The complexity of promise problems with applications to public-key cryptography
Information and Control
Random generation of combinatorial structures from a uniform
Theoretical Computer Science
Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity class
Journal of Computer and System Sciences - 17th Annual ACM Symposium in the Theory of Computing, May 6-8, 1985
Journal of the ACM (JACM)
Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
A few logs suffice to build (almost) all trees (l): part I
Random Structures & Algorithms
Fast convergence of the Glauber dynamics for sampling independent sets
Random Structures & Algorithms - Special issue on statistical physics methods in discrete probability, combinatorics, and theoretical computer science
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
A complete problem for statistical zero knowledge
Journal of the ACM (JACM)
Direct Minimum-Knowledge Computations
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
Everything Provable is Provable in Zero-Knowledge
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Optimal phylogenetic reconstruction
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Distorted Metrics on Trees and Phylogenetic Forests
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Learning Factor Graphs in Polynomial Time and Sample Complexity
The Journal of Machine Learning Research
Reconstruction of Markov Random Fields from Samples: Some Observations and Algorithms
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Theoretical Computer Science
High-dimensional Gaussian graphical model selection: walk summability and local separation criterion
The Journal of Machine Learning Research
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Markov random fields are often used to model high dimensional distributions in a number of applied areas. A number of recent papers have studied the problem of reconstructing a dependency graph of bounded degree from independent samples from the Markov random field. These results require observing samples of the distribution at all nodes of the graph. It was heuristically recognized that the problem of reconstructing the model where there are hidden variables (some of the variables are not observed) is much harder.Here we prove that the problem of reconstructing bounded-degree models with hidden nodes is hard. Specifically, we show that unless NP = RP,It is impossible to decide in randomized polynomial time if two models generate distributions whose statistical distance is at most 1/3 or at least 2/3.Given two generating models whose statistical distance is promised to be at least 1/3, and oracle access to independent samples from one of the models, it is impossible to decide in randomized polynomial time which of the two samples is consistent with the model.The second problem remains hard even if the samples are generated efficiently, albeit under a stronger assumption.