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Biased Monte Carlo sampling in RBMs

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Post-edited
Authors : Seoane, Beatriz (Author of the conference)
CIRM (Publisher )

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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
Abstract : 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

MSC Codes :
65C05 - Monte Carlo methods
 82C44 - Dynamics of disordered systems (random Ising systems, etc.)
 68T07 - Artificial neural networks and deep learning
Additional resources :
https://www.cirm-math.fr/RepOrga/2389/Slides/Seoane.pdf
    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 18/11/2021
    Conference Date : 30/09/2021
    Subseries : Research talks
    arXiv category : Machine Learning ; Disordered Systems and Neural Networks ; Statistical Mechanics
    Mathematical Area(s) : Mathematics in Science & Technology ; Probability & Statistics
    Format : MP4 (.mp4) - HD
    Video Time : 00:47:19
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2021-09-30_Seoane.mp4
Information on the Event

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

Citation Data

DOI : 10.24350/CIRM.V.19817903
Cite this video as: 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

See Also

Bibliography

  • 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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