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Multimodal learning with deep Boltzmann machines (DBMs) is an generative approach to fuse multimodal inputs, and can learn the shared representation via Contrastive Divergence (CD) for classification and information retrieval tasks.…

Uncertainty quantification in neural networks gained a lot of attention in the past years. The most popular approaches, Bayesian neural networks (BNNs), Monte Carlo dropout, and deep ensembles have one thing in common: they are all based on…

We propose an expectation-maximization-like(EMlike) method to train Boltzmann machine with unconstrained connectivity. It adopts Monte Carlo approximation in the E-step, and replaces the intractable likelihood objective with efficiently…

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…

Mean Field inference is central to statistical physics. It has attracted much interest in the Computer Vision community to efficiently solve problems expressible in terms of large Conditional Random Fields. However, since it models the…

Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…

Distributions of data or sensory stimuli often enjoy underlying invariances. How and to what extent those symmetries are captured by unsupervised learning methods is a relevant question in machine learning and in computational neuroscience.…

Restricted Boltzmann Machines (RBMs) are one of the fundamental building blocks of deep learning. Approximate maximum likelihood training of RBMs typically necessitates sampling from these models. In many training scenarios, computationally…

Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…

In this paper, we aim at establishing an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN). In contrast to the classical regression methods, the input variables of distribution…

We examine a wide class of stochastic approximation algorithms for solving (stochastic) nonlinear problems on Riemannian manifolds. Such algorithms arise naturally in the study of Riemannian optimization, game theory and optimal transport,…

Restricted Boltzmann Machines are simple and powerful generative models that can encode any complex dataset. Despite all their advantages, in practice the trainings are often unstable and it is difficult to assess their quality because the…

We propose a probability distribution for multivariate binary random variables. The probability distribution is expressed as principal minors of the parameter matrix, which is a matrix analogous to the inverse covariance matrix in the…

We analyze the structure of stochastic dynamics near either a stable or unstable fixed point, where force can be approximated by linearization. We find that a cost function that determines a Boltzmann-like stationary distribution can always…

Probabilistic Cellular Automata are a generalization of Cellular Automata. Despite their simple definition, they exhibit fascinating and complex behaviours. The stationary behaviour of these models changes when model parameters are varied,…

Recent advances in variational inference enable the modelling of highly structured joint distributions, but are limited in their capacity to scale to the high-dimensional setting of stochastic neural networks. This limitation motivates a…

Variational inference, such as the mean-field (MF) approximation, requires certain conjugacy structures for efficient computation. These can impose unnecessary restrictions on the viable prior distribution family and further constraints on…

There are many advantages to use probability method for nonlinear system identification, such as the noises and outliers in the data set do not affect the probability models significantly; the input features can be extracted in probability…

This work deals with uncertainty quantification for a generic input distribution to some resource-intensive simulation, e.g., requiring the solution of a partial differential equation. While efficient numerical methods exist to compute…

For better clustering performance, appropriate representations are critical. Although many neural network-based metric learning methods have been proposed, they do not directly train neural networks to improve clustering performance. We…