Lorenzo Rosset

Alessandra Carbone, Aurélien Decelle, Lorenzo Rosset et al.

In this study, we address the challenge of using energy-based models to produce high-quality, label-specific data in complex structured datasets, such as population genetics, RNA or protein sequences data. Traditional training methods encounter difficulties due to inefficient Markov chain Monte Carlo mixing, which affects the diversity of synthetic data and increases generation times. To address these issues, we use a novel training algorithm that exploits non-equilibrium effects. This approach, applied on the Restricted Boltzmann Machine, improves the model's ability to correctly classify samples and generate high-quality synthetic data in only a few sampling steps. The effectiveness of this method is demonstrated by its successful application to four different types of data: handwritten digits, mutations of human genomes classified by continental origin, functionally characterized sequences of an enzyme protein family, and homologous RNA sequences from specific taxonomies.

Aurélien Decelle, Lorenzo Rosset, Beatriz Seoane

Datasets in the real world are often complex and to some degree hierarchical, with groups and sub-groups of data sharing common characteristics at different levels of abstraction. Understanding and uncovering the hidden structure of these datasets is an important task that has many practical applications. To address this challenge, we present a new and general method for building relational data trees by exploiting the learning dynamics of the Restricted Boltzmann Machine (RBM). Our method is based on the mean-field approach, derived from the Plefka expansion, and developed in the context of disordered systems. It is designed to be easily interpretable. We tested our method in an artificially created hierarchical dataset and on three different real-world datasets (images of digits, mutations in the human genome, and a homologous family of proteins). The method is able to automatically identify the hierarchical structure of the data. This could be useful in the study of homologous protein sequences, where the relationships between proteins are critical for understanding their function and evolution.

Nicolas Béreux, Aurélien Decelle, Cyril Furtlehner et al.

Restricted Boltzmann Machines (RBMs) are effective tools for modeling complex systems and deriving insights from data. However, training these models with highly structured data presents significant challenges due to the slow mixing characteristics of Markov Chain Monte Carlo processes. In this study, we build upon recent theoretical advancements in RBM training, to significantly reduce the computational cost of training (in very clustered datasets), evaluating and sampling in RBMs in general. The learning process is analogous to thermodynamic continuous phase transitions observed in ferromagnetic models, where new modes in the probability measure emerge in a continuous manner. Such continuous transitions are associated with the critical slowdown effect, which adversely affects the accuracy of gradient estimates, particularly during the initial stages of training with clustered data. To mitigate this issue, we propose a pre-training phase that encodes the principal components into a low-rank RBM through a convex optimization process. This approach enables efficient static Monte Carlo sampling and accurate computation of the partition function. We exploit the continuous and smooth nature of the parameter annealing trajectory to achieve reliable and computationally efficient log-likelihood estimations, enabling online assessment during the training, and propose a novel sampling strategy named parallel trajectory tempering (PTT) which outperforms previously optimized MCMC methods. Our results show that this training strategy enables RBMs to effectively address highly structured datasets that conventional methods struggle with. We also provide evidence that our log-likelihood estimation is more accurate than traditional, more computationally intensive approaches in controlled scenarios. The PTT algorithm significantly accelerates MCMC processes compared to existing and conventional methods.

Lorenzo Rosset, Roberto Netti, Anna Paola Muntoni et al.

In this methods article, we provide a flexible but easy-to-use implementation of Direct Coupling Analysis (DCA) based on Boltzmann machine learning, together with a tutorial on how to use it. The package \texttt{adabmDCA 2.0} is available in different programming languages (C++, Julia, Python) usable on different architectures (single-core and multi-core CPU, GPU) using a common front-end interface. In addition to several learning protocols for dense and sparse generative DCA models, it allows to directly address common downstream tasks like residue-residue contact prediction, mutational-effect prediction, scoring of sequence libraries and generation of artificial sequences for sequence design. It is readily applicable to protein and RNA sequence data.