Approximate Bayesian Computation for Discrete Spaces
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-03-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/3/312 |
| _version_ | 1797413186568192000 |
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| author | Ilze A. Auzina Jakub M. Tomczak |
| author_facet | Ilze A. Auzina Jakub M. Tomczak |
| author_sort | Ilze A. Auzina |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T05:14:01Z |
| format | Article |
| id | doaj.art-76afb917a8a14d53835fc867bb4afea1 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T05:14:01Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-76afb917a8a14d53835fc867bb4afea12023-12-03T12:47:00ZengMDPI AGEntropy1099-43002021-03-0123331210.3390/e23030312Approximate Bayesian Computation for Discrete SpacesIlze A. Auzina0Jakub M. Tomczak1Department of Computer Science, Faculty of Science, Vrije Universiteit Amsterdam, De Boelelaan 1111, 1081 HV Amsterdam, The NetherlandsDepartment of Computer Science, Faculty of Science, Vrije Universiteit Amsterdam, De Boelelaan 1111, 1081 HV Amsterdam, The NetherlandsMany 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.https://www.mdpi.com/1099-4300/23/3/312Approximate Bayesian Computationdifferential evolutionMCMCMarkov kernelsdiscrete state space |
| spellingShingle | Ilze A. Auzina Jakub M. Tomczak Approximate Bayesian Computation for Discrete Spaces Entropy Approximate Bayesian Computation differential evolution MCMC Markov kernels discrete state space |
| title | Approximate Bayesian Computation for Discrete Spaces |
| title_full | Approximate Bayesian Computation for Discrete Spaces |
| title_fullStr | Approximate Bayesian Computation for Discrete Spaces |
| title_full_unstemmed | Approximate Bayesian Computation for Discrete Spaces |
| title_short | Approximate Bayesian Computation for Discrete Spaces |
| title_sort | approximate bayesian computation for discrete spaces |
| topic | Approximate Bayesian Computation differential evolution MCMC Markov kernels discrete state space |
| url | https://www.mdpi.com/1099-4300/23/3/312 |
| work_keys_str_mv | AT ilzeaauzina approximatebayesiancomputationfordiscretespaces AT jakubmtomczak approximatebayesiancomputationfordiscretespaces |