Probabilistic graphical models are powerful tools for analyzing constrained, continuous domains. However, finding most-probable explanations (MPEs) in these models can be computationally expensive. In this paper, we improve the scalability of MPE inference in a class of graphical models with piecewise-linear and piecewise-quadratic dependencies and linear constraints over continuous domains. We...

This work aims to design a detection and segmentationmethod using a graphical model in the context of multi-object brain image segmentation. We resort to dynamic programming as the optimization strategy to find the global minimum energy for the relation graph. Compared to other graphical models like tree structures, the proposed approach offers flexibility in accommodating more interactions amo...

This work presents a set of three simple and explicit equations as a function of temperature, pressure, and mass fraction for calculation of the entropy of the ammonia-water mixture in saturated and super heated conditions. They are intended for use in the optimization and second law efficiency of absorption processes. The equations are constructed by the least square method for curve fitting u...

Statistical model learning problems are traditionally solved using either heuristic greedy optimization or stochastic simulation, such as Markov chain Monte Carlo or simulated annealing. Recently, there has been an increasing interest in the use of combinatorial search methods, including those based on computational logic. Some of these methods are particularly attractive since they can also be...

1. Introduction. We thank all the discussants for their careful reading of our paper, and for their insightful critiques. We would also like to thank the editors for organizing this discussion. Our paper contributes to the area of high-dimensional statistics which has received much attention over the past several years across the statistics, machine learning and signal processing communities. I...

1. Matrix perturbation bounds. Given a low-rank matrix we consider what happens to the invariant subspaces when the matrix is perturbed by a small amount. We assume without loss of generality that the matrix under consideration is square and symmetric, and our methods can be extended to the general non-symmetric non-square case. We refer the interested reader to [1, 3] for more details, as the ...

We wish to congratulate the authors for their innovative contribution, which is bound to inspire much further research. We find latent variable model selection to be a fantastic application of matrix decomposition methods, namely, the superposition of low-rank and sparse elements. Clearly, the methodology introduced in this paper is of potential interest across many disciplines. In the followin...

Belief Propagation algorithms are instruments used broadly to solve graphical model optimization and statistical inference problems. In the general case of a loopy Graphical Model, Belief Propagation is a heuristic which is quite successful in practice, even though its empirical success, typically, lacks theoretical guarantees. This paper extends the short list of special cases where correctnes...

The R package vdg provides a flexible interface for producing various graphical summaries of the prediction variance associated with specific linear model specifications and experimental designs. These methods include variance dispersion graphs, fraction of design space plots and quantile plots which can assist in choosing between a catalogue of candidate experimental designs. Instead of restri...