# Copyright (c) 2022 The BayesFlow Developers
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# Corresponds to Task T.4 from the paper https://arxiv.org/pdf/2101.04653.pdf
import numpy as np
from scipy.stats import multivariate_t
bayesflow_benchmark_info = {
"simulator_is_batched": False,
"parameter_names": [r"$\theta_{}$".format(i) for i in range(1, 6)],
"configurator_info": "posterior",
}
[docs]
def get_random_student_t(dim=2, mu_scale=15, shape_scale=0.01, rng=None):
"""A helper function to create a "frozen" multivariate student-t distribution of dimensions `dim`.
Parameters
----------
dim : int, optional, default: 2
The dimensionality of the student-t distribution.
mu_scale : float, optional, default: 15
The scale of the zero-centered Gaussian prior from which the mean vector
of the student-t distribution is drawn.
shape_scale : float, optional, default: 0.01
The scale of the assumed `np.eye(dim)` shape matrix. The default is chosen to keep
the scale of the distractors and observations relatively similar.
rng : np.random.Generator or None, default: None
An optional random number generator to use.
Returns
-------
student : callable (scipy.stats._multivariate.multivariate_t_frozen)
The student-t generator.
"""
# Use default RNG, if None provided
if rng is None:
rng = np.random.default_rng()
# Draw mean
mu = mu_scale * rng.normal(size=dim)
# Return student-t object
return multivariate_t(loc=mu, shape=shape_scale, df=2, allow_singular=True, seed=rng)
[docs]
def draw_mixture_student_t(num_students, n_draws=46, dim=2, mu_scale=15.0, rng=None):
"""Helper function to generate `n_draws` random draws from a mixture of `num_students`
multivariate Student-t distributions.
Uses the function `get_random_student_t` to create each of the studen-t callable objects.
Parameters
----------
num_students : int
The number of multivariate student-t mixture components
n_draws : int, optional, default: 46
The number of draws to obtain from the mixture distribution.
dim : int, optional, default: 2
The dimensionality of each student-t distribution in the mixture.
mu_scale : float, optional, default: 15
The scale of the zero-centered Gaussian prior from which the mean vector
of each student-t distribution in the mixture is drawn.
rng : np.random.Generator or None, default: None
An optional random number generator to use.
Returns
-------
sample : np.ndarray of shape (n_draws, dim)
The random draws from the mixture of students.
"""
# Use default RNG, if None provided
if rng is None:
rng = np.random.default_rng()
# Obtain a list of scipy frozen distributions (each will have a different mean)
students = [get_random_student_t(dim, mu_scale, rng=rng) for _ in range(num_students)]
# Obtain the sample of n_draws from the mixture and return
sample = [students[rng.integers(low=0, high=num_students)].rvs() for _ in range(n_draws)]
return np.array(sample)
[docs]
def prior(lower_bound=-3.0, upper_bound=3.0, rng=None):
"""Generates a random draw from a 5-dimensional uniform prior bounded between
`lower_bound` and `upper_bound`.
Parameters
----------
lower_bound : float, optional, default : -3
The lower bound of the uniform prior.
upper_bound : float, optional, default : 3
The upper bound of the uniform prior.
rng : np.random.Generator or None, default: None
An optional random number generator to use.
Returns
-------
theta : np.ndarray of shape (5, )
A single draw from the 5-dimensional uniform prior.
"""
if rng is None:
rng = np.random.default_rng()
return rng.uniform(low=lower_bound, high=upper_bound, size=5)
[docs]
def simulator(theta, n_obs=4, n_dist=46, dim=2, mu_scale=15.0, flatten=True, rng=None):
"""Generates data from the SLCP model designed as a benchmark for a simple likelihood
and a complex posterior due to a non-linear pushforward theta -> x. In addition, it
outputs uninformative distractor data.
See https://arxiv.org/pdf/2101.04653.pdf, Benchmark Task T.4
Parameters
----------
theta : np.ndarray of shape (theta, D)
The location parameters of the Gaussian likelihood.
n_obs : int, optional, default: 4
The number of observations to generate from the slcp likelihood.
n_dist : int, optional, default: 46
The number of distractor to draw from the distractor likelihood.
dim : int, optional, default: 2
The dimensionality of each student-t distribution in the mixture.
mu_scale : float, optional, default: 15
The scale of the zero-centered Gaussian prior from which the mean vector
of each student-t distribution in the mixture is drawn.
flatten : bool, optional, default: True
A flag to indicate whather a 1D (`flatten=True`) or a 2D (`flatten=False`)
representation of the simulated data is returned.
rng : np.random.Generator or None, default: None
An optional random number generator to use.
Returns
-------
x : np.ndarray of shape (n_obs*2 + n_dist*2,) if `flatten=True`, otherwise
np.ndarray of shape (n_obs + n_dist, 2) if `flatten=False`
"""
# Use default RNG, if None specified
if rng is None:
rng = np.random.default_rng()
# Specify 2D location
loc = np.array([theta[0], theta[1]])
# Specify 2D covariance matrix
s1 = theta[2] ** 2
s2 = theta[3] ** 2
rho = np.tanh(theta[4])
cov = rho * s1 * s2
S_theta = np.array([[s1**2, cov], [cov, s2**2]])
# Obtain informative part of the data
x_info = rng.multivariate_normal(loc, S_theta, size=n_obs)
# Obtain uninformative part of the data
x_uninfo = draw_mixture_student_t(num_students=20, n_draws=n_dist, dim=dim, mu_scale=mu_scale, rng=rng)
# Concatenate informative with uninformative and return
x = np.concatenate([x_info, x_uninfo], axis=0)
if flatten:
return x.flatten()
return x
[docs]
def configurator(forward_dict, mode="posterior", scale_data=50.0, as_summary_condition=False):
"""Configures simulator outputs for use in BayesFlow training."""
# Case only posterior configuration
if mode == "posterior":
input_dict = _config_posterior(forward_dict, scale_data, as_summary_condition)
# Case only likelihood configuration
elif mode == "likelihood":
input_dict = _config_likelihood(forward_dict, scale_data)
# Case posterior and likelihood configuration
elif mode == "joint":
input_dict = {}
input_dict["posterior_inputs"] = _config_posterior(forward_dict, scale_data, as_summary_condition)
input_dict["likelihood_inputs"] = _config_likelihood(forward_dict, scale_data)
# Throw otherwise
else:
raise NotImplementedError('For now, only a choice between ["posterior", "likelihood", "joint"] is available!')
return input_dict
def _config_posterior(forward_dict, scale_data, as_summary_condition):
"""Helper function for posterior configuration."""
input_dict = {}
input_dict["parameters"] = forward_dict["prior_draws"].astype(np.float32)
if as_summary_condition:
input_dict["summary_conditions"] = forward_dict["sim_data"].astype(np.float32) / scale_data
else:
input_dict["direct_conditions"] = forward_dict["sim_data"].astype(np.float32) / scale_data
return input_dict
def _config_likelihood(forward_dict, scale_data):
"""Helper function for likelihood configuration."""
input_dict = {}
input_dict["observables"] = forward_dict["sim_data"].astype(np.float32) / scale_data
input_dict["conditions"] = forward_dict["prior_draws"].astype(np.float32)
return input_dict
