def brownian_motion(locs, innovation_noise, observation_noise):
"""Brownian Motion model.
Args:
locs: Array of loc parameters with np.nan value if loc is unobserved in
shape (num_timesteps,)
innovation_noise: Python `float`.
observation_noise: Python `float`.
Returns:
model: `StanModel`.
"""
code = """
data {
int<lower=0> num_timesteps;
int<lower=0> num_observations;
int<lower = 1, upper = num_timesteps> observation_indices[num_observations];
vector[num_observations] observations;
real<lower=0> innovation_noise;
real<lower=0> observation_noise;
}
parameters {
vector[num_timesteps] loc;
}
model {
loc[1] ~ normal(0, innovation_noise);
for (t in 2:num_timesteps){
loc[t] ~ normal(loc[t-1], innovation_noise);
}
observations ~ normal(loc[observation_indices], observation_noise);
}
"""
stan_data = {
'num_timesteps': len(locs),
'num_observations': len(locs[np.isfinite(locs)]),
'observation_indices': np.arange(1,
len(locs) + 1)[np.isfinite(locs)],
'observations': locs[np.isfinite(locs)],
'innovation_noise': innovation_noise,
'observation_noise': observation_noise
}
model = util.cached_stan_model(code)
def _ext_identity(samples):
"""Extracts the values of all latent variables."""
locs = util.get_columns(samples, r'^loc\.\d+$')
return locs
extract_fns = {'identity': _ext_identity}
return stan_model.StanModel(
extract_fns=extract_fns,
sample_fn=util.make_sample_fn(model, data=stan_data),
)
def log_gaussian_cox_process(
train_locations,
train_extents,
train_counts,
):
"""Log-Gaussian Cox Process model.
Args:
train_locations: Float `Tensor` with shape `[num_train_points, D]`. Training
set locations where counts were measured.
train_extents: Float `Tensor` with shape `[num_train_points]`. Training set
location extents, must be positive.
train_counts: Integer `Tensor` with shape `[num_train_points]`. Training set
counts, must be positive.
Returns:
model: `StanModel`.
"""
code = """
data {
int<lower=0> num_points;
int<lower=0> num_features;
vector[num_features] locations[num_points];
real<lower=0> extents[num_points];
int<lower=0> counts[num_points];
}
transformed data {
vector[num_points] loc;
real mean_log_intensity;
{
mean_log_intensity = 0;
for (i in 1:num_points) {
mean_log_intensity += (
log(counts[i]) - log(extents[i])) / num_points;
}
for (i in 1:num_points) loc[i] = mean_log_intensity; // otherwise nan!
}
}
parameters {
real<lower=0> amplitude;
real<lower=0> length_scale;
vector[num_points] log_intensity;
}
model {
{
matrix[num_points, num_points] L_K;
matrix[num_points, num_points] K = gp_matern32_cov(
locations, amplitude + .001, length_scale + .001);
for (i in 1:num_points) K[i,i] += 1e-6; // GP jitter
L_K = cholesky_decompose(K);
amplitude ~ lognormal(-1., .5);
length_scale ~ lognormal(-1., 1.);
log_intensity ~ multi_normal_cholesky(loc, L_K);
for (i in 1:num_points) {
counts[i] ~ poisson_log(
log(extents[i]) + log_intensity[i]);
}
}
}
"""
num_points = train_locations.shape[0]
num_features = train_locations.shape[1]
stan_data = {
'num_points': num_points,
'num_features': num_features,
'locations': train_locations,
'extents': train_extents,
'counts': train_counts,
}
model = util.cached_stan_model(code)
def _ext_identity(samples):
"""Extract all the parameters."""
res = collections.OrderedDict()
res['amplitude'] = util.get_columns(
samples,
r'^amplitude$',
)[:, 0]
res['length_scale'] = util.get_columns(
samples,
r'^length_scale$',
)[:, 0]
res['log_intensity'] = util.get_columns(
samples,
r'^log_intensity\.\d+$',
)
return res
extract_fns = {'identity': _ext_identity}
return stan_model.StanModel(
extract_fns=extract_fns,
sample_fn=util.make_sample_fn(model, data=stan_data),
)
def logistic_regression(
train_features,
train_labels,
test_features=None,
test_labels=None,
):
"""Bayesian logistic regression with a Gaussian prior.
