Arithmetic circuits (ACs) exploit context-specific independence and determinism to allow exact inference even in networks with high treewidth. In this paper, we introduce the first ever approximate inference methods using ACs, for domains where exact inference remains intractable. We propose and evaluate a variety of techniques based on exact compilation, forward sampling, AC structure learning...

As is well-known, the use of Shannon sampling to interpolate functions with discontinuous jump points leads to the Gibbs’ overshoot. In image processing, it can lead to the problem of artifacts close to edges, known as Gibbs ringring. Its amplitude cannot be reduced by increasing the sample density. Here we consider a generalized Shannon sampling method which allows the use of timevarying sampl...

Gibbs sampling on factor graphs is a widely used inference technique, which often produces good empirical results. Theoretical guarantees for its performance are weak: even for tree structured graphs, the mixing time of Gibbs may be exponential in the number of variables. To help understand the behavior of Gibbs sampling, we introduce a new (hyper)graph property, called hierarchy width. We show...

This paper proposes and compares two new sampling schemes for sparse deconvolution using a Bernoulli-Gaussian model. To tackle such a deconvolution problem in a blind and unsupervised context, the Markov Chain Monte Carlo (MCMC) framework is usually adopted, and the chosen sampling scheme is most often the Gibbs sampler. However, such a sampling scheme fails to explore the state space efficient...

Single nucleotide polymorphisms (SNPs) are genetic changes that can occur within a DNA sequence. Due to the high frequency of SNPs in the human genome, it is desirable to select a small set of SNPs (tagging SNPs) that can be used to represent the majority of SNPs. We propose a Gibbs sampling approach to find a small set of SNPs with minimum redundancy for tagging purposes. Preclustering is adde...

Machine learning models of music typically break up the task of composition into a chronological process, composing a piece of music in a single pass from beginning to end. On the contrary, human composers write music in a nonlinear fashion, scribbling motifs here and there, often revisiting choices previously made. In order to better approximate this process, we train a convolutional neural ne...

Standard Gibbs sampling applied to a multivariate normal distribution with a specified precision matrix is equivalent in fundamental ways to the Gauss–Seidel iterative solution of linear equations in the precision matrix. Specifically, the iteration operators, the conditions under which convergence occurs, and geometric convergence factors (and rates) are identical. These results hold for arbit...

This paper proposes a novel model estimationmethod, which uses nested Gibbs sampling to develop amixture-of-mixture model to represent the distribution of the model’s components with a mixture model. This model is suitable for analyzing multilevel data comprising frame-wise observations, such as videos and acoustic signals, which are composed of frame-wise observations. Deterministic procedures...