Abstract
Many real-life processes are black-box problems, i.e., the internal workings are inaccessible or a closed-form mathematical expression of the likelihood function cannot be defined. For continuous random variables, likelihood-free inference problems can be solved via Approximate Bayesian Computation (ABC). However, an optimal alternative for discrete random variables is yet to be formulated. Here, we aim to fill this research gap. We propose an adjusted population-based MCMC ABC method by re-defining the standard ABC parameters to discrete ones and by introducing a novel Markov kernel that is inspired by differential evolution. We first assess the proposed Markov kernel on a likelihood-based inference problem, namely discovering the underlying diseases based on a QMR-DTnetwork and, subsequently, the entire method on three likelihood-free inference problems: (i) the QMR-DT network with the unknown likelihood function, (ii) the learning binary neural network, and (iii) neural architecture search. The obtained results indicate the high potential of the proposed framework and the superiority of the new Markov kernel.
Highlights
In various scientific domains, an accurate simulation model can be designed, yet formulating the corresponding likelihood function remains a challenge
We focus on the Markov Chain Monte Carlo (MCMC)-Approximate Bayesian Computation (ABC) version [14] for discrete data application, as it can be more readily implemented and the computational costs are lower [15]
We evaluate our approach on four test-beds: (i) we verify our proposal on a benchmark problem of the QMR-DTnetwork presented by [19]; (ii) we modify the first problem and formulate it as a likelihood-free inference problem; (iii) we assess the applicability of our method for high-dimensional data, namely training binary neural networks on MNIST data; (iv) we apply the proposed approach to Neural Architecture Search (NAS) using the benchmark dataset proposed by [20]
Summary
An accurate simulation model can be designed, yet formulating the corresponding likelihood function remains a challenge. We aim at providing a solution to this problem by translating the existing likelihood-free inference methods to discrete space applications. Likelihood-free inference problems for continuous data are solved via a group of methods known under the term Approximate Bayesian Computation (ABC) [2,7]. We focus on the MCMC-ABC version [14] for discrete data application, as it can be more readily implemented and the computational costs are lower [15]. The efficiency of our newly proposed likelihood-free inference method will depend on two parts, namely (i) on the design of the proposal distribution for the MCMC algorithm and (ii) the selected hyperparameter values for the ABC algorithm
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