def model_fn(self):
# regression in latent space
w = yield JDCRoot(
Independent(
tfd.Normal(loc=tf.zeros([self.num_factors, self.k]),
scale=tf.fill([self.num_factors, self.k], 10.0))))
z_scale = yield JDCRoot(
Independent(
tfd.HalfCauchy(loc=tf.zeros([self.num_factors, self.k]),
scale=1.0)))
F_test = yield JDCRoot(
Independent(
tfd.OneHotCategorical(logits=tf.zeros([
self.num_testing_samples, self.num_factors -
self.num_confounders
]))))
F_full = tf.concat([tf.expand_dims(self.F, 0), F_test], axis=-2)
z = yield Independent(
tfd.Normal(loc=tf.matmul(F_full, w),
scale=tf.matmul(F_full, z_scale)))
x_bias = yield JDCRoot(
Independent(
tfd.Normal(loc=tf.fill([self.num_features],
np.float32(self.x_bias_loc0)),
scale=np.float32(self.x_bias_scale0))))
# decoded log-expression space
x_loc = x_bias + self.decoder(z) - self.sample_scales
x_scale_concentration_c = yield JDCRoot(
Independent(
tfd.HalfCauchy(loc=tf.zeros([self.kernel_regression_degree]),
scale=1.0)))
x_scale_mode_c = yield JDCRoot(
Independent(
tfd.HalfCauchy(loc=tf.zeros([self.kernel_regression_degree]),
scale=1.0)))
weights = kernel_regression_weights(self.kernel_regression_bandwidth,
x_bias, self.x_scale_hinges)
x_scale = yield Independent(
mean_variance_model(weights, x_scale_concentration_c,
x_scale_mode_c))
# log expression distribution
x = yield Independent(tfd.StudentT(df=1.0, loc=x_loc, scale=x_scale))
if not self.use_point_estimates:
rnaseq_reads = yield tfd.Independent(
rnaseq_approx_likelihood_from_vars(self.vars, x))
def eight_schools_log_pdf(z, centered=EIGHT_SCHOOL_CENTERED):
prior_mu = tfd.Normal(loc=0, scale=5)
prior_tau = tfd.HalfCauchy(loc=0, scale=5)
mu, log_tau = z[:, -2], z[:, -1]
# Adapt size of mu an tau.
mu = tf.transpose(eight_schools_replicate * mu)
log_tau = tf.transpose(eight_schools_replicate * log_tau)
if centered:
# shapes, thetas=(8,N), mu=(N,), tau=(N,)
thetas = z[:, 0:eight_schools_K]
likelihood = tfd.Normal(loc=thetas,
scale=eight_schools_sigma[0:eight_schools_K])
prior_theta = tfd.Normal(loc=mu, scale=math.exp(log_tau))
log_det_jac = math.log(math.exp(
log_tau)) # kept log(exp()) for mathematical understanding.
return likelihood.log_prob(
eight_schools_y[0:eight_schools_K]) + prior_theta.log_prob(
thetas) + prior_mu.log_prob(mu) + prior_tau.log_prob(
math.exp(log_tau)) + log_det_jac
else:
# shapes, thetas=(8,N), mu=(N,), tau=(N,)
thetas_tilde = z[:, 0:eight_schools_K]
zeros = tf.zeros(mu.shape)
ones = tf.ones(log_tau.shape)
thetas = mu + thetas_tilde * math.exp(log_tau)
likelihood = tfd.Normal(loc=thetas,
scale=eight_schools_sigma[0:eight_schools_K])
prior_theta = tfd.Normal(loc=zeros, scale=ones)
log_det_jac = math.log(math.exp(
log_tau)) # kept log(exp()) for mathematical understanding.
return likelihood.log_prob(
eight_schools_y[0:eight_schools_K]) + prior_theta.log_prob(
thetas_tilde) + prior_mu.log_prob(mu) + prior_tau.log_prob(
math.exp(log_tau)) + log_det_jac
def pdf_2D(z, density_name=''):
assert density_name in AVAILABLE_2D_DISTRIBUTIONS, "Incorrect density name."
