# Copyright (c) 2022 The BayesFlow Developers
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
# Corresponds to Task T.5 from the paper https://arxiv.org/pdf/2101.04653.pdf
import numpy as np
from scipy.special import expit
bayesflow_benchmark_info = {
"simulator_is_batched": False,
"parameter_names": [r"$\beta$"] + [r"$f_{}$".format(i) for i in range(1, 10)],
"configurator_info": "posterior",
}
# Global covariance matrix computed once for efficiency
F = np.zeros((9, 9))
for i in range(9):
F[i, i] = 1 + np.sqrt(i / 9)
if i >= 1:
F[i, i - 1] = -2
if i >= 2:
F[i, i - 2] = 1
Cov = np.linalg.inv(F.T @ F)
[docs]
def prior(rng=None):
"""Generates a random draw from the custom prior over the 10
Bernoulli GLM parameters (1 intercept and 9 weights). Uses a
global covariance matrix `Cov` for the multivariate Gaussian prior
over the model weights, which is pre-computed for efficiency.
Parameters
----------
rng : np.random.Generator or None, default: None
An optional random number generator to use.
Returns
-------
theta : np.ndarray of shape (10,)
A single draw from the prior.
"""
if rng is None:
rng = np.random.default_rng()
beta = rng.normal(0, 2)
f = rng.multivariate_normal(np.zeros(9), Cov)
return np.append(beta, f)
[docs]
def simulator(theta, T=100, scale_by_T=True, rng=None):
"""Simulates data from the custom Bernoulli GLM likelihood, see
https://arxiv.org/pdf/2101.04653.pdf, Task T.5
Important: `scale_sum` should be set to False if the simulator is used
with variable `T` during training, otherwise the information of `T` will
be lost.
Parameters
----------
theta : np.ndarray of shape (10,)
The vector of model parameters (`theta[0]` is intercept, `theta[i], i > 0` are weights).
T : int, optional, default: 100
The simulated duration of the task (eq. the number of Bernoulli draws).
scale_by_T : bool, optional, default: True
A flag indicating whether to scale the summayr statistics by T.
rng : np.random.Generator or None, default: None
An optional random number generator to use.
Returns
-------
x : np.ndarray of shape (10,)
The vector of sufficient summary statistics of the data.
"""
# Use default RNG, if None provided
if rng is None:
rng = np.random.default_rng()
# Unpack parameters
beta, f = theta[0], theta[1:]
# Generate design matrix
V = rng.normal(size=(9, T))
# Draw from Bernoulli GLM
z = rng.binomial(n=1, p=expit(V.T @ f + beta))
# Compute and return (scaled) sufficient summary statistics
x1 = np.sum(z)
x_rest = V @ z
x = np.append(x1, x_rest)
if scale_by_T:
x /= T
return x
[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 likelihood 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
