fdb7b99e0b
commit
9364efc755
3 changed files with 60 additions and 88 deletions
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@ -168,23 +168,23 @@ def student_t_f_check():
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m.randomize()
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m['t_no'] = 0.3
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m.likelihood.X = X
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print m
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#print m
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plt.figure()
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plt.subplot(511)
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m.plot()
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print m
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#print m
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plt.subplot(512)
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m.optimize(max_f_eval=15)
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m.plot()
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print m
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#print m
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plt.subplot(513)
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m.optimize(max_f_eval=15)
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m.plot()
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print m
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#print m
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plt.subplot(514)
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m.optimize(max_f_eval=15)
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m.plot()
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print m
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#print m
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plt.subplot(515)
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m.optimize()
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m.plot()
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@ -89,7 +89,8 @@ class Laplace(likelihood):
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expl = 0.5*expl_a + 0.5*expl_b # Might need to be -?
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dL_dthetaK_exp = dK_dthetaK(expl, X)
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dL_dthetaK_imp = dK_dthetaK(impl, X)
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print "dL_dthetaK_exp: {} dL_dthetaK_implicit: {}".format(dL_dthetaK_exp, dL_dthetaK_imp)
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#print "dL_dthetaK_exp: {} dL_dthetaK_implicit: {}".format(dL_dthetaK_exp, dL_dthetaK_imp)
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#print "expl_a: {}, {} expl_b: {}, {}".format(np.mean(expl_a), np.std(expl_a), np.mean(expl_b), np.std(expl_b))
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dL_dthetaK = dL_dthetaK_exp + dL_dthetaK_imp
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return dL_dthetaK
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@ -165,8 +166,7 @@ class Laplace(likelihood):
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self.aA = 0.5*self.ln_det_K_Wi__Bi
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self.bB = - 0.5*self.f_Ki_f
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self.cC = 0.5*self.y_Wi_Ki_i_y
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Z_tilde = (#+ 100*self.NORMAL_CONST
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+ self.lik
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Z_tilde = (+ self.lik
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+ 0.5*self.ln_det_K_Wi__Bi
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- 0.5*self.f_Ki_f
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+ 0.5*self.y_Wi_Ki_i_y
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@ -379,7 +379,8 @@ class Laplace(likelihood):
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#difference = abs(new_obj - old_obj)
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#old_obj = new_obj.copy()
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difference = np.abs(np.sum(f - f_old))
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#difference = np.abs(np.sum(f - f_old))
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difference = np.abs(np.sum(a - old_a))
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#old_a = self.a.copy() #a
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old_a = a.copy()
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i += 1
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@ -391,42 +392,43 @@ class Laplace(likelihood):
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print "Iterations: {}, Final_difference: {}".format(i, difference)
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if difference > 1e-4:
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print "FAIL FAIL FAIL FAIL FAIL FAIL"
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import ipdb; ipdb.set_trace() ### XXX BREAKPOINT
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if hasattr(self, 'X'):
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import pylab as pb
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pb.figure()
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pb.subplot(311)
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pb.title('old f_hat')
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pb.plot(self.X, self.f_hat)
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pb.subplot(312)
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pb.title('old ff')
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pb.plot(self.X, self.old_ff)
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pb.subplot(313)
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pb.title('new f_hat')
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pb.plot(self.X, f)
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pb.figure()
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pb.subplot(121)
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pb.title('old K')
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pb.imshow(np.diagflat(self.old_K), interpolation='none')
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pb.colorbar()
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pb.subplot(122)
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pb.title('new K')
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pb.imshow(np.diagflat(K), interpolation='none')
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pb.colorbar()
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pb.figure()
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pb.subplot(121)
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pb.title('old W')
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pb.imshow(np.diagflat(self.old_W), interpolation='none')
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pb.colorbar()
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pb.subplot(122)
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pb.title('new W')
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pb.imshow(np.diagflat(W), interpolation='none')
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pb.colorbar()
