def test_beta_sample_grad(self):
self._set_rng_seed()
num_samples = 20
for alpha, beta in product([1e-2, 1e0, 1e2], [1e-2, 1e0, 1e2]):
alphas = Variable(torch.Tensor([alpha] * num_samples),
requires_grad=True)
betas = Variable(torch.Tensor([beta] * num_samples))
x = Beta(alphas, betas).rsample()
x.sum().backward()
x, ind = x.data.sort()
x = x.numpy()
actual_grad = alphas.grad.data[ind].numpy()
# Compare with expected gradient dx/dalpha along constant cdf(x,alpha,beta).
cdf = scipy.stats.beta.cdf
pdf = scipy.stats.beta.pdf
eps = 0.02 * alpha / (1.0 + np.sqrt(alpha))
cdf_alpha = (cdf(x, alpha + eps, beta) -
cdf(x, alpha - eps, beta)) / (2 * eps)
cdf_x = pdf(x, alpha, beta)
expected_grad = -cdf_alpha / cdf_x
rel_error = np.abs(actual_grad - expected_grad) / (expected_grad +
1e-100)
self.assertLess(
np.max(rel_error), 0.01, '\n'.join([
'Bad gradients for Beta({}, {})'.format(alpha, beta),
'x {}'.format(x), 'expected {}'.format(expected_grad),
'actual {}'.format(actual_grad),
'rel error {}'.format(rel_error),
'max error {}'.format(rel_error.max())
]))
def log_prob_density(x, dist_args, args):
if args.stat_policy == "Gaussian":
log_prob_density = -(x - dist_args[0]).pow(2) / (2 * dist_args[1].pow(2)) \
- 0.5 * math.log(2 * math.pi)
elif args.stat_policy == "Beta":
log_prob_density = Beta(dist_args[0], dist_args[1]).log_prob(x)
return log_prob_density.sum(1, keepdim=True)
def log_prior(self, reals, params, idx):
lp = 0.0
for key in reals:
if key == 'v':
if self.use_stick_break:
tmp = Beta(params['alpha'], 1).log_prob(params['v'])
else:
tmp = Beta(params['alpha'] / self.K,
1).log_prob(params['v'])
tmp += self.mp['v'].logabsdetJ(reals['v'], params['v'])
lp += tmp.sum()
elif key != 'y':
tmp = self.priors[key].log_prob(params[key])
tmp += self.mp[key].logabsdetJ(reals[key], params[key])
lp += tmp.sum()
return lp