Args:
train_features: Floating-point `Tensor` with shape `[num_train_points,
num_features]`. Training features.
train_labels: Integer `Tensor` with shape `[num_train_points]`. Training
labels.
test_features: Floating-point `Tensor` with shape `[num_test_points,
num_features]`. Testing features. Can be `None`, in which case
test-related sample transformations are not computed.
test_labels: Integer `Tensor` with shape `[num_test_points]`. Testing
labels. Can be `None`, in which case test-related sample transformations
are not computed.
Returns:
model: `StanModel`.
"""
code = """
data {
int<lower=0> num_train_points;
int<lower=0> num_test_points;
int<lower=0> num_features;
matrix[num_train_points,num_features] train_features;
int<lower=0,upper=1> train_labels[num_train_points];
matrix[num_test_points,num_features] test_features;
int<lower=0,upper=1> test_labels[num_test_points];
}
parameters {
vector[num_features] weights;
}
model {
{
vector[num_train_points] logits;
logits = train_features * weights;
weights ~ normal(0, 1);
train_labels ~ bernoulli_logit(logits);
}
}
generated quantities {
real test_nll;
real per_example_test_nll[num_test_points];
{
vector[num_test_points] logits;
logits = test_features * weights;
test_nll = -bernoulli_logit_lpmf(test_labels | logits);
for (i in 1:num_test_points) {
per_example_test_nll[i] = -bernoulli_logit_lpmf(
test_labels[i] | logits[i]);
}
}
}
"""
have_test = test_features is not None
train_features = _add_bias(train_features)
if have_test:
test_features = _add_bias(test_features)
else:
# cmdstanpy can't handle zero-sized arrays at the moment:
# https://github.com/stan-dev/cmdstanpy/issues/203
test_features = train_features[:1]
test_labels = train_labels[:1]
stan_data = {
'num_train_points': train_features.shape[0],
'num_test_points': test_features.shape[0],
'num_features': train_features.shape[1],
'train_features': train_features,
'train_labels': train_labels,
'test_features': test_features,
'test_labels': test_labels,
}
model = util.cached_stan_model(code)
def _ext_identity(samples):
return util.get_columns(samples, r'^weights\.\d+$')
def _ext_test_nll(samples):
return util.get_columns(samples, r'^test_nll$')[:, 0]
def _ext_per_example_test_nll(samples):
return util.get_columns(samples, r'^per_example_test_nll\.\d+$')
extract_fns = {'identity': _ext_identity}
if have_test:
extract_fns['test_nll'] = _ext_test_nll
extract_fns['per_example_test_nll'] = _ext_per_example_test_nll
return stan_model.StanModel(
extract_fns=extract_fns,
sample_fn=util.make_sample_fn(model, data=stan_data),
)
def radon_contextual_effects(num_counties, train_log_uranium, train_floor,
train_county, train_floor_by_county,
train_log_radon):
"""Heirarchical model of measured radon concentration in homes.
The Stan model is cut and pasted from:
https://mc-stan.org/users/documentation/case-studies/radon.html#Correlations-among-levels
Args:
num_counties: `int`, number of counties represented in the data.
train_log_uranium: Floating-point `Tensor` with shape
`[num_train_points]`. Soil uranium measurements.
train_floor: Integer `Tensor` with shape `[num_train_points]`. Floor of
the house on which the measurement was taken.
train_county: Integer `Tensor` with values in `range(0, num_counties)` of
shape `[num_train_points]`. County in which the measurement was taken.
train_floor_by_county: Floating-point `Tensor` with shape
`[num_train_points]`. Average floor on which the measurement was taken
for the county in which each house is located (the `Tensor` will have
`num_counties` unique values). This represents the contextual effect.
train_log_radon: Floating-point `Tensor` with shape `[num_train_points]`.
Radon measurement for each house (the dependent variable in the model).
Returns:
model: `StanModel`.