if density_name == '':
return 1
elif density_name == 'banana':
z1, z2 = z[:, 0], z[:, 1]
mu = np.array([0.5, 0.5], dtype='float32')
cov = np.array([[0.06, 0.055], [0.055, 0.06]], dtype='float32')
scale = tf.linalg.cholesky(cov)
p = tfd.MultivariateNormalTriL(loc=mu, scale_tril=scale)
z2 = z1**2 + z2
z1, z2 = tf.expand_dims(z1, 1), tf.expand_dims(z2, 1)
z = tf.concat([z1, z2], axis=1)
return p.prob(z)
elif density_name == 'circle':
z1, z2 = z[:, 0], z[:, 1]
norm = (z1**2 + z2**2)**0.5
exp1 = math.exp(-0.2 * ((z1 - 2) / 0.8)**2)
exp2 = math.exp(-0.2 * ((z1 + 2) / 0.8)**2)
u = 0.5 * ((norm - 4) / 0.4)**2 - math.log(exp1 + exp2)
return math.exp(-u)
elif density_name == 'eight_schools':
y_i = 0
sigma_i = 10
thetas, mu, log_tau = z[:, 0], z[:, 1], z[:, 2]
likelihood = tfd.Normal(loc=thetas, scale=sigma_i)
prior_theta = tfd.Normal(loc=mu, scale=math.exp(log_tau))
prior_mu = tfd.Normal(loc=0, scale=5)
prior_tau = tfd.HalfCauchy(loc=0, scale=5)
return likelihood.prob(y_i) * prior_theta.prob(thetas) * prior_mu.prob(
mu) * prior_tau.prob(math.exp(log_tau)) * math.exp(log_tau)
elif density_name == 'figure_eight':
mu1 = 1 * np.array([-1, -1], dtype='float32')
mu2 = 1 * np.array([1, 1], dtype='float32')
scale = 0.45 * np.array([1, 1], dtype='float32')
pi = 0.5
comp1 = tfd.MultivariateNormalDiag(loc=mu1, scale_diag=scale)
comp2 = tfd.MultivariateNormalDiag(loc=mu2, scale_diag=scale)
return (1 - pi) * comp1.prob(z) + pi * comp2.prob(z)
def _init_distribution(conditions, **kwargs):
scale = conditions["scale"]
return tfd.HalfCauchy(loc=0, scale=scale, **kwargs)
def create_distributions(self):
"""Create distribution objects
"""
self.bijectors = {
'u': tfb.Softplus(),
'v': tfb.Softplus(),
'u_eta': tfb.Softplus(),
'u_tau': tfb.Softplus(),
's': tfb.Softplus(),
's_eta': tfb.Softplus(),
's_tau': tfb.Softplus(),
'w': tfb.Softplus()
}
symmetry_breaking_decay = self.symmetry_breaking_decay**tf.cast(
tf.range(self.latent_dim), self.dtype)[tf.newaxis, ...]
distribution_dict = {
'v':
tfd.Independent(tfd.HalfNormal(scale=0.1 * tf.ones(
(self.latent_dim, self.feature_dim), dtype=self.dtype)),
reinterpreted_batch_ndims=2),
'w':
tfd.Independent(tfd.HalfNormal(
scale=tf.ones((1, self.feature_dim), dtype=self.dtype)),
reinterpreted_batch_ndims=2)
}
if self.horseshoe_plus:
distribution_dict = {
**distribution_dict,
'u':
lambda u_eta, u_tau: tfd.Independent(tfd.HalfNormal(
scale=u_eta * u_tau * symmetry_breaking_decay),
reinterpreted_batch_ndims=
2),
'u_eta':
tfd.Independent(tfd.HalfCauchy(
loc=tf.zeros((self.feature_dim, self.latent_dim),
dtype=self.dtype),
scale=tf.ones((self.feature_dim, self.latent_dim),
dtype=self.dtype)),
reinterpreted_batch_ndims=2),
'u_tau':
tfd.Independent(tfd.HalfCauchy(
loc=tf.zeros((1, self.latent_dim), dtype=self.dtype),
scale=tf.ones((1, self.latent_dim), dtype=self.dtype) *
self.u_tau_scale),
reinterpreted_batch_ndims=2),
}
distribution_dict['s'] = lambda s_eta, s_tau: tfd.Independent(
tfd.HalfNormal(scale=s_eta * s_tau),
reinterpreted_batch_ndims=2)
distribution_dict['s_eta'] = tfd.Independent(
tfd.HalfCauchy(loc=tf.zeros((2, self.feature_dim),
dtype=self.dtype),
scale=tf.ones((2, self.feature_dim),
dtype=self.dtype)),
reinterpreted_batch_ndims=2)
