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The inverse Potts problem for estimating evolutionary single-site fields and pairwise couplings in homologous protein sequences from their single-site and pairwise amino acid frequencies observed in their multiple sequence alignment would…

Statistical analysis of evolutionary-related protein sequences provides insights about their structure, function, and history. We show that Restricted Boltzmann Machines (RBM), designed to learn complex high-dimensional data and their…

The analysis of mixed data has been raising challenges in statistics and machine learning. One of two most prominent challenges is to develop new statistical techniques and methodologies to effectively handle mixed data by making the data…

Many real-world tasks, from associative memory to symbolic reasoning, benefit from discrete, structured representations that standard continuous latent models can struggle to express. We introduce the Gaussian-Multinoulli Restricted…

Graphical models are a rich language for describing high-dimensional distributions in terms of their dependence structure. While there are algorithms with provable guarantees for learning undirected graphical models in a variety of…

The restricted Boltzmann machine (RBM) is a flexible tool for modeling complex data, however there have been significant computational difficulties in using RBMs to model high-dimensional multinomial observations. In natural language…

Restricted Boltzmann machines (RBM) and deep Boltzmann machines (DBM) are important models in machine learning, and recently found numerous applications in quantum many-body physics. We show that there are fundamental connections between…

The success of any machine learning system depends critically on effective representations of data. In many cases, it is desirable that a representation scheme uncovers the parts-based, additive nature of the data. Of current representation…

Representation by neural networks, in particular by restricted Boltzmann machines (RBM), has provided a powerful computational tool to solve quantum many-body problems. An important open question is how to characterize which class of…

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…

Restricted Boltzmann Machine (RBM) is an importan- t generative model modeling vectorial data. While applying an RBM in practice to images, the data have to be vec- torized. This results in high-dimensional data and valu- able spatial…

The restricted Boltzmann machine is a network of stochastic units with undirected interactions between pairs of visible and hidden units. This model was popularized as a building block of deep learning architectures and has continued to…

We develop a machine learning method to construct accurate ground-state wave functions of strongly interacting and entangled quantum spin as well as fermionic models on lattices. A restricted Boltzmann machine algorithm in the form of an…

As a problem in data science the inverse Ising (or Potts) problem is to infer the parameters of a Gibbs-Boltzmann distributions of an Ising (or Potts) model from samples drawn from that distribution. The algorithmic and computational…

Deep generative models have become ubiquitous due to their ability to learn and sample from complex distributions. Despite the proliferation of various frameworks, the relationships among these models remain largely unexplored, a gap that…

We set up Restricted Boltzmann Machines (RBM) to reproduce the Long Range Ising (LRI) models of the Ohmic type in one dimension. The RBM parameters are tuned by using the standard machine learning procedure with an additional method of…

In this article, we extend the conventional framework of convolutional-Restricted-Boltzmann-Machine to learn highly abstract features among abitrary number of time related input maps by constructing a layer of multiplicative units, which…

The deep extension of the restricted Boltzmann machine (RBM), known as the deep Boltzmann machine (DBM), is an expressive family of machine learning models which can serve as compact representations of complex probability distributions.…

Geometric frustration gives rise to emergent quantum phenomena and exotic phases of matter. While Monte Carlo methods are traditionally used to simulate such systems, their sampling efficiency is limited by the complexity of interactions…

Restricted Boltzmann Machines are key tools in Machine Learning and are described by the energy function of bipartite spin-glasses. From a statistical mechanical perspective, they share the same Gibbs measure of Hopfield networks for…