"""
code = """
data {
int<lower=0> num_counties;
int<lower=0> num_train;
int<lower=0,upper=num_counties-1> county[num_train];
vector[num_train] log_uranium;
vector[num_train] which_floor;
vector[num_train] floor_by_county;
vector[num_train] log_radon;
}
parameters {
vector[num_counties] county_effect;
vector[3] weight;
real county_effect_mean;
real<lower=0,upper=100> county_effect_scale;
real<lower=0,upper=100> log_radon_scale;
}
transformed parameters {
vector[num_train] log_radon_mean;
for (i in 1:num_train)
log_radon_mean[i] <- county_effect[county[i] + 1]
+ log_uranium[i] * weight[1]
+ which_floor[i] * weight[2]
+ floor_by_county[i] * weight[3];
}
model {
county_effect_mean ~ normal(0, 1);
county_effect ~ normal(county_effect_mean, county_effect_scale);
weight ~ normal(0, 1);
log_radon ~ normal(log_radon_mean, log_radon_scale);
}
"""
stan_data = {
'num_train': train_log_radon.shape[0],
'num_counties': num_counties,
'county': np.array(train_county),
'log_uranium': np.array(train_log_uranium),
'floor_by_county': np.array(train_floor_by_county),
'which_floor':
np.array(train_floor), # `floor` conflicts with a Stan fn
'log_radon': np.array(train_log_radon)
}
model = util.cached_stan_model(code)
def _ext_identity(samples):
"""Extracts the values of all latent variables."""
res = collections.OrderedDict()
res['county_effect_mean'] = util.get_columns(
samples, r'^county_effect_mean$')[:, 0]
res['county_effect_scale'] = util.get_columns(
samples, r'^county_effect_scale$')[:, 0]
res['county_effect'] = util.get_columns(samples,
r'^county_effect\.\d+$')
res['weight'] = util.get_columns(samples, r'^weight\.\d+$')
res['log_radon_scale'] = util.get_columns(samples,
r'^log_radon_scale$')[:, 0]
return res
extract_fns = {'identity': _ext_identity}
return stan_model.StanModel(
extract_fns=extract_fns,
sample_fn=util.make_sample_fn(model, data=stan_data),
)
def stochastic_volatility(centered_returns):
# pylint: disable=long-lines
"""Stochastic volatility model.
This formulation is inspired by (a version in the Stan users' manual)[
https://mc-stan.org/docs/2_21/stan-users-guide/stochastic-volatility-models.html].
Args:
centered_returns: float `Tensor` of shape `[num_timesteps]` giving the
mean-adjusted return (change in asset price, minus the average change)
observed at each step.
Returns:
model: `StanModel`.
"""
# pylint: enable=long-lines
# This model is specified in 'noncentered' parameterization, in terms of
# standardized residuals `log_volatilities_std`. We expect this form of the
# model to mix more easily than a direct specification would. This makes
# it valuable for obtaining ground truth, but caution should be used when
# comparing performance of inference algorithms across parameterizations.
code = """
data {
int<lower=0> num_timesteps;
vector[num_timesteps] centered_returns;
}
parameters {
real<lower=-1,upper=1> persistence;
real mean_log_volatility;
real<lower=0> white_noise_shock_scale;
vector[num_timesteps] log_volatilities_std;
}
transformed parameters {
vector[num_timesteps] log_volatilities = (
log_volatilities_std * white_noise_shock_scale);
log_volatilities[1] /= sqrt(1 - square(persistence));
log_volatilities += mean_log_volatility;
for (t in 2:num_timesteps)
log_volatilities[t] += persistence * (
log_volatilities[t - 1] - mean_log_volatility);
}
model {
(persistence + 1) * 0.5 ~ beta(20, 1.5);
white_noise_shock_scale ~ cauchy(0, 2);
mean_log_volatility ~ cauchy(0, 5);
log_volatilities_std ~ std_normal();
centered_returns ~ normal(0, exp(log_volatilities / 2));
}
"""
stan_data = {
'num_timesteps': len(centered_returns),
'centered_returns': centered_returns
}
model = util.cached_stan_model(code)
def _ext_identity(samples):
"""Extracts the values of all latent variables."""
res = collections.OrderedDict()
res['mean_log_volatility'] = util.get_columns(
samples, r'^mean_log_volatility$')
res['white_noise_shock_scale'] = util.get_columns(
samples, r'^white_noise_shock_scale$')
res['persistence_of_volatility'] = util.get_columns(
samples, r'^persistence$')
res['log_volatility'] = util.get_columns(
samples,
r'^log_volatilities\.\d+$',
)
return res
extract_fns = {'identity': _ext_identity}
return stan_model.StanModel(
extract_fns=extract_fns,
sample_fn=util.make_sample_fn(model, data=stan_data),
)
def item_response_theory(
train_student_ids,
train_question_ids,
train_correct,
test_student_ids=None,
test_question_ids=None,
test_correct=None,
):
"""One-parameter logistic item-response theory (IRT) model.
