# Copyright (c) 2022 The BayesFlow Developers
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# Corresponds to Task T.3 from the paper https://arxiv.org/pdf/2101.04653.pdf
import numpy as np
bayesflow_benchmark_info = {
"simulator_is_batched": False,
"parameter_names": [r"$\theta_{}$".format(i) for i in range(1, 6)],
"configurator_info": "posterior",
}
[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` which represents the 5 parameters of the SLCP
simulator.
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, 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.
See https://arxiv.org/pdf/2101.04653.pdf, Benchmark Task T.3
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.
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, ) or (n_obs, 2), as indictated by the `flatten`
boolean flag. The sample of simulated data from the SLCP model.
"""
# 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 given number of draws from the MVN likelihood
x = rng.multivariate_normal(loc, S_theta, size=n_obs)
if flatten:
return x.flatten()
return x
[docs]
def configurator(forward_dict, mode="posterior", scale_data=30.0, 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
