
Newtontype Methods for Inference in HigherOrder Markov Random Fields
Linear programming relaxations are central to map inference in discrete...
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Information Bottleneck on General Alphabets
We prove a source coding theorem that can probably be considered folklor...
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Continuous Multiclass Labeling Approaches and Algorithms
We study convex relaxations of the image labeling problem on a continuou...
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Generalizing Bottleneck Problems
Given a pair of random variables (X,Y)∼ P_XY and two convex functions f_...
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A class of random fields on complete graphs with tractable partition function
The aim of this short note is to draw attention to a method by which the...
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Language modeling with Neural transdimensional random fields
Transdimensional random field language models (TRF LMs) have recently b...
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High Performance Evaluation of Helmholtz Potentials usingthe MultiLevel Fast Multipole Algorithm
Evaluation of pair potentials is critical in a number of areas of physic...
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Bottleneck potentials in Markov Random Fields
We consider general discrete Markov Random Fields(MRFs) with additional bottleneck potentials which penalize the maximum (instead of the sum) over local potential value taken by the MRFassignment. Bottleneck potentials or analogous constructions have been considered in (i) combinatorial optimization (e.g. bottleneck shortest path problem, the minimum bottleneck spanning tree problem, bottleneck function minimization in greedoids), (ii) inverse problems with L_∞norm regularization, and (iii) valued constraint satisfaction on the (,)presemirings. Bottleneck potentials for general discrete MRFs are a natural generalization of the above direction of modeling work to MaximumAPosteriori (MAP) inference in MRFs. To this end, we propose MRFs whose objective consists of two parts: terms that factorize according to (i) (,+), i.e. potentials as in plain MRFs, and (ii) (,), i.e. bottleneck potentials. To solve the ensuing inference problem, we propose highquality relaxations and efficient algorithms for solving them. We empirically show efficacy of our approach on large scale seismic horizon tracking problems.
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