Related papers: Composite Likelihood Estimation for Restricted Bol…

Approximate Bayesian computation (ABC) is a popular technique for approximating likelihoods and is often used in parameter estimation when the likelihood functions are analytically intractable. Although the use of ABC is widespread in many…

We present explicit classes of probability distributions that can be learned by Restricted Boltzmann Machines (RBMs) depending on the number of units that they contain, and which are representative for the expressive power of the model. We…

Associated to each graph G is a Gaussian graphical model. Such models are often used in high-dimensional settings, i.e. where there are relatively few data points compared to the number of variables. The maximum likelihood threshold of a…

Software for computation of maximum likelihood estimates in linear structural equation models typically employs general techniques from non-linear optimization, such as quasi-Newton methods. In practice, careful tuning of initial values is…

In this work an iterative algorithm based on unsupervised learning is presented, specifically on a Restricted Boltzmann Machine (RBM) to solve a perfect matching problem on a bipartite weighted graph. Iteratively is calculated the weights…

Maximum likelihood estimation is effective for identifying dynamical systems, but applying it to large networks becomes computationally prohibitive. This paper introduces a maximum likelihood estimation method that enables identification of…

We consider constructing model selection criteria for evaluating nonlinear mixed effects models via basis expansions. Mean functions and random functions in the mixed effects model are expressed by basis expansions, then they are estimated…

Among many efforts to facilitate timely access to safe and effective medicines to children, increased attention has been given to extrapolation. Loosely, it is the leveraging of conclusions or available data from adults or older age groups…

We propose a refined iterative likelihood-maximization algorithm for reconstructing a quantum state from a set of tomographic measurements. The algorithm is characterized by a very high convergence rate and features a simple adaptive…

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 restricted Boltzmann machine is a graphical model for binary random variables. Based on a complete bipartite graph separating hidden and observed variables, it is the binary analog to the factor analysis model. We study this graphical…

Algorithms for jointly obtaining projection estimates of the density and distribution function of a random variable using Legendre polynomials are proposed. For these algorithms, a problem of the conditional optimization is solved. Such…

Restricted Boltzmann Machines (RBMs) are a common family of undirected graphical models with latent variables. An RBM is described by a bipartite graph, with all observed variables in one layer and all latent variables in the other. We…

The article addresses the problem of image sampling with minimal possible sampling rates and reviews the recent advances in sampling theory and methods: modern formulations of the sampling theorems, potentials and limitations of Compressed…

Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…

This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…

Restricted Boltzmann machine (RBM) provide a general framework for modeling physical systems, but their behavior is dependent on hyperparameters such as the learning rate, the number of hidden nodes and the form of the threshold function.…

Graphical models are powerful tools for modeling high-dimensional data, but learning graphical models in the presence of latent variables is well-known to be difficult. In this work we give new results for learning Restricted Boltzmann…

Random effect models are popular statistical models for detecting and correcting spurious sample correlations due to hidden confounders in genome-wide gene expression data. In applications where some confounding factors are known,…

We propose a relaxation-based approximate inference algorithm that samples near-MAP configurations of a binary pairwise Markov random field. We experiment on MAP inference tasks in several restricted Boltzmann machines. We also use our…