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      AKL-ABC: An Automatic Approximate Bayesian Computation Approach Based on Kernel Learning

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          Abstract

          Bayesian statistical inference under unknown or hard to asses likelihood functions is a very challenging task. Currently, approximate Bayesian computation (ABC) techniques have emerged as a widely used set of likelihood-free methods. A vast number of ABC-based approaches have appeared in the literature; however, they all share a hard dependence on free parameters selection, demanding expensive tuning procedures. In this paper, we introduce an automatic kernel learning-based ABC approach, termed AKL-ABC, to automatically compute posterior estimations from a weighting-based inference. To reach this goal, we propose a kernel learning stage to code similarities between simulation and parameter spaces using a centered kernel alignment (CKA) that is automated via an Information theoretic learning approach. Besides, a local neighborhood selection (LNS) algorithm is used to highlight local dependencies over simulations relying on graph theory. Attained results on synthetic and real-world datasets show our approach is a quite competitive method compared to other non-automatic state-of-the-art ABC techniques.

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          Most cited references38

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          Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems.

          Approximate Bayesian computation (ABC) methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper, we discuss and apply an ABC method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC provides information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well-known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus.
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            Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation

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              Population growth of human Y chromosomes: a study of Y chromosome microsatellites.

              We use variation at a set of eight human Y chromosome microsatellite loci to investigate the demographic history of the Y chromosome. Instead of assuming a population of constant size, as in most of the previous work on the Y chromosome, we consider a model which permits a period of recent population growth. We show that for most of the populations in our sample this model fits the data far better than a model with no growth. We estimate the demographic parameters of this model for each population and also the time to the most recent common ancestor. Since there is some uncertainty about the details of the microsatellite mutation process, we consider several plausible mutation schemes and estimate the variance in mutation size simultaneously with the demographic parameters of interest. Our finding of a recent common ancestor (probably in the last 120,000 years), coupled with a strong signal of demographic expansion in all populations, suggests either a recent human expansion from a small ancestral population, or natural selection acting on the Y chromosome.
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                Author and article information

                Journal
                Entropy (Basel)
                Entropy (Basel)
                entropy
                Entropy
                MDPI
                1099-4300
                24 September 2019
                October 2019
                : 21
                : 10
                Affiliations
                [1 ]Automatics Research Group, Universidad Tecnológica de Pereira, Pereira 660003, Colombia; j.hernandez12@ 123456utp.edu.co (J.H.-M.); aaog@ 123456utp.edu.co (Á.O.-G.)
                [2 ]Signal Processing and Recognition Group, Universidad Nacional de Colombia, Manizales 170003, Colombia; amalvarezme@ 123456unal.edu.co
                Author notes
                Article
                entropy-21-00932
                10.3390/e21100932
                7514265
                86770811-1405-459c-8354-12f3d99bbff8
                © 2019 by the authors.

                Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

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