distribution_dict['s_tau'] = tfd.Independent(
tfd.HalfCauchy(loc=tf.zeros((1, self.feature_dim),
dtype=self.dtype),
scale=tf.ones(
(1, self.feature_dim), dtype=self.dtype) *
self.s_tau_scale),
reinterpreted_batch_ndims=2)
self.bijectors['u_eta_a'] = tfb.Softplus()
self.bijectors['u_tau_a'] = tfb.Softplus()
self.bijectors['s_eta_a'] = tfb.Softplus()
self.bijectors['s_tau_a'] = tfb.Softplus()
distribution_dict['u_eta'] = lambda u_eta_a: tfd.Independent(
SqrtInverseGamma(concentration=0.5 * tf.ones(
(self.feature_dim, self.latent_dim), dtype=self.dtype),
scale=1.0 / u_eta_a),
reinterpreted_batch_ndims=2)
distribution_dict['u_eta_a'] = tfd.Independent(
tfd.InverseGamma(concentration=0.5 * tf.ones(
(self.feature_dim, self.latent_dim), dtype=self.dtype),
scale=tf.ones(
(self.feature_dim, self.latent_dim),
dtype=self.dtype)),
reinterpreted_batch_ndims=2)
distribution_dict['u_tau'] = lambda u_tau_a: tfd.Independent(
SqrtInverseGamma(concentration=0.5 * tf.ones(
(1, self.latent_dim), dtype=self.dtype),
scale=1.0 / u_tau_a),
reinterpreted_batch_ndims=2)
distribution_dict['u_tau_a'] = tfd.Independent(
tfd.InverseGamma(concentration=0.5 * tf.ones(
(1, self.latent_dim), dtype=self.dtype),
scale=tf.ones(
(1, self.latent_dim), dtype=self.dtype) /
self.u_tau_scale**2),
reinterpreted_batch_ndims=2)
distribution_dict['s_eta'] = lambda s_eta_a: tfd.Independent(
SqrtInverseGamma(concentration=0.5 * tf.ones(
(2, self.feature_dim), dtype=self.dtype),
scale=1.0 / s_eta_a),
reinterpreted_batch_ndims=2)
distribution_dict['s_eta_a'] = tfd.Independent(
tfd.InverseGamma(concentration=0.5 * tf.ones(
(2, self.feature_dim), dtype=self.dtype),
scale=tf.ones((2, self.feature_dim),
dtype=self.dtype)),
reinterpreted_batch_ndims=2)
distribution_dict['s_tau'] = lambda s_tau_a: tfd.Independent(
SqrtInverseGamma(concentration=0.5 * tf.ones(
(1, self.feature_dim), dtype=self.dtype),
scale=1.0 / s_tau_a),
reinterpreted_batch_ndims=2)
distribution_dict['s_tau_a'] = tfd.Independent(
tfd.InverseGamma(concentration=0.5 * tf.ones(
(1, self.feature_dim), dtype=self.dtype),
scale=tf.ones(
(1, self.feature_dim), dtype=self.dtype) /
self.s_tau_scale**2),
reinterpreted_batch_ndims=2)
else:
distribution_dict = {
**distribution_dict, 'u':
tfd.Independent(
AbsHorseshoe(
scale=(self.u_tau_scale * symmetry_breaking_decay *
tf.ones((self.feature_dim, self.latent_dim),
dtype=self.dtype)),
reinterpreted_batch_ndims=2)),
's':
tfd.Independent(AbsHorseshoe(
scale=self.s_tau_scale *
tf.ones((1, self.feature_dim), dtype=self.dtype)),
reinterpreted_batch_ndims=2)
}
self.prior_distribution = tfd.JointDistributionNamed(distribution_dict)
surrogate_dict = {
'v':
self.bijectors['v'](build_trainable_normal_dist(
-6. * tf.ones(
(self.latent_dim, self.feature_dim), dtype=self.dtype),
5e-4 * tf.ones(
(self.latent_dim, self.feature_dim), dtype=self.dtype),
2,
strategy=self.strategy)),
'w':
self.bijectors['w'](build_trainable_normal_dist(
-6 * tf.ones((1, self.feature_dim), dtype=self.dtype),
5e-4 * tf.ones((1, self.feature_dim), dtype=self.dtype),
2,
strategy=self.strategy))
}
if self.horseshoe_plus:
surrogate_dict = {
**surrogate_dict,
'u':
self.bijectors['u'](build_trainable_normal_dist(
-6. * tf.ones(
(self.feature_dim, self.latent_dim), dtype=self.dtype),
5e-4 * tf.ones(
(self.feature_dim, self.latent_dim), dtype=self.dtype),
2,
strategy=self.strategy)),
'u_eta':
self.bijectors['u_eta'](build_trainable_InverseGamma_dist(
3 * tf.ones(
(self.feature_dim, self.latent_dim), dtype=self.dtype),
tf.ones((self.feature_dim, self.latent_dim),
dtype=self.dtype),
2,
strategy=self.strategy)),
'u_tau':
self.bijectors['u_tau'](build_trainable_InverseGamma_dist(
3 * tf.ones((1, self.latent_dim), dtype=self.dtype),
tf.ones((1, self.latent_dim), dtype=self.dtype),
2,
strategy=self.strategy)),
}
surrogate_dict['s_eta'] = self.bijectors['s_eta'](
build_trainable_InverseGamma_dist(tf.ones(
(2, self.feature_dim), dtype=self.dtype),
tf.ones(
(2, self.feature_dim),
dtype=self.dtype),
2,
strategy=self.strategy))
surrogate_dict['s_tau'] = self.bijectors['s_tau'](
build_trainable_InverseGamma_dist(1 * tf.ones(
(1, self.feature_dim), dtype=self.dtype),
tf.ones(
(1, self.feature_dim),
dtype=self.dtype),
2,
strategy=self.strategy))
surrogate_dict['s'] = self.bijectors['s'](
build_trainable_normal_dist(
tf.ones((2, self.feature_dim), dtype=self.dtype) *
tf.cast([[-2.], [-1.]], dtype=self.dtype),
1e-3 * tf.ones((2, self.feature_dim), dtype=self.dtype),
2,
strategy=self.strategy))
self.bijectors['u_eta_a'] = tfb.Softplus()
self.bijectors['u_tau_a'] = tfb.Softplus()
surrogate_dict['u_eta_a'] = self.bijectors['u_eta_a'](
build_trainable_InverseGamma_dist(
2. * tf.ones(
(self.feature_dim, self.latent_dim), dtype=self.dtype),
tf.ones((self.feature_dim, self.latent_dim),
dtype=self.dtype),
2,
strategy=self.strategy))
surrogate_dict['u_tau_a'] = self.bijectors['u_tau_a'](
build_trainable_InverseGamma_dist(
2. * tf.ones((1, self.latent_dim), dtype=self.dtype),
tf.ones((1, self.latent_dim), dtype=self.dtype) /
self.u_tau_scale**2,
2,
strategy=self.strategy))
self.bijectors['s_eta_a'] = tfb.Softplus()
self.bijectors['s_tau_a'] = tfb.Softplus()
surrogate_dict['s_eta_a'] = self.bijectors['s_eta_a'](
build_trainable_InverseGamma_dist(2. * tf.ones(
(2, self.feature_dim), dtype=self.dtype),
tf.ones(
(2, self.feature_dim),
dtype=self.dtype),
2,
strategy=self.strategy))
surrogate_dict['s_tau_a'] = self.bijectors['s_tau_a'](
build_trainable_InverseGamma_dist(
2. * tf.ones((1, self.feature_dim), dtype=self.dtype),
(tf.ones((1, self.feature_dim), dtype=self.dtype) /
self.s_tau_scale**2),
2,
strategy=self.strategy))
else:
surrogate_dict = {
**surrogate_dict, 's':
self.bijectors['s'](build_trainable_normal_dist(
tf.ones((2, self.feature_dim), dtype=self.dtype) *
tf.cast([[-2.], [-1.]], dtype=self.dtype),
1e-3 * tf.ones((2, self.feature_dim), dtype=self.dtype),
2,
strategy=self.strategy)),
'u':
self.bijectors['u'](build_trainable_normal_dist(
-9. * tf.ones(
(self.feature_dim, self.latent_dim), dtype=self.dtype),
5e-4 * tf.ones(
(self.feature_dim, self.latent_dim), dtype=self.dtype),
2,
strategy=self.strategy))
}
self.surrogate_distribution = tfd.JointDistributionNamed(
surrogate_dict)
self.surrogate_vars = self.surrogate_distribution.variables
self.var_list = list(surrogate_dict.keys())
self.set_calibration_expectations()
def estimate_gmm_precision(qx_loc,
qx_scale,
fixed_expression=False,
profile_trace=False,
tensorboard_summaries=False,
batch_size=100,
