def log_ml_estimate(self, proposal, n=1):
"""
Computes an estimate for the marginal likelihood p(y) using importance
sampling the provided proposal distribution
"""
prior = self.get_gp_prior()
# sample from proposal
samples = proposal.sample(n).samples
# compute log likelihoods of samples
log_likelihood = self.log_likelihood_multiple(samples)
log_prior = prior.log_pdf(samples)
log_proposal = proposal.log_pdf(samples)
# compute estimate of marginal likelihood, log sum exp trick
X = log_likelihood + log_prior - log_proposal
return GPTools.log_mean_exp(X)
def log_ml_estimate(self, proposal, n=1):
"""
Computes an estimate for the marginal likelihood p(y) using importance
sampling the provided proposal distribution
"""
prior = self.get_gp_prior()
# sample from proposal
samples = proposal.sample(n).samples
# compute log likelihoods of samples
log_likelihood=self.log_likelihood_multiple(samples)
log_prior = prior.log_pdf(samples)
log_proposal = proposal.log_pdf(samples)
# compute estimate of marginal likelihood, log sum exp trick
X=log_likelihood+log_prior-log_proposal
return GPTools.log_mean_exp(X)
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)
def test_log_sum_exp(self):
X = asarray([0.1, 0.2, 0.3, 0.4])
direct = log(sum(exp(X)))
indirect = GPTools.log_sum_exp(X)
self.assertLessEqual(norm(direct - indirect), 1e-10)
def test_log_sum_exp(self):
X=asarray([0.1,0.2,0.3,0.4])
direct=log(sum(exp(X)))
indirect=GPTools.log_sum_exp(X)
self.assertLessEqual(norm(direct-indirect), 1e-10)