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Biased Monte Carlo sampling in RBMs

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Post-edited
Auteurs : Seoane, Beatriz (Auteur de la Conférence)
CIRM (Editeur )

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Generative models Restricetd Boltzmann machine Training an RBM Interpretability of machine learning Sampling problems RBM operational regimes Mixing time Metastability problems Biased sampling
Résumé : RBMs are generative models capable of fitting complex dataset's probability distributions. Thanks to their simple structure, they are particularly well suited for interpretability and pattern extraction, a feature particularly appealing for scientific use. In this talk, we show that RBMs operate in two distinct regimes, depending on the procedure followed to estimate the log-likelihood gradient during the training. Short sampling times fit machines that are trained to reproduce exactly the dynamics followed to train them, long samplings (as compared to the MCMC mixing time) are need to learn a good model for the data. The non-equilibrium regime should be used to generate high quality samples in short learning and sampling times, but cannot be used to extract the unnormalized data probability of the data necessary for interpretability. In practice, it is hard to extract good equilibrium models for structured datasets (which is the typical case in biological applications) due to a divergence of the Monte Carlo mixing times. In this work, we show this barrier can be surmounted using biased Monte Carlo methods.

Keywords : restricted Boltzmann machines; energy based models; generative models; unsupervised learning; mixing time

Codes MSC :
65C05 - Monte Carlo methods
 82C44 - Dynamics of disordered systems (random Ising systems, etc.)
 68T07 - Artificial neural networks and deep learning
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2389/Slides/Seoane.pdf
    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 18/11/2021
    Date de captation : 30/09/2021
    Sous collection : Research talks
    arXiv category : Machine Learning ; Disordered Systems and Neural Networks ; Statistical Mechanics
    Domaine : Mathematics in Science & Technology ; Probability & Statistics
    Format : MP4 (.mp4) - HD
    Durée : 00:47:19
    Audience : Researchers
    Download : https://videos.cirm-math.fr/2021-09-30_Seoane.mp4
Informations sur la Rencontre

Nom de la rencontre : On Future Synergies for Stochastic and Learning Algorithms / Sur les synergies futures autour des algorithmes d'apprentissage et stochastiques
Organisateurs de la rencontre : Durmus, Alain ; Michel, Manon ; Roberts, Gareth ; Zdeborova, Lenka
Dates : 27/09/2021 - 01/10/2021
Année de la rencontre : 2021
URL Congrès : https://conferences.cirm-math.fr/2389.html

Données de citation

DOI : 10.24350/CIRM.V.19817903
Citer cette vidéo: Seoane, Beatriz (2021). Biased Monte Carlo sampling in RBMs. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19817903
URI : http://dx.doi.org/10.24350/CIRM.V.19817903

Voir aussi

Bibliographie

  • DECELLE, Aurélien, FURTLEHNER, Cyril, et SEOANE, Beatriz. Equilibrium and non-Equilibrium regimes in the learning of Restricted Boltzmann Machines. arXiv preprint arXiv:2105.13889, 2021. - https://arxiv.org/abs/2105.13889

  • DECELLE, Aurélien, FISSORE, Giancarlo, et FURTLEHNER, Cyril. Thermodynamics of restricted Boltzmann machines and related learning dynamics. Journal of Statistical Physics, 2018, vol. 172, no 6, p. 1576-1608. - http://dx.doi.org/10.1007/s10955-018-2105-y

  • DECELLE, Aurélien et FURTLEHNER, Cyril. Exact training of Restricted Boltzmann machines on intrinsically low dimensional data. arXiv preprint arXiv:2103.10755, 2021. - https://arxiv.org/abs/2103.10755

  • MARTIN-MAYOR, V., SEOANE, B., et YLLANES, D. Tethered Monte Carlo: Managing rugged free-energy landscapes with a Helmholtz-potential formalism. Journal of Statistical Physics, 2011, vol. 144, no 3, p. 554-596. - http://dx.doi.org/10.1007/s10955-011-0261-4

  • FERNÁNDEZ, L. A., MARTÍN-MAYOR, Víctor, SEOANE, B., et al. Equilibrium fluid-solid coexistence of hard spheres. Physical review letters, 2012, vol. 108, no 16, p. 165701. - http://dx.doi.org/10.1103/PhysRevLett.108.165701


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