err_scale=0.2,
edge_cutoff=0.7):
num_samples = qx_loc.shape[0]
n = qx_loc.shape[1]
batch_size = min(batch_size, n)
# [num_samples, n]
if fixed_expression:
qx = qx_loc
else:
qx = ed.Normal(loc=qx_loc, scale=qx_scale, name="qx")
b = np.mean(qx_loc, axis=0)
# variational estimate of w
# -------------------------
qw_loc_init = tf.placeholder(tf.float32, (batch_size, n),
name="qw_loc_init")
qw_loc_init_value = np.zeros((batch_size, n), dtype=np.float32)
qw_loc = tf.Variable(qw_loc_init, name="qw_loc")
qw = qw_loc
# variational estimate of w_scale
# -------------------------------
qw_scale_loc_init_value = np.full((batch_size, n), -3.0, dtype=np.float32)
qw_scale_loc_init = tf.placeholder(tf.float32, (batch_size, n),
name="qw_scale_loc_init")
qw_scale_loc = tf.Variable(qw_scale_loc_init, name="qw_scale_loc")
qw_scale = tf.nn.softplus(qw_scale_loc)
# estimate of b
# -------------
by_init_value = np.zeros((batch_size, ), dtype=np.float32)
by_init = tf.placeholder(tf.float32, (batch_size, ), name="by_init")
by = tf.Variable(by_init, name="by", trainable=False) # [batch_size]
# w
# -
w_scale_prior = tfd.HalfCauchy(loc=0.0, scale=1.0, name="w_scale_prior")
# qw_scale can be shrunk all the way to zero, producing NaNs
qw_scale = tf.clip_by_value(qw_scale, 1e-4, 10000.0)
scale_tau = 0.1
w_prior = tfd.Normal(loc=0.0, scale=qw_scale * scale_tau, name="w_prior")
# [n, batch_size]
mask_init = tf.placeholder(tf.float32, (batch_size, n), name="mask_init")
mask_init_value = np.empty([batch_size, n], dtype=np.float32)
mask = tf.Variable(mask_init, name="mask", trainable=False)
qw_masked = qw * mask # [batch_size, n]
qx_std = qx - b # [num_samples, n]
# CONDITIONAL CORRELATION
# qxqw = tf.matmul(qx_std, qw_masked, transpose_b=True) # [num_samples, batch_size]
# y_dist_loc = qxqw + by
# UNCONDITIONAL CORRELATION
qxqw = tf.expand_dims(qx_std, 1) * tf.expand_dims(
qw_masked, 0) # [num_samples, num_batches, n]
y_dist_loc = tf.expand_dims(tf.expand_dims(by, 0),
-1) + qxqw # [num_samples, num_batches, n]
y_dist = tfd.StudentT(loc=y_dist_loc, scale=err_scale, df=10.0)
y_slice_start_init = tf.placeholder(
tf.int32, 2, name="y_slice_start_init") # set to [0, j]
y_slice_start = tf.Variable(y_slice_start_init,
name="y_slice_start",
trainable=False)
y = tf.slice(qx, y_slice_start,
[num_samples, batch_size]) # [num_samples, batch_size]
# y = tf.Print(y, [tf.square(y_dist_loc - tf.expand_dims(y, -1))], "y", summarize=16)
# objective function
# ------------------
y = tf.expand_dims(y, -1)
y_log_prob = tf.reduce_sum(y_dist.log_prob(y))
w_log_prob = tf.reduce_sum(w_prior.log_prob(qw_masked))
w_scale_log_prob = tf.reduce_sum(w_scale_prior.log_prob(qw_scale))
log_posterior = y_log_prob + w_log_prob + w_scale_log_prob
elbo = log_posterior
optimizer = tf.train.AdamOptimizer(learning_rate=1e-2)
train = optimizer.minimize(-elbo)
sess = tf.Session()
niter = 1000
feed_dict = dict()
feed_dict[qw_scale_loc_init] = qw_scale_loc_init_value
feed_dict[qw_loc_init] = qw_loc_init_value
feed_dict[mask_init] = mask_init_value
feed_dict[by_init] = by_init_value
qx_loc_means = np.mean(qx_loc, axis=0)
# check_ops = tf.add_check_numerics_ops()
if tensorboard_summaries:
