Towards end‐to‐end likelihood‐free inference with convolutional neural networks
Complex simulator‐based models with non‐standard sampling distributions require sophisticated design choices for reliable approximate parameter inference. We introduce a fast, end‐to‐end approach for approximate Bayesian computation (ABC) based on fully convolutional neural networks. The method enab...
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Veröffentlicht in: | British journal of mathematical & statistical psychology 2020-02, Vol.73 (1), p.23-43 |
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creator | Radev, Stefan T. Mertens, Ulf K. Voss, Andreas Köthe, Ullrich |
description | Complex simulator‐based models with non‐standard sampling distributions require sophisticated design choices for reliable approximate parameter inference. We introduce a fast, end‐to‐end approach for approximate Bayesian computation (ABC) based on fully convolutional neural networks. The method enables users of ABC to derive simultaneously the posterior mean and variance of multidimensional posterior distributions directly from raw simulated data. Once trained on simulated data, the convolutional neural network is able to map real data samples of variable size to the first two posterior moments of the relevant parameter's distributions. Thus, in contrast to other machine learning approaches to ABC, our approach allows us to generate reusable models that can be applied by different researchers employing the same model. We verify the utility of our method on two common statistical models (i.e., a multivariate normal distribution and a multiple regression scenario), for which the posterior parameter distributions can be derived analytically. We then apply our method to recover the parameters of the leaky competing accumulator (LCA) model and we reference our results to the current state‐of‐the‐art technique, which is the probability density estimation (PDA). Results show that our method exhibits a lower approximation error compared with other machine learning approaches to ABC. It also performs similarly to PDA in recovering the parameters of the LCA model. |
doi_str_mv | 10.1111/bmsp.12159 |
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We introduce a fast, end‐to‐end approach for approximate Bayesian computation (ABC) based on fully convolutional neural networks. The method enables users of ABC to derive simultaneously the posterior mean and variance of multidimensional posterior distributions directly from raw simulated data. Once trained on simulated data, the convolutional neural network is able to map real data samples of variable size to the first two posterior moments of the relevant parameter's distributions. Thus, in contrast to other machine learning approaches to ABC, our approach allows us to generate reusable models that can be applied by different researchers employing the same model. We verify the utility of our method on two common statistical models (i.e., a multivariate normal distribution and a multiple regression scenario), for which the posterior parameter distributions can be derived analytically. We then apply our method to recover the parameters of the leaky competing accumulator (LCA) model and we reference our results to the current state‐of‐the‐art technique, which is the probability density estimation (PDA). Results show that our method exhibits a lower approximation error compared with other machine learning approaches to ABC. 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We introduce a fast, end‐to‐end approach for approximate Bayesian computation (ABC) based on fully convolutional neural networks. The method enables users of ABC to derive simultaneously the posterior mean and variance of multidimensional posterior distributions directly from raw simulated data. Once trained on simulated data, the convolutional neural network is able to map real data samples of variable size to the first two posterior moments of the relevant parameter's distributions. Thus, in contrast to other machine learning approaches to ABC, our approach allows us to generate reusable models that can be applied by different researchers employing the same model. We verify the utility of our method on two common statistical models (i.e., a multivariate normal distribution and a multiple regression scenario), for which the posterior parameter distributions can be derived analytically. We then apply our method to recover the parameters of the leaky competing accumulator (LCA) model and we reference our results to the current state‐of‐the‐art technique, which is the probability density estimation (PDA). Results show that our method exhibits a lower approximation error compared with other machine learning approaches to ABC. It also performs similarly to PDA in recovering the parameters of the LCA model.