A robust estimator of mutual information for deep learning interpretability
We develop the use of mutual information (MI), a well-established metric in information theory, to interpret the inner workings of deep learning (DL) models. To accurately estimate MI from a finite number of samples, we present GMM-MI (pronounced ‘Jimmie’), an algorithm based on Gaussian mixture mod...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | Machine Learning: Science and Technology |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/2632-2153/acc444 |
| _version_ | 1797844611258908672 |
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| author | Davide Piras Hiranya V Peiris Andrew Pontzen Luisa Lucie-Smith Ningyuan Guo Brian Nord |
| author_facet | Davide Piras Hiranya V Peiris Andrew Pontzen Luisa Lucie-Smith Ningyuan Guo Brian Nord |
| author_sort | Davide Piras |
| collection | DOAJ |
| description | We develop the use of mutual information (MI), a well-established metric in information theory, to interpret the inner workings of deep learning (DL) models. To accurately estimate MI from a finite number of samples, we present GMM-MI (pronounced ‘Jimmie’), an algorithm based on Gaussian mixture models that can be applied to both discrete and continuous settings. GMM-MI is computationally efficient, robust to the choice of hyperparameters and provides the uncertainty on the MI estimate due to the finite sample size. We extensively validate GMM-MI on toy data for which the ground truth MI is known, comparing its performance against established MI estimators. We then demonstrate the use of our MI estimator in the context of representation learning, working with synthetic data and physical datasets describing highly non-linear processes. We train DL models to encode high-dimensional data within a meaningful compressed (latent) representation, and use GMM-MI to quantify both the level of disentanglement between the latent variables, and their association with relevant physical quantities, thus unlocking the interpretability of the latent representation. We make GMM-MI publicly available in this GitHub repository. |
| first_indexed | 2024-04-09T17:25:05Z |
| format | Article |
| id | doaj.art-8563df984bc14bcc9d888b2478eaf82f |
| institution | Directory Open Access Journal |
| issn | 2632-2153 |
| language | English |
| last_indexed | 2024-04-09T17:25:05Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj.art-8563df984bc14bcc9d888b2478eaf82f2023-04-18T13:53:05ZengIOP PublishingMachine Learning: Science and Technology2632-21532023-01-014202500610.1088/2632-2153/acc444A robust estimator of mutual information for deep learning interpretabilityDavide Piras0https://orcid.org/0000-0002-9836-2661Hiranya V Peiris1Andrew Pontzen2Luisa Lucie-Smith3Ningyuan Guo4Brian Nord5Department of Physics & Astronomy, University College London , Gower Street, London WC1E 6BT, United Kingdom; Département de Physique Théorique, Université de Genève , 24 Quai Ernest Ansermet, 1211 Genève 4, SwitzerlandDepartment of Physics & Astronomy, University College London , Gower Street, London WC1E 6BT, United Kingdom; The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University , AlbaNova, Stockholm SE-10691, SwedenDepartment of Physics & Astronomy, University College London , Gower Street, London WC1E 6BT, United KingdomMax-Planck-Institut für Astrophysik , Karl-Schwarzschild-Str. 1, 85748 Garching, GermanyDepartment of Physics & Astronomy, University College London , Gower Street, London WC1E 6BT, United KingdomFermi National Accelerator Laboratory , PO Box 500, Batavia, IL 60510, United States of America; Department of Astronomy & Astrophysics, University of Chicago , Chicago, IL 60637, United States of America; Kavli Institute for Cosmological Physics, University of Chicago , Chicago, IL 60637, United States of AmericaWe develop the use of mutual information (MI), a well-established metric in information theory, to interpret the inner workings of deep learning (DL) models. To accurately estimate MI from a finite number of samples, we present GMM-MI (pronounced ‘Jimmie’), an algorithm based on Gaussian mixture models that can be applied to both discrete and continuous settings. GMM-MI is computationally efficient, robust to the choice of hyperparameters and provides the uncertainty on the MI estimate due to the finite sample size. We extensively validate GMM-MI on toy data for which the ground truth MI is known, comparing its performance against established MI estimators. We then demonstrate the use of our MI estimator in the context of representation learning, working with synthetic data and physical datasets describing highly non-linear processes. We train DL models to encode high-dimensional data within a meaningful compressed (latent) representation, and use GMM-MI to quantify both the level of disentanglement between the latent variables, and their association with relevant physical quantities, thus unlocking the interpretability of the latent representation. We make GMM-MI publicly available in this GitHub repository.https://doi.org/10.1088/2632-2153/acc444deep learningmutual informationinterpretabilityrepresentation learning |
| spellingShingle | Davide Piras Hiranya V Peiris Andrew Pontzen Luisa Lucie-Smith Ningyuan Guo Brian Nord A robust estimator of mutual information for deep learning interpretability Machine Learning: Science and Technology deep learning mutual information interpretability representation learning |
| title | A robust estimator of mutual information for deep learning interpretability |
| title_full | A robust estimator of mutual information for deep learning interpretability |
| title_fullStr | A robust estimator of mutual information for deep learning interpretability |
| title_full_unstemmed | A robust estimator of mutual information for deep learning interpretability |
| title_short | A robust estimator of mutual information for deep learning interpretability |
| title_sort | robust estimator of mutual information for deep learning interpretability |
| topic | deep learning mutual information interpretability representation learning |
| url | https://doi.org/10.1088/2632-2153/acc444 |
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