# tf.summary.histogram("qw_loc_param", qw_loc)
# tf.summary.histogram("qw_scale_param", qw_scale_param)
tf.summary.scalar("y_log_prob", y_log_prob)
tf.summary.scalar("w_log_prob", w_log_prob)
tf.summary.scalar("w_scale_log_prob", w_scale_log_prob)
tf.summary.scalar("qw min", tf.reduce_min(qw))
tf.summary.scalar("qw max", tf.reduce_max(qw))
tf.summary.scalar("qw_scale min", tf.reduce_min(qw_scale))
tf.summary.scalar("qw_scale max", tf.reduce_max(qw_scale))
# tf.summary.histogram("qw_scale_loc_param", qw_scale_loc)
# tf.summary.histogram("qw_scale_scale_param", qw_scale_scale)
edges = dict()
count = 0
num_batches = math.ceil(n / batch_size)
for batch_num in range(num_batches):
# deal with n not necessarily being divisible by batch_size
if batch_num == num_batches - 1:
start_j = n - batch_size
else:
start_j = batch_num * batch_size
fillmask(mask_init_value, start_j, batch_size)
feed_dict[y_slice_start_init] = np.array([0, start_j], dtype=np.int32)
for k in range(batch_size):
by_init_value[k] = b[start_j + k]
sess.run(tf.global_variables_initializer(), feed_dict=feed_dict)
# if requested, just benchmark one run of the training operation and return
if profile_trace:
print("WRITING PROFILING DATA")
options = tf.RunOptions(trace_level=tf.RunOptions.FULL_TRACE)
run_metadata = tf.RunMetadata()
sess.run(train, options=options, run_metadata=run_metadata)
fetched_timeline = timeline.Timeline(run_metadata.step_stats)
chrome_trace = fetched_timeline.generate_chrome_trace_format()
with open('log/timeline.json', 'w') as f:
f.write(chrome_trace)
break
if tensorboard_summaries:
train_writer = tf.summary.FileWriter(
"log/" + "batch-" + str(batch_num), sess.graph)
tf.summary.scalar("elbo", elbo)
merged_summary = tf.summary.merge_all()
for t in range(niter):
# _, elbo_val = sess.run([train, elbo])
# _, entropy_val, log_posterior_val, elbo_val = sess.run([train, entropy, log_posterior, elbo])
_, y_log_prob_value, w_log_prob_value, w_scale_log_prob_value = sess.run(
[train, y_log_prob, w_log_prob, w_scale_log_prob])
if t % 100 == 0:
# print((t, elbo_val, log_posterior_val, entropy_val))
print((y_log_prob_value, w_log_prob_value,
w_scale_log_prob_value))
# print((t, elbo_val))
if tensorboard_summaries:
train_writer.add_summary(sess.run(merged_summary), t)
print("")
print("batch")
print(start_j)
# qw_scale_min, qw_scale_mean, qw_scale_max = sess.run(
# [tf.reduce_min(qw_scale), tf.reduce_mean(qw_scale), tf.reduce_max(qw_scale)])
# print(("qw_scale span", qw_scale_min, qw_scale_mean, qw_scale_max))
# lower_credible = sess.run(qw.distribution.quantile(0.01))
# upper_credible = sess.run(qw.distribution.quantile(0.99))
lower_credible = upper_credible = sess.run(qw)
print("credible span")
print(np.max(lower_credible))
print(np.min(upper_credible))
print("nonzeros")
print(np.sum((lower_credible > edge_cutoff)))
print(np.sum((upper_credible < -edge_cutoff)))
for k in range(batch_size):
neighbors = []
for j in range(n):
if lower_credible[k, j] > edge_cutoff or upper_credible[
k, j] < -edge_cutoff:
neighbors.append(
(j, lower_credible[k, j], upper_credible[k, j]))
edges[start_j + k] = neighbors
count += 1
if count > 4:
break
return edges
def _base_dist(self, beta: TensorLike, *args, **kwargs):
return tfd.HalfCauchy(loc=0, scale=beta)