</description><subject>Accumulators</subject><subject>Algorithms</subject><subject>approximate Bayesian computation</subject><subject>Artificial neural networks</subject><subject>Bayes Theorem</subject><subject>Computer Simulation</subject><subject>convolutional network</subject><subject>Humans</subject><subject>Inference</subject><subject>leaky competing accumulator</subject><subject>Likelihood Functions</subject><subject>likelihood‐free inference</subject><subject>Machine Learning</subject><subject>Neural networks</subject><subject>Neural Networks, Computer</subject><subject>Normal distribution</subject><subject>Parameters</subject><subject>Regression Analysis</subject><subject>Statistical analysis</subject><subject>Statistical methods</subject><subject>Statistical models</subject><issn>0007-1102</issn><issn>2044-8317</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNp9kM1Kw0AQxxdRbK1efAAJeBEhdT_zcdTiF1QUbM8hm8zStEm27iaW3nwEn9EncdtUDx6cw8ww_Pgx_BE6JXhIXF3Jyi6HhBIR76E-xZz7ESPhPupjjEOfEEx76MjaOcaEChwcoh7DYcxoHPfRdKJXqcmtB3X-9fHZaNfc6pXFAspipvXmqgyAV9QKDNQZeKuimXmZrt912TaFrtPSq6E129GstFnYY3Sg0tLCyW4O0PTudjJ68MfP94-j67GfMRHGvmRZCJhLxTKlaB6pABMZpZIJThUjAQGeMlA5D9y3OZPACVVRJkTKpczDkA3QReddGv3Wgm2SqrAZlGVag25tQkkkBI9jRhx6_ged69a43x3FuKBhQOON8LKjMqOtNaCSpSmq1KwTgpNN2Mkm7GQbtoPPdspWVpD_oj_pOoB0wKooYf2PKrl5en3ppN9GO42s</recordid><startdate>202002</startdate><enddate>202002</enddate><creator>Radev, Stefan T.</creator><creator>Mertens, Ulf K.</creator><creator>Voss, Andreas</creator><creator>Köthe, Ullrich</creator><general>British Psychological Society</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope><scope>K9.</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0002-6702-9559</orcidid></search><sort><creationdate>202002</creationdate><title>Towards end‐to‐end likelihood‐free inference with convolutional neural networks</title><author>Radev, Stefan T. ; Mertens, Ulf K. ; Voss, Andreas ; Köthe, Ullrich</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3579-b3c7e04bf3cff2d8f601b8ab3542f3161e4a3efd46932d3be412f8c55a4bbd773</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Accumulators</topic><topic>Algorithms</topic><topic>approximate Bayesian computation</topic><topic>Artificial neural networks</topic><topic>Bayes Theorem</topic><topic>Computer Simulation</topic><topic>convolutional network</topic><topic>Humans</topic><topic>Inference</topic><topic>leaky competing accumulator</topic><topic>Likelihood Functions</topic><topic>likelihood‐free inference</topic><topic>Machine Learning</topic><topic>Neural networks</topic><topic>Neural Networks, Computer</topic><topic>Normal distribution</topic><topic>Parameters</topic><topic>Regression Analysis</topic><topic>Statistical analysis</topic><topic>Statistical methods</topic><topic>Statistical models</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Radev, Stefan T.</creatorcontrib><creatorcontrib>Mertens, Ulf K.</creatorcontrib><creatorcontrib>Voss, Andreas</creatorcontrib><creatorcontrib>Köthe, Ullrich</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><collection>MEDLINE - Academic</collection><jtitle>British journal of mathematical & statistical psychology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Radev, Stefan T.</au><au>Mertens, Ulf K.</au><au>Voss, Andreas</au><au>Köthe, Ullrich</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Towards end‐to‐end likelihood‐free inference with convolutional neural networks</atitle><jtitle>British journal of mathematical & statistical psychology</jtitle><addtitle>Br J Math Stat Psychol</addtitle><date>2020-02</date><risdate>2020</risdate><volume>73</volume><issue>1</issue><spage>23</spage><epage>43</epage><pages>23-43</pages><issn>0007-1102</issn><eissn>2044-8317</eissn><abstract>Complex simulator‐based models with non‐standard sampling distributions require sophisticated design choices for reliable approximate parameter inference. We introduce a fast, end‐to‐end approach for approximate Bayesian computation (ABC) based on fully convolutional neural networks. The method enables users of ABC to derive simultaneously the posterior mean and variance of multidimensional posterior distributions directly from raw simulated data. Once trained on simulated data, the convolutional neural network is able to map real data samples of variable size to the first two posterior moments of the relevant parameter's distributions. Thus, in contrast to other machine learning approaches to ABC, our approach allows us to generate reusable models that can be applied by different researchers employing the same model. We verify the utility of our method on two common statistical models (i.e., a multivariate normal distribution and a multiple regression scenario), for which the posterior parameter distributions can be derived analytically. We then apply our method to recover the parameters of the leaky competing accumulator (LCA) model and we reference our results to the current state‐of‐the‐art technique, which is the probability density estimation (PDA). Results show that our method exhibits a lower approximation error compared with other machine learning approaches to ABC. It also performs similarly to PDA in recovering the parameters of the LCA model.</abstract><cop>England</cop><pub>British Psychological Society</pub><pmid>30793299</pmid><doi>10.1111/bmsp.12159</doi><tpages>21</tpages><orcidid>https://orcid.org/0000-0002-6702-9559</orcidid></addata></record> |
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subjects | Accumulators Algorithms approximate Bayesian computation Artificial neural networks Bayes Theorem Computer Simulation convolutional network Humans Inference leaky competing accumulator Likelihood Functions likelihood‐free inference Machine Learning Neural networks Neural Networks, Computer Normal distribution Parameters Regression Analysis Statistical analysis Statistical methods Statistical models |
title | Towards end‐to‐end likelihood‐free inference with convolutional neural networks |
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