We give an algorithm for learning O(logn)juntas in polynomial-time with respect to Markov Random Fields (MRFs) in a smoothed analysis framework where only the external field has been randomly perturbed. This is a broad generalization1 of the work of Kalai and Teng, who gave an algorithm that succeeded with respect to smoothed product distributions (i.e., MRFs whose dependency graph has no edges). Our algorithm has two phases: (1) an unsupervised structure learning phase and (2) a greedy supervised learning algorithm. This is the first example where algorithms for learning the structure of undirected graphical models have downstream applications to supervised learning.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

In this regime (n > m), learning a sparse model may not lead to significant improvements inprediction accuracy(compared toadensemodel).

Weconsider the task of learning an RBM given samples generated according to it.

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This makes parsing intractable and requires image grammars to be severely restricted in practice, for example by allowing only rectangular regions.

This work addresses the problem of efficient sampling of Markov random fields (MRF). The sampling of Potts or Ising MRF is most often based on Gibbs sampling, and is thus computationally expensive. We consider in this work how to circumvent this bottleneck through a link with Gaussian Markov Random fields. The latter can be sampled in several cost-effective ways, and we introduce a mapping from real-valued GMRF to discrete-valued MRF. The resulting new class of MRF benefits from a few theoretical properties that validate the new model. Numerical results show the drastic performance gain in terms of computational efficiency, as we sample at least 35x faster than Gibbs sampling using at least 37x less energy, all the while exhibiting empirical properties close to classical MRFs.

We would like to thank the reviewers for the insightful remarks and comments. In our experiment, we show that FGNN outperforms the Max-Product algorithm. MRF whose length ranges from 15 to 45 (the potentials are generated using the same protocol as Dataset3). This also further addresses the overfitting issue raised by R1. Factor without trivial representation of fixed dimension: R3.