def testBeta(self, a, b, dtype):
key = random.PRNGKey(0)
rand = lambda key, a, b: random.beta(key, a, b, (10000, ), dtype)
crand = api.jit(rand)
uncompiled_samples = rand(key, a, b)
compiled_samples = crand(key, a, b)
for samples in [uncompiled_samples, compiled_samples]:
self._CheckKolmogorovSmirnovCDF(samples,
scipy.stats.beta(a, b).cdf)
def testBeta(self, a, b, dtype):
if not config.x64_enabled:
raise SkipTest("skip test except on X64")
key = random.PRNGKey(0)
rand = lambda key, a, b: random.beta(key, a, b, (10000,), dtype)
crand = api.jit(rand)
uncompiled_samples = rand(key, a, b)
compiled_samples = crand(key, a, b)
for samples in [uncompiled_samples, compiled_samples]:
self._CheckKolmogorovSmirnovCDF(samples, scipy.stats.beta(a, b).cdf)
def mixup(key, alpha, image_and_label):
"""https://arxiv.org/abs/1710.09412 mixup."""
image, label = image_and_label
batch_size = image.shape[0]
weight = random.beta(key, alpha, alpha, (batch_size, 1))
mixed_label = weight * label + (1.0 - weight) * label[::-1]
weight = np.reshape(weight, (batch_size, 1, 1, 1))
mixed_image = weight * image + (1.0 - weight) * image[::-1]
return mixed_image, mixed_label
def mixup(key, alpha, image_and_label):
image, label = image_and_label
N = image.shape[0]
weight = random.beta(key, alpha, alpha, (N, 1))
mixed_label = weight * label + (1.0 - weight) * label[::-1]
weight = np.reshape(weight, (N, 1, 1, 1))
mixed_image = weight * image + (1.0 - weight) * image[::-1]
return mixed_image, mixed_label
def body(state):
(key, i, u_test, x_test, log_L_test) = state
key, uniform_key, beta_key = random.split(key, 3)
# [M]
U_scale = random.uniform(uniform_key,
shape=spawn_point_U.shape,
minval=t_L,
maxval=t_R)
t_shrink = random.beta(beta_key, live_points_U.shape[0],
1)**jnp.reciprocal(spawn_point_U.size)
u_test_white = U_scale / t_shrink
# y_j =
# = dx + sum_i p_i * u_i
# = dx + R @ u
# x_i = x0_i + R_ij u_j
if whiten:
u_test = L @ (spawn_point_U + R @ u_test_white) + u_mean
else:
u_test = u_test_white
u_test = jnp.clip(u_test, 0., 1.)
x_test = prior_transform(u_test)
log_L_test = loglikelihood_from_constrained(**x_test)
return (key, i + 1, u_test, x_test, log_L_test)
def stochastic_result_computation(n_per_sample, key, samples, log_L_samples):
"""
Args:
n_per_sample:
key:
samples:
log_L_samples:
Returns:
"""
# N
t = jnp.where(n_per_sample == jnp.inf, 1., random.beta(key, n_per_sample, 1))
log_t = jnp.log(t)
log_X = jnp.cumsum(log_t)
log_L_samples = jnp.concatenate([jnp.array([-jnp.inf]), log_L_samples])
log_X = jnp.concatenate([jnp.array([0.]), log_X])
# log_dX = log(1-t_i) + log(X[i-1])
log_dX = jnp.log(1. - t) + log_X[:-1] # jnp.log(-jnp.diff(jnp.exp(log_X))) #-inf where n_per_sample=inf
log_avg_L = jnp.logaddexp(log_L_samples[:-1], log_L_samples[1:]) - jnp.log(2.)
log_p = log_dX + log_avg_L
# param calculation
logZ = logsumexp(log_p)
log_w = log_p - logZ
weights = jnp.exp(log_w)
m = dict_multimap(lambda samples: jnp.sum(left_broadcast_mul(weights, samples), axis=0), samples)
dsamples = dict_multimap(jnp.subtract, samples, m)
cov = dict_multimap(lambda dsamples: jnp.sum(
left_broadcast_mul(weights, (dsamples[..., :, None] * dsamples[..., None, :])), axis=0), dsamples)
# Kish's ESS = [sum weights]^2 / [sum weights^2]
ESS = jnp.exp(2. * logsumexp(log_w) - logsumexp(2. * log_w))
# H = sum w_i log(L)
_H = jnp.exp(log_w) * log_avg_L
H = jnp.sum(jnp.where(jnp.isnan(_H), 0., _H))
return logZ, m, cov, ESS, H
def sample(self, rng_key, sample_shape=()):
shape = sample_shape + self.batch_shape + self.event_shape
return random.beta(rng_key, self.a, self.b, shape=shape)
def beta(a, b, size=None):
a = a.value if isinstance(a, JaxArray) else a
b = b.value if isinstance(b, JaxArray) else b
return JaxArray(
jr.beta(DEFAULT.split_key(), a=a, b=b, shape=_size2shape(size)))
def weights_one_concentration(concentration, key, num_draws, num_components):
beta_draws = random.beta(
key=key, a=1, b=concentration, shape=(num_draws, num_components)
)
occupied_probability, weights = vmap(stick_breaking_weights)(beta_draws)
return occupied_probability, weights
def step(stick_length: float, key, concentration: float):
fraction = random.beta(key, a=1, b=concentration)
stick = stick_length * fraction
remainder = stick_length - stick
return remainder, stick
def sample(self, rng_key, sample_shape=()):
shape = sample_shape + self.batch_shape + self.event_shape
p = random.beta(rng_key, self.a, self.b, shape=shape)
n_max = jnp.max(self.n).item()
return _random_binomial(rng_key, p, self.n, n_max, shape)
