Related papers: Boltzmann machines and energy-based models
We compare and contrast the statistical physics and quantum physics inspired approaches for unsupervised generative modeling of classical data. The two approaches represent probabilities of observed data using energy-based models and…
Restricted Boltzmann machines are energy models made of a visible and a hidden layer. We identify an effective energy function describing the zero-temperature landscape on the visible units and depending only on the tail behaviour of the…
It is widely known that Boltzmann machines are capable of representing arbitrary probability distributions over the values of their visible neurons, given enough hidden ones. However, sampling -- and thus training -- these models can be…
The Boltzmann machine provides a useful framework to learn highly complex, multimodal and multiscale data distributions that occur in the real world. The default method to learn its parameters consists of minimizing the Kullback-Leibler…
We present a concise derivation of the Boltzmann form for single-particle energy distributions in classical many-body Hamiltonian systems. The derivation relies on two physical facts: coarse-graining-scale invariance of the empirical…
Many computer vision applications involve modeling complex spatio-temporal patterns in high-dimensional motion data. Recently, restricted Boltzmann machines (RBMs) have been widely used to capture and represent spatial patterns in a single…
We study a generic ensemble of deep belief networks which is parametrized by the distribution of energy levels of the hidden states of each layer. We show that, within a random energy approach, statistical dependence can propagate from the…
We present the Boltzmann classifier, a novel distance based probabilistic classification algorithm inspired by the Boltzmann distribution. Unlike traditional classifiers that produce hard decisions or uncalibrated probabilities, the…
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.…
Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled. Deep Boltzmann Machines (DBMs) are generative neural networks with these desired properties. We integrate a DBM…
Training in machine learning generally consists in finding one model, whose parameters minimize a data-dependent loss. Yet, empirical work shows that ensemble learning, an approach in which multiple models are sampled, can improve…
Generative models offer a direct way of modeling complex data. Energy-based models attempt to encode the statistical correlations observed in the data at the level of the Boltzmann weight associated with an energy function in the form of a…
Traditional interpretations of probability, whether frequentist or subjective, make no reference to the concept of energy. In this paper, we propose that assigning hypothetical energy levels to the outcomes of a random variable can yield…
In this chapter we provide a thorough overview of the use of energy-based models (EBMs) in the context of inverse imaging problems. EBMs are probability distributions modeled via Gibbs densities $p(x) \propto \exp{-E(x)}$ with an…
Energy-Based Models (EBMs), also known as non-normalized probabilistic models, specify probability density or mass functions up to an unknown normalizing constant. Unlike most other probabilistic models, EBMs do not place a restriction on…
Energy-based models (EBMs) are powerful probabilistic models, but suffer from intractable sampling and density evaluation due to the partition function. As a result, inference in EBMs relies on approximate sampling algorithms, leading to a…
The probability density function for the visible sector of a Riemann-Theta Boltzmann machine can be taken conditional on a subset of the visible units. We derive that the corresponding conditional density function is given by a…
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…
This is a tutorial and survey paper on Boltzmann Machine (BM), Restricted Boltzmann Machine (RBM), and Deep Belief Network (DBN). We start with the required background on probabilistic graphical models, Markov random field, Gibbs sampling,…
The use of generative models to sample equilibrium distributions of many-body systems, as first demonstrated by Boltzmann Generators, has attracted substantial interest due to their ability to produce unbiased and uncorrelated samples in…