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The cutting plane method is an augmentative constrained optimization procedure that is often used with continuous-domain optimization techniques such as linear and convex programs. We investigate the viability of a similar idea within message passing – which produces integral solutions in the context of two com-binatorial problems: 1) For Traveling Salesman… (More)

- Siamak Ravanbakhsh, Philip Liu, Trent C. Bjorndahl, Rupasri Mandal, Jason R. Grant, Michael Wilson +6 others
- ArXiv
- 2015

Many diseases cause significant changes to the concentrations of small molecules (a.k.a. metabolites) that appear in a person's biofluids, which means such diseases can often be readily detected from a person's " metabolic profile"—i.e., the list of concentrations of those metabolites. This information can be extracted from a biofluids Nuclear Magnetic… (More)

We introduce an efficient message passing scheme for solving Constraint Satisfaction Problems (CSPs), which uses stochastic perturbation of Belief Propagation (BP) and Survey Propagation (SP) messages to bypass decimation and directly produce a single satisfying assignment. Our first CSP solver, called Perturbed Belief Propagation, smoothly interpolates two… (More)

We study the min-max problem in factor graphs, which seeks the assignment that minimizes the maximum value over all factors. We reduce this problem to both min-sum and sum-product inference , and focus on the later. In this approach the min-max inference problem is reduced to a sequence of Constraint Satisfaction Problems (CSP), which allows us to solve the… (More)

Some real-world problems are partially decomposable, in that they can be decomposed into a set of coupled sub-problems, that are each relatively easy to solve. However, when these sub-problem share some common variables, it is not sufficient to simply solve each sub-problem in isolation. We develop a technology for such problems, and use it to address the… (More)

Belief Propagation (BP) is one of the most popular methods for inference in probabilis-tic graphical models. BP is guaranteed to return the correct answer for tree structures, but can be incorrect or non-convergent for loopy graphical models. Recently, several new approximate inference algorithms based on cavity distribution have been proposed. These… (More)

This paper studies the form and complexity of inference in graphical models using the abstraction offered by algebraic structures. In particular, we broadly formalize inference problems in graphical models by viewing them as a sequence of operations based on commutative semigroups. We then study the computational complexity of inference by organizing… (More)

We propose a Laplace approximation that creates a stochastic unit from any smooth monotonic activation function, using only Gaussian noise. This paper investigates the application of this stochastic approximation in training a family of Restricted Boltzmann Machines (RBM) that are closely linked to Bregman divergences. This family, that we call exponential… (More)

A key bottleneck in structured output prediction is the need for inference during training and testing, usually requiring some form of dynamic programming. Rather than using approximate inference or tailoring a specialized inference method for a particular structure—standard responses to the scaling challenge— we propose to embed prediction constraints… (More)

A grand challenge of the 21 st century cosmol-ogy is to accurately estimate the cosmological parameters of our Universe. A major approach in estimating the cosmological parameters is to use the large scale matter distribution of the Universe. Galaxy surveys provide the means to map out cosmic large-scale structure in three dimensions. Information about… (More)