Likelihood-Free Inference with Generative Neural Networks via Scoring Rule Minimization

Abstract

Bayesian Likelihood-Free Inference methods yield posterior approximations for simulator models with intractable likelihood. Recently, many works trained neural networks to approximate either the intractable likelihood or the posterior directly. Most proposals use normalizing flows, namely neural networks parametrizing invertible maps used to transform samples from an underlying base measure; the probability density of the transformed samples is then accessible and the normalizing flow can be trained via maximum likelihood on simulated parameter-observation pairs. A recent work [Ramesh et al., 2022] approximated instead the posterior with generative networks, which drop the invertibility requirement and are thus a more flexible class of distributions scaling to high-dimensional and structured data. However, generative networks only allow sampling from the parametrized distribution; for this reason, Ramesh et al. [2022] follows the common solution of adversarial training, where the generative network plays a min-max game against a "critic" network. This procedure is unstable and can lead to a learned distribution underestimating the uncertainty -in extreme cases collapsing to a single point. Here, we propose to approximate the posterior with generative networks trained by Scoring Rule minimization, an overlooked adversarial-free method enabling smooth training and better uncertainty quantification. In simulation studies, the Scoring Rule approach yields better performances with shorter training time with respect to the adversarial framework.

Joint Generalized Neural Models and Censored Spatial Copulas for Probabilistic Rainfall Forecasting

“…It is important to note that the computation of the maximum likelihood estimator of the kernel parameters is infeasible as we do not have knowledge of f * i,s (y * i,s ) and F * i,s (y * i,s ) for y * i,s ≤ 0, ∀i ∈ I. As a result, we propose an innovative estimation methodology based on the minimum Scoring Rules estimator [Dawid et al, 2016, Pacchiardi andDutta, 2022b], which requires only simulations from the censored latent Gaussian copula.…”

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