def test_log_lik_multiple2(self): n = 3 y = randint(0, 2, n) * 2 - 1 F = randn(10, n) X = randn(n, 2) covariance = SquaredExponentialCovariance(sigma=1, scale=1) likelihood = LogitLikelihood() gp = GaussianProcess(y, X, covariance, likelihood) singles = asarray([gp.log_likelihood(f) for f in F]) multiples = gp.log_likelihood_multiple(F) self.assertLessEqual(norm(singles - multiples), 1e-10)
def test_log_lik_multiple1(self): n = 3 y = randint(0, 2, n) * 2 - 1 f = randn(n) X = randn(n, 2) covariance = SquaredExponentialCovariance(sigma=1, scale=1) likelihood = LogitLikelihood() gp = GaussianProcess(y, X, covariance, likelihood) single = gp.log_likelihood(f) multiple = gp.log_likelihood_multiple(f.reshape(1, n)) self.assertLessEqual(norm(single - multiple), 1e-10)
def test_log_mean_exp(self): X = asarray([-1, 1]) X = reshape(X, (len(X), 1)) y = asarray([+1. if x >= 0 else -1. for x in X]) covariance = SquaredExponentialCovariance(sigma=1, scale=1) likelihood = LogitLikelihood() gp = GaussianProcess(y, X, covariance, likelihood) laplace = LaplaceApproximation(gp, newton_start=asarray([3, 3])) proposal = laplace.get_gaussian() n = 200 prior = gp.get_gp_prior() samples = proposal.sample(n).samples log_likelihood = asarray([gp.log_likelihood(f) for f in samples]) log_prior = prior.log_pdf(samples) log_proposal = proposal.log_pdf(samples) X = log_likelihood + log_prior - log_proposal a = log(mean(exp(X))) b = GPTools.log_mean_exp(X) self.assertLessEqual(a - b, 1e-5)
def test_log_mean_exp(self): X = asarray([-1, 1]) X = reshape(X, (len(X), 1)) y = asarray([+1. if x >= 0 else -1. for x in X]) covariance = SquaredExponentialCovariance(sigma=1, scale=1) likelihood = LogitLikelihood() gp = GaussianProcess(y, X, covariance, likelihood) laplace = LaplaceApproximation(gp, newton_start=asarray([3, 3])) proposal=laplace.get_gaussian() n=200 prior = gp.get_gp_prior() samples = proposal.sample(n).samples log_likelihood=asarray([gp.log_likelihood(f) for f in samples]) log_prior = prior.log_pdf(samples) log_proposal = proposal.log_pdf(samples) X=log_likelihood+log_prior-log_proposal a=log(mean(exp(X))) b=GPTools.log_mean_exp(X) self.assertLessEqual(a-b, 1e-5)