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if False:
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import ipdb; ipdb.set_trace() ### XXX BREAKPOINT
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pb.close('all')
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if hasattr(self, 'X'):
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import pylab as pb
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pb.figure()
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pb.subplot(311)
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pb.title('old f_hat')
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pb.plot(self.X, self.f_hat)
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pb.subplot(312)
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pb.title('old ff')
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pb.plot(self.X, self.old_ff)
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pb.subplot(313)
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pb.title('new f_hat')
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pb.plot(self.X, f)
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pb.figure()
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pb.subplot(121)
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pb.title('old K')
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pb.imshow(np.diagflat(self.old_K), interpolation='none')
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pb.colorbar()
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pb.subplot(122)
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pb.title('new K')
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pb.imshow(np.diagflat(K), interpolation='none')
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pb.colorbar()
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pb.figure()
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pb.subplot(121)
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pb.title('old W')
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pb.imshow(np.diagflat(self.old_W), interpolation='none')
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pb.colorbar()
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pb.subplot(122)
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pb.title('new W')
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pb.imshow(np.diagflat(W), interpolation='none')
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pb.colorbar()
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import ipdb; ipdb.set_trace() ### XXX BREAKPOINT
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pb.close('all')
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#FIXME: DELETE THESE
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self.old_W = W.copy()
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@ -239,7 +239,7 @@ class student_t(likelihood_function):
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"""
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assert y.shape == f.shape
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e = y - f
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hess = ((self.v + 1)*(e**2 - self.v*self.sigma2)) / (((self.sigma2*self.v) + e**2)**2)
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hess = ((self.v + 1)*(e**2 - self.v*self.sigma2)) / ((self.sigma2*self.v + e**2)**2)
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return hess
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def d3lik_d3f(self, y, f, extra_data=None):
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@ -277,7 +277,7 @@ class student_t(likelihood_function):
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"""
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assert y.shape == f.shape
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e = y - f
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dlik_grad_dsigma = (-self.v*(self.v+1)*e)/((self.sigma2*self.v + e**2)**2)
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dlik_grad_dsigma = (self.v*(self.v+1)*(-e))/((self.sigma2*self.v + e**2)**2)
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return dlik_grad_dsigma
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def d2lik_d2f_dstd(self, y, f, extra_data=None):
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@ -289,7 +289,7 @@ class student_t(likelihood_function):
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assert y.shape == f.shape
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e = y - f
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dlik_hess_dsigma = ( (self.v*(self.v+1)*(self.sigma2*self.v - 3*(e**2)))
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/ (self.sigma2*self.v + (e**2))**3
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/ ((self.sigma2*self.v + (e**2))**3)
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)
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return dlik_hess_dsigma
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@ -479,7 +479,8 @@ class gaussian(likelihood_function):
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def _set_params(self, x):
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self._variance = float(x)
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self.covariance_matrix = np.eye(self.N) * self._variance
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self.I = np.eye(self.N)
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self.covariance_matrix = self.I * self._variance
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self.Ki, _, _, self.ln_K = pdinv(self.covariance_matrix) # THIS MAY BE WRONG
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def link_function(self, y, f, extra_data=None):
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@ -505,8 +506,6 @@ class gaussian(likelihood_function):
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"""
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Gradient of the link function at y, given f w.r.t f
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$$\frac{dp(y_{i}|f_{i})}{df} = \frac{(v+1)(y_{i}-f_{i})}{(y_{i}-f_{i})^{2} + \sigma^{2}v}$$
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:y: data
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:f: latent variables f
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:extra_data: extra_data which is not used in student t distribution
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@ -514,8 +513,8 @@ class gaussian(likelihood_function):
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"""
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assert y.shape == f.shape
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e = y - f
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grad = ((self.v + 1) * e) / (self.v * self.sigma2 + (e**2))
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s2_i = (1.0/self._variance)*self.I
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grad = np.dot(s2_i, y) - 0.5*np.dot(s2_i, f)
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return grad
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def d2lik_d2f(self, y, f, extra_data=None):
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@ -526,16 +525,14 @@ class gaussian(likelihood_function):
