J. Kilian and M. Naor. On the Complexity of Statistical Reasoning. In Proceedings, Israeli Symposium on Theory of Computing and Systems, pages 209{ 217, 1995.  Home/Search Document Details and Download
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Learning with Maximum-Entropy Distributions - Mansour, Schain (2001) (4 citations) (Correct)
....of special interest in physics [SWG85] One of the basic results is the form of the maximumentropy distribution, given a set of constraints. Unfortunately, from a computational point of view, it is NP complete to decide if there is any distribution that satisfies the set of pair wise constraints [KM93, KN95]. As stated before, learning the read once DNF concept class over arbitrary distribution is equivalent to DNF [HKLW90] Constraining the underlying probability distribution to uniform or product distribution enables to learn read once DNF [KLV94] However, the algorithms for learning the read once ....
....is to delete such a variable from the input domain since it is deterministic. As stated in the introduction, the related computational problem is hard since testing the consistency of the given expectations (existence of any distribution satisfying those constraints) is known to be NP Complete [KN95, KM93]. 4 Properties of MEM distributions In this section we derive a few properties of MEM distributions. One basic property which will be very important for us is relating the probabilities when a variable is fixed to one or zero. We show that for MEM distributions those probabilities are fairly ....
Joe Kilian and Moni Naor. On the complexity of statistical reasoning. In Proceedings of the 3rd Israel Symposium on Theory of Computing and Systems, pages 209--217, 1995.
Probabilistically Checkable Proofs with Zero Knowledge - Kilian, Petrank, Tardos Self-citation (Kilian) (Correct)
....greater than U . Robust PCPs and the hardness of approximation Our motivation for this investigation is primarily philosophical. However, it is worth noting that constructions for robust PCPs, or variants thereof have been used to prove results on the hardness of approximation. Kilian and Naor [8] directly use robust PCPs to establish the strongest known hardness of approximation results for certain problems in statistical inference. Feige and Kilian [4] use PCPs inspired by robust PCPs, though with slightly weaker properties, to show the strongest known results for approximating the ....
J. Kