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# Corresponds to Task T.8 from the paper https://arxiv.org/pdf/2101.04653.pdf
import numpy as np
bayesflow_benchmark_info = {
'simulator_is_batched': False,
'parameter_names': [r'$\theta_1$', r'$\theta_2$'],
'configurator_info': 'posterior'
}
[docs]def prior(lower_bound=-1., upper_bound=1., rng=None):
"""Generates a random draw from a 2-dimensional uniform prior bounded between
`lower_bound` and `upper_bound` which represents the two parameters of the two moons simulator.
Parameters
----------
lower_bound : float, optional, default : -1
The lower bound of the uniform prior.
upper_bound : float, optional, default : 1
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 (2,)
A single draw from the 2-dimensional uniform prior.
"""
if rng is None:
rng = np.random.default_rng()
return rng.uniform(low=lower_bound, high=upper_bound, size=2)
[docs]def simulator(theta, rng=None):
""" Implements data generation from the two-moons model with a bimodal posterior.
See https://arxiv.org/pdf/2101.04653.pdf, Benchmark Task T.8
Parameters
----------
theta : np.ndarray of shape (2,)
The vector of two model parameters.
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 two moons simulator.
"""
# Use default RNG, if None specified
if rng is None:
rng = np.random.default_rng()
# Generate noise
alpha = rng.uniform(low=-0.5*np.pi, high=0.5*np.pi)
r = rng.normal(loc=0.1, scale=0.01)
# Forward process
rhs1 = np.array([
r*np.cos(alpha) + 0.25,
r*np.sin(alpha)
])
rhs2 = np.array([
-np.abs(theta[0] + theta[1]) / np.sqrt(2.),
(-theta[0] + theta[1]) / np.sqrt(2.)
])
return rhs1 + rhs2
[docs]def configurator(forward_dict, mode='posterior'):
"""Configures simulator outputs for use in BayesFlow training."""
# Case only posterior configuration
if mode == 'posterior':
input_dict = _config_posterior(forward_dict)
# Case only plikelihood configuration
elif mode == 'likelihood':
input_dict = _config_likelihood(forward_dict)
# Case posterior and likelihood configuration (i.e., joint inference)
elif mode == 'joint':
input_dict = {}
input_dict['posterior_inputs'] = _config_posterior(forward_dict)
input_dict['likelihood_inputs'] = _config_likelihood(forward_dict)
# Throw otherwise
else:
raise NotImplementedError('For now, only a choice between ["posterior", "likelihood", "joint"] is available!')
return input_dict
def _config_posterior(forward_dict):
"""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)
return input_dict
def _config_likelihood(forward_dict):
"""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)
return input_dict