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Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
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(the distribution for y_{i} depends only on f_{i} not on f_{j!=i}
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$$\frac{d^{2}p(y_{i}|f_{i})}{d^{3}f} = \frac{(v+1)((y_{i}-f_{i})^{2} - \sigma^{2}v)}{((y_{i}-f_{i})^{2} + \sigma^{2}v)^{2}}$$
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:y: data
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:f: latent variables f
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:extra_data: extra_data which is not used in student t distribution
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:returns: array which is diagonal of covariance matrix (second derivative of likelihood evaluated at points)
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"""
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assert y.shape == f.shape
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e = y - f
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hess = ((self.v + 1)*(e**2 - self.v*self.sigma2)) / (((self.sigma2*self.v) + e**2)**2)
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s2_i = (1.0/self._variance)*self.I
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hess = np.diagonal(-0.5*s2_i)
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return hess
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def d3lik_d3f(self, y, f, extra_data=None):
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@ -545,46 +542,25 @@ class gaussian(likelihood_function):
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$$\frac{d^{3}p(y_{i}|f_{i})}{d^{3}f} = \frac{-2(v+1)((y_{i} - f_{i})^3 - 3(y_{i} - f_{i}) \sigma^{2} v))}{((y_{i} - f_{i}) + \sigma^{2} v)^3}$$
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"""
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assert y.shape == f.shape
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e = y - f
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d3lik_d3f = ( -(2*(self.v + 1)*(-e)*(e**2 - 3*self.v*self.sigma2)) /
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((e**2 + self.sigma2*self.v)**3)
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)
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d3lik_d3f = np.diagonal(0*self.I)
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return d3lik_d3f
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def lik_dstd(self, y, f, extra_data=None):
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"""
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Gradient of the likelihood (lik) w.r.t sigma parameter (standard deviation)
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Terms relavent to derivatives wrt sigma are:
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-log(sqrt(v*pi)*s) -(1/2)*(v + 1)*log(1 + (1/v)*((y-f)/(s))^2))
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$$\frac{dp(y_{i}|f_{i})}{d\sigma} = -\frac{1}{\sigma} + \frac{(1+v)(y_{i}-f_{i})^2}{\sigma^3 v(1 + \frac{1}{v}(\frac{(y_{i} - f_{i})}{\sigma^2})^2)}$$
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"""
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assert y.shape == f.shape
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e = y - f
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sigma = np.sqrt(self.sigma2)
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#dlik_dsigma = ( - (1/sigma) +
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#((1+self.v)*(e**2))/((sigma*self.sigma2)*self.v*(1 + ((e**2) / (self.sigma2*self.v)) ) )
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#)
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#dlik_dsigma = ( - 1 +
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#((1+self.v)*(e**2))/((self.sigma2*self.sigma2)*self.v*(1 + ((e**2) / (self.sigma2*self.v)) ) )
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#)
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#dlik_dsigma = (((self.v + 1)*(e**2))/((e**2) + self.v*(self.sigma**2))) - 1
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dlik_dsigma = (self.v*((e**2)-self.sigma2))/(sigma*((e**2)+self.sigma2*self.v))
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dlik_dsigma = -0.5*self.N*self._variance - 0.5*np.dot(e.T, e)
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return dlik_dsigma
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def dlik_df_dstd(self, y, f, extra_data=None):
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"""
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Gradient of the dlik_df w.r.t sigma parameter (standard deviation)
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$$\frac{d}{d\sigma}(\frac{dp(y_{i}|f_{i})}{df}) = \frac{-2\sigma v(v + 1)(y_{i}-f_{i})}{(y_{i}-f_{i})^2 + \sigma^2 v)^2}$$
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"""
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assert y.shape == f.shape
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e = y - f
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sigma = np.sqrt(self.sigma2)
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dlik_grad_dsigma = ((-2*sigma*self.v*(self.v + 1)*e) #2 might not want to be here?
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/ ((self.v*self.sigma2 + e**2)**2)
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)
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s_4 = 1.0/(self._variance**2)
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dlik_grad_dsigma = -np.dot(s_4, np.dot(self.I, y)) + 0.5*np.dot(s_4, np.dot(self.I, f))
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return dlik_grad_dsigma
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def d2lik_d2f_dstd(self, y, f, extra_data=None):
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@ -594,13 +570,7 @@ class gaussian(likelihood_function):
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$$\frac{d}{d\sigma}(\frac{d^{2}p(y_{i}|f_{i})}{d^{2}f}) = \frac{2\sigma v(v + 1)(\sigma^2 v - 3(y-f)^2)}{((y-f)^2 + \sigma^2 v)^3}$$
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"""
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assert y.shape == f.shape
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e = y - f
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sigma = np.sqrt(self.sigma2)
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dlik_hess_dsigma = ( (2*sigma*self.v*(self.v + 1)*(self.sigma2*self.v - 3*(e**2))) /
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((e**2 + self.sigma2*self.v)**3)
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)
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#dlik_hess_dsigma = ( 2*(self.v + 1)*self.v*(self.sigma**2)*((e**2) + (self.v*(self.sigma**2)) - 4*(e**2))
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#/ ((e**2 + (self.sigma**2)*self.v)**3) )
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dlik_hess_dsigma = 1.0/(2*(self._variance**2))
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return dlik_hess_dsigma
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def _gradients(self, y, f, extra_data=None):
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