Args:
train_student_ids: integer `tensor` with shape `[num_train_points]`.
training student ids, ranging from 0 to `num_students`.
train_question_ids: integer `tensor` with shape `[num_train_points]`.
training question ids, ranging from 0 to `num_questions`.
train_correct: integer `tensor` with shape `[num_train_points]`. whether the
student in the training set answered the question correctly, either 0 or
1.
test_student_ids: Integer `Tensor` with shape `[num_test_points]`. Testing
student ids, ranging from 0 to `num_students`. Can be `None`, in which
case test-related sample transformations are not computed.
test_question_ids: Integer `Tensor` with shape `[num_test_points]`. Testing
question ids, ranging from 0 to `num_questions`. Can be `None`, in which
case test-related sample transformations are not computed.
test_correct: Integer `Tensor` with shape `[num_test_points]`. Whether the
student in the testing set answered the question correctly, either 0 or 1.
Can be `None`, in which case test-related sample transformations are not
computed.
Returns:
target: `StanModel`.
"""
code = """
data {
int<lower=0> num_students;
int<lower=0> num_questions;
int<lower=0> num_train_pairs;
int<lower=0> num_test_pairs;
int<lower=1,upper=num_students> train_student_ids[num_train_pairs];
int<lower=1,upper=num_questions> train_question_ids[num_train_pairs];
int<lower=0,upper=1> train_responses[num_train_pairs];
int<lower=1,upper=num_students> test_student_ids[num_test_pairs];
int<lower=1,upper=num_questions> test_question_ids[num_test_pairs];
int<lower=0,upper=1> test_responses[num_test_pairs];
}
parameters {
real mean_student_ability;
vector[num_students] student_ability;
vector[num_questions] question_difficulty;
}
model {
{
mean_student_ability ~ normal(0.75, 1);
student_ability ~ normal(0, 1);
question_difficulty ~ normal(0, 1);
for (i in 1:num_train_pairs) {
real pair_logit;
pair_logit = (
mean_student_ability + student_ability[train_student_ids[i]] -
question_difficulty[train_question_ids[i]]
);
train_responses[i] ~ bernoulli_logit(pair_logit);
}
}
}
generated quantities {
real test_nll = 0.;
real per_example_test_nll[num_test_pairs];
{
for (i in 1:num_test_pairs) {
real pair_logit;
pair_logit = (
mean_student_ability + student_ability[test_student_ids[i]] -
question_difficulty[test_question_ids[i]]
);
per_example_test_nll[i] = -bernoulli_logit_lpmf(test_responses[i] | pair_logit);
}
test_nll = sum(per_example_test_nll);
}
}
"""
have_test = test_student_ids is not None
# cmdstanpy can't handle zero-sized arrays at the moment:
# https://github.com/stan-dev/cmdstanpy/issues/203
if not have_test:
test_student_ids = train_student_ids[:1]
test_question_ids = train_question_ids[:1]
test_correct = train_correct[:1]
stan_data = {
'num_train_pairs':
train_student_ids.shape[0],
'num_test_pairs':
test_student_ids.shape[0],
'num_students':
max(int(train_student_ids.max()), int(test_student_ids.max())) + 1,
'num_questions':
max(int(train_question_ids.max()), int(test_question_ids.max())) + 1,
'train_student_ids':
train_student_ids + 1, # N.B. Stan arrays are 1-indexed.
'train_question_ids':
train_question_ids + 1,
'train_responses':
train_correct,
'test_student_ids':
test_student_ids + 1,
'test_question_ids':
test_question_ids + 1,
'test_responses':
test_correct,
}
model = util.cached_stan_model(code)
def _ext_identity(samples):
"""Extracts all the parameters."""
res = collections.OrderedDict()
res['mean_student_ability'] = util.get_columns(
samples,
r'^mean_student_ability$',
)[:, 0]
res['student_ability'] = util.get_columns(
samples,
r'^student_ability\.\d+$',
)
res['question_difficulty'] = util.get_columns(
samples,
r'^question_difficulty\.\d+$',
)
return res
def _ext_test_nll(samples):
return util.get_columns(samples, r'^test_nll$')[:, 0]
def _ext_per_example_test_nll(samples):
return util.get_columns(samples, r'^per_example_test_nll\.\d+$')
extract_fns = {'identity': _ext_identity}
if have_test:
extract_fns['test_nll'] = _ext_test_nll
extract_fns['per_example_test_nll'] = _ext_per_example_test_nll
return stan_model.StanModel(
extract_fns=extract_fns,
sample_fn=util.make_sample_fn(model, data=stan_data),
)