# Copyright (c) 2022 The BayesFlow Developers
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# Corresponds to Task T.6 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, rng=None):
"""Simulates data from the custom Bernoulli GLM likelihood, see:
https://arxiv.org/pdf/2101.04653.pdf, Task T.6
Returns the raw Bernoulli data.
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).
rng : np.random.Generator or None, default: None
An optional random number generator to use.
Returns
-------
x : np.ndarray of shape (T, 10)
The full simulated set of Bernoulli draws and design matrix.
Should be configured with an additional trailing dimension if the data is (properly) to be treated as a set.
"""
# 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 and return
z = rng.binomial(n=1, p=expit(V.T @ f + beta))
return np.c_[np.expand_dims(z, axis=-1), V.T]
[docs]
def configurator(forward_dict, mode="posterior", 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, as_summary_condition)
# Case only likelihood configuration
elif mode == "likelihood":
input_dict = _config_likelihood(forward_dict)
# Case posterior and likelihood configuration
elif mode == "joint":
input_dict = {}
input_dict["posterior_inputs"] = _config_posterior(forward_dict, as_summary_condition)
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, as_summary_condition):
"""Helper function for posterior configuration."""
input_dict = {}
input_dict["parameters"] = forward_dict["prior_draws"].astype(np.float32)
# Return 3D output
if as_summary_condition:
input_dict["summary_conditions"] = forward_dict["sim_data"].astype(np.float32)
# Flatten along 2nd and 3rd axis
else:
x = forward_dict["sim_data"]
x = x.reshape(x.shape[0], -1)
input_dict["direct_conditions"] = x.astype(np.float32)
return input_dict
def _config_likelihood(forward_dict):
"""Helper function for likelihood configuration."""
input_dict = {}
# Create observables (adding a dummy var)
obs = forward_dict["sim_data"][:, :, 0]
obs_dummy = np.random.randn(obs.shape[0], obs.shape[1])
input_dict["observables"] = np.stack([obs, obs_dummy], axis=2).astype(np.float32)
# Create condition (repeating param draws)
design = forward_dict["sim_data"][:, :, 1:]
T = design.shape[1]
params_rep = np.stack([forward_dict["prior_draws"]] * T, axis=1)
input_dict["conditions"] = np.concatenate([design, params_rep], axis=-1).astype(np.float32)
return input_dict
