Source code for bayesflow.benchmarks.bernoulli_glm_raw

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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,) The full simulated set of Bernoulli draws. 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 return rng.binomial(n=1, p=expit(V.T @ f + beta))
[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) if as_summary_condition: input_dict['summary_conditions'] = forward_dict['sim_data'].astype(np.float32)[:, :, np.newaxis] else: 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['observables'] = forward_dict['sim_data'].astype(np.float32) input_dict['conditions'] = forward_dict['prior_draws'].astype(np.float32) return input_dict