Efficient Exact Inference in Planar Ising Models

We give polynomial-time algorithms for the exact computation of lowest-energy (ground) states, worst margin violators, log partition functions, and marginal edge probabilities in certain binary undirected graphical models. Our approach provides an interesting alternative to the well-known graph cut paradigm in that it does not impose any submodularity constraints; instead we require planarity to establish a correspondence with perfect matchings (dimer coverings) in an expanded dual graph. We implement a unified framework while delegating complex but well-understood subproblems (planar embedding, maximum-weight perfect matching) to established algorithms for which efficient implementations are freely available. Unlike graph cut methods, we can perform penalized maximum-likelihood as well as maximum-margin parameter estimation in the associated conditional random fields (CRFs), and employ marginal posterior probabilities as well as maximum a posteriori (MAP) states for prediction. Maximum-margin CRF parameter estimation on image denoising and segmentation problems shows our approach to be efficient and effective. A C++ implementation is available from http://nic.schraudolph.org/isinf/Comment: Fixed a number of bugs in v1; added 10 pages of additional figures, explanations, proofs, and experiment

Latent Sentiment Detection in Online Social Networks: A Communications-oriented View

In this paper, we consider the problem of latent sentiment detection in Online Social Networks such as Twitter. We demonstrate the benefits of using the underlying social network as an Ising prior to perform network aided sentiment detection. We show that the use of the underlying network results in substantially lower detection error rates compared to strictly features-based detection. In doing so, we introduce a novel communications-oriented framework for characterizing the probability of error, based on information-theoretic analysis. We study the variation of the calculated error exponent for several stylized network topologies such as the complete network, the star network and the closed-chain network, and show the importance of the network structure in determining detection performance.Comment: 13 pages, 6 figures, Submitted to ICC 201

Global Minimum Depth In Edwards-Anderson Model

In the literature the most frequently cited data are quite contradictory, and there is no consensus on the global minimum value of 2D Edwards-Anderson (2D EA) Ising model. By means of computer simulations, with the help of exact polynomial Schraudolph-Kamenetsky algorithm, we examined the global minimum depth in 2D EA-type models. We found a dependence of the global minimum depth on the dimension of the problem N and obtained its asymptotic value in the limit $N\to\infty$. We believe these evaluations can be further used for examining the behavior of 2D Bayesian models often used in machine learning and image processing.Comment: 10 pages, 4 figures, 2 tables, submitted to conference on Engineering Applications of Neural Networks (EANN 2019