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trying to fix optimisation problem, fixed a few bugs but still fails at very low noise
This commit is contained in:
Alan Saul
parent
d4bfd99c21
commit
e80fad197c
2 changed files with 49 additions and 34 deletions
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@ -90,7 +90,7 @@ def debug_student_t_noise_approx():
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real_var = 0.1
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#Start a function, any function
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X = np.linspace(0.0, 10.0, 50)[:, None]
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#X = np.array([0.5])[:, None]
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#X = np.array([0.5, 1])[:, None]
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Y = np.sin(X) + np.random.randn(*X.shape)*real_var
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X_full = np.linspace(0.0, 10.0, 50)[:, None]
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@ -99,7 +99,7 @@ def debug_student_t_noise_approx():
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Y = Y/Y.max()
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#Add student t random noise to datapoints
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deg_free = 10
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deg_free = 100000
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real_sd = np.sqrt(real_var)
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print "Real noise std: ", real_sd
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@ -51,6 +51,8 @@ class Laplace(likelihood):
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self.Z = 0
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self.YYT = None
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self.old_a = None
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def predictive_values(self, mu, var, full_cov):
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if full_cov:
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raise NotImplementedError("Cannot make correlated predictions with an Laplace likelihood")
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@ -83,7 +85,7 @@ class Laplace(likelihood):
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impl = mdot(dlp, dL_dfhat, I_KW_i)
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expl_a = mdot(self.Ki_f, self.Ki_f.T)
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expl_b = self.Wi_K_i
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expl = 0.5*expl_a - 0.5*expl_b # Might need to be -?
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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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@ -265,7 +267,7 @@ class Laplace(likelihood):
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f_hat = sp.optimize.fmin_ncg(obj, f, fprime=obj_grad, fhess=obj_hess, disp=False)
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return f_hat[:, None]
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def rasm_mode(self, K, MAX_ITER=500000, MAX_RESTART=50):
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def rasm_mode(self, K, MAX_ITER=500, MAX_RESTART=40):
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"""
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Rasmussens numerically stable mode finding
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For nomenclature see Rasmussen & Williams 2006
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@ -275,7 +277,12 @@ class Laplace(likelihood):
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:MAX_RESTART: Maximum number of restarts (reducing step_size) before forcing finish of optimisation
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:returns: f_mode
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"""
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f = np.zeros((self.N, 1))
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if self.old_a is None:
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old_a = np.zeros((self.N, 1))
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else:
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old_a = self.old_a
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f = np.dot(self.K, old_a)
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new_obj = -np.inf
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old_obj = np.inf
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@ -292,7 +299,7 @@ class Laplace(likelihood):
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#f_old = f.copy()
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W = -self.likelihood_function.d2lik_d2f(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-5 # FIXME-HACK: This is a hack since GPy can't handle negative variances which can occur
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W[W < 0] = 1e-8 # FIXME-HACK: This is a hack since GPy can't handle negative variances which can occur
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# If the likelihood is non-log-concave. We wan't to say that there is a negative variance
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# To cause the posterior to become less certain than the prior and likelihood,
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# This is a property only held by non-log-concave likelihoods
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@ -300,38 +307,46 @@ class Laplace(likelihood):
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W_f = W*f
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grad = self.likelihood_function.dlik_df(self.data, f, extra_data=self.extra_data)
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#Find K_i_f
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b = W_f + grad
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b = step_size*b
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#Need this to find the f we have a stepsize which we need to move in, rather than a full unit movement
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#c = np.dot(K, W_f) + f*(1-step_size) + step_size*np.dot(K, grad)
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#solve_L = cho_solve((L, True), W_12*c)
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#f = c - np.dot(K, W_12*solve_L)
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#FIXME: Can't we get rid of this? Don't we want to evaluate obj(c,f) and this is our new_obj?
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#Why did I choose to evaluate the objective function at the new f with the old hessian? I'm sure there was a good reason,
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#Document it!
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solve_L = cho_solve((L, True), W_12*np.dot(K, b))
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a = b - W_12*solve_L
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f = np.dot(K, a)
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#Work out the DIRECTION that we want to move in, but don't choose the stepsize yet
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full_step_a = b - W_12*solve_L
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da = full_step_a - old_a
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tmp_old_obj = old_obj
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old_obj = new_obj
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new_obj = obj(a, f)
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difference = new_obj - old_obj
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if difference < 0:
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#print "Objective function rose", difference
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#If the objective function isn't rising, restart optimization
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step_size *= 0.9
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#print "Reducing step-size to {ss:.3} and restarting optimization".format(ss=step_size)
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#objective function isn't increasing, try reducing step size
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#f = f_old #it's actually faster not to go back to old location and just zigzag across the mode
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old_obj = tmp_old_obj
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rs += 1
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update_passed = False
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while not update_passed:
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a = old_a + step_size*da
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f = np.dot(K, a)
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difference = abs(difference)
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old_obj = new_obj
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new_obj = np.float(obj(a, f))
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difference = new_obj - old_obj
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#print "difference: ",difference
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if difference < 0:
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#print grad
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print "Objective function rose", np.float(difference)
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#If the objective function isn't rising, restart optimization
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step_size *= 0.8
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print "Reducing step-size to {ss:.3} and restarting optimization".format(ss=step_size)
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#objective function isn't increasing, try reducing step size
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#f = f_old #it's actually faster not to go back to old location and just zigzag across the mode
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#old_obj = tmp_old_obj
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old_obj = new_obj
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rs += 1
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else:
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update_passed = True
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#print "Iter difference: ", difference
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#print "F: ", f
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#print "A: ", a
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old_a = a
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#print "Positive difference obj: ", np.float(difference)
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difference = np.float(abs(difference))
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i += 1
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self.i = i
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#print "Positive difference obj: ", np.float(difference)
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print "Iterations: ",i
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print "Step size reductions", rs
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print "Final difference: ", difference
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return f
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