# Copyright (c) 2022 The BayesFlow Developers
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# SOFTWARE.
# Corresponds to Task T.7 from the paper https://arxiv.org/pdf/2101.04653.pdf
# NOTE: The paper description uses variances insteas of scales for the likelihood
# but the implementation uses scales. Our implmenetation uses variances
import numpy as np
bayesflow_benchmark_info = {
"simulator_is_batched": False,
"parameter_names": [r"$\mu_1$", r"$\mu_2$"],
"configurator_info": "posterior",
}
[docs]
def prior(lower_bound=-10.0, upper_bound=10.0, D=2, rng=None):
"""Generates a random draw from a 2-dimensional uniform prior bounded between
`lower_bound` and `upper_bound` representing the common mean of a 2D Gaussian
mixture model (GMM).
Parameters
----------
lower_bound : float, optional, default : -10
The lower bound of the uniform prior
upper_bound : float, optional, default : 10
The upper bound of the uniform prior
D : int, optional, default: 2
The dimensionality of the mixture model
rng : np.random.Generator or None, default: None
An optional random number generator to use
Returns
-------
theta : np.ndarray of shape (D, )
A single draw from the D-dimensional uniform prior
"""
if rng is None:
rng = np.random.default_rng()
return rng.uniform(low=lower_bound, high=upper_bound, size=D)
[docs]
def simulator(theta, prob=0.5, scale_c1=1.0, scale_c2=0.1, rng=None):
"""Simulates data from the Gaussian mixture model (GMM) with
shared location vector. For more details, see
https://arxiv.org/pdf/2101.04653.pdf, Benchmark Task T.7
Important: The parameterization uses scales, so use sqrt(var),
if you want to be working with variances instead of scales.
Parameters
----------
theta : np.ndarray of shape (D,)
The D-dimensional vector of parameter locations.
prob : float, optional, default: 0.5
The mixture probability (coefficient).
scale_c1 : float, optional, default: 1.
The scale of the first component
scale_c2 : float, optional, default: 0.1
The scale of the second component
rng : np.random.Generator or None, default: None
An optional random number generator to use
Returns
-------
x : np.ndarray of shape (2,)
The 2D vector generated from the GMM simulator.
"""
# Use default RNG, if None specified
if rng is None:
rng = np.random.default_rng()
# Draw component index
idx = rng.binomial(n=1, p=prob)
# Draw 2D-Gaussian sample according to component index
if idx == 0:
return rng.normal(loc=theta, scale=scale_c1)
return rng.normal(loc=theta, scale=scale_c2)
[docs]
def configurator(forward_dict, mode="posterior", scale_data=12):
"""Configures simulator outputs for use in BayesFlow training."""
# Case only posterior configuration
if mode == "posterior":
input_dict = _config_posterior(forward_dict, scale_data)
# 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)
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):
"""Helper function for posterior configuration."""
input_dict = {}
input_dict["parameters"] = forward_dict["prior_draws"].astype(np.float32)
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["conditions"] = forward_dict["prior_draws"].astype(np.float32)
input_dict["observables"] = forward_dict["sim_data"].astype(np.float32) / scale_data
return input_dict
