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We study a simple notion of structural invariance that readily suggests a parameter-sharing scheme in deep neural networks. In particular, we define structure as a collection of relations, and derive graph convolution and recurrent neural networks as special cases. We study composition of basic structures in defining models that are invariant to more(More)
—Boolean factor analysis is the task of decomposing a binary matrix to the Boolean product of two binary factors. This unsupervised data-analysis approach is desirable due to its interpretability, but hard to perform due its NP-hardness. A closely related problem is low-rank Boolean matrix completion from noisy observations. We treat these problems as(More)
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 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 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)
—Understanding the nature of dark energy, the mysterious force driving the accelerated expansion of the Universe, is a major challenge of modern cosmology. The next generation of cosmological surveys, specifically designed to address this issue, rely on accurate measurements of the apparent shapes of distant galaxies. However, shape measurement methods(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)
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)
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)