Performance vs computational efficiency for optimizing single and dynamic MRFs: Setting the state of the art with primal-dual strategies - ScienceDirect
ExportJavaScript is disabled on your browser. Please enable JavaScript to use all the features on this page., October 2008, Pages 14-29Author links open overlay panelShow moreAbstractIn this paper we introduce a novel method to address minimization of static and dynamic MRFs. Our approach is based on principles from linear programming and, in particular, on primal-dual strategies. It generalizes prior state-of-the-art methods such as α-expansion, while it can also be used for efficiently minimizing NP-hard problems with complex pair-wise potential functions. Furthermore, it offers a substantial speedup – of a magnitude 10 – over existing techniques, due to the fact that it exploits information coming not only from the original MRF problem, but also from a dual one. The proposed technique consists of recovering pair of solutions for the primal and the dual such that the gap between them is minimized. Therefore, it can also boost performance of dynamic MRFs, where one should expect that the new pair of primal-dual solutions is closed to the previous one. Promising results in a number of applications, and theoretical, as well as numerical comparisons with the state of the art demonstrate the extreme potentials of this approach.KeywordsMarkov random fieldsLinear programmingPrimal-dual schemaDiscrete optimizationGraph cutsChoose an option to locate/access this article:Check if you have access through your login credentials or your institution.ororRecommended articlesCiting articles (0)Browser Not Supported
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AbstractPrediction problems such as image segmentation, sentence parsing, and gene prediction involve complex output spaces for which multiple decisions must be coordinated to achieve optimal results. Unfortunately, this means that there are generally an exponential number of possible predictions for every input. Markov random fields can be used to express structure in these output spaces, reducing the number of model parameters
however, the problem of learning those parameters from a training sample remains NP-hard in general. We review some recent results on approximate learning of structured prediction problems. There are two distinct approaches. In the first, results from the well-studied field of approximate inference are adapted to the learning setting. In the second, learning performance is characterized directly, producing bounds even when the underlying inference method does not offer formal approximation guarantees. While the literature on this topic is still sparse, we review the strengths and weaknesses of current results, and discuss issues that remain for future work.Do you want to read the rest of this article?Request full-text
Conference PaperFull-text availableAug 2011Conference PaperJanuary 2007In many structured prediction problems, the highest-scoring labeling is hard to compute exactly, leading to the use of approximate inference methods. However, when inference is used in a learning algorithm, a good approximation of the score may not be sufficient. We show in particular that learning can fail even with an approximate inference method with rigorous approximation guarantees. There... [Show full abstract]ArticleJuly 2012 · Determinantal point processes (DPPs) are elegant probabilistic models of
repulsion that arise in quantum physics and random matrix theory. In contrast
to traditional structured models like Markov random fields, which become
intractable and hard to approximate in the presence of negative correlations,
DPPs offer efficient and exact algorithms for sampling, marginalization,
conditioning, and... [Show full abstract]ArticleDecember 2010We present a novel probabilistic model for distributions over sets of structures— for example, sets of sequences, trees, or graphs. The critical characteristic of our model is a preference for diversity: sets containing dissimilar structures are more likely. Our model is a marriage of structured probabilistic models, like Markov random fields and context free grammars, with determinantal point... [Show full abstract]Conference PaperNovember 2010We present a novel probabilistic model for distributions over sets of structures— for example, sets of sequences, trees, or graphs. The critical characteristic of our model is a preference for diversity: sets containing dissimilar structures are more likely. Our model is a marriage of structured probabilistic models, like Markov random fields and context free grammars, with determinantal point... [Show full abstract]Browser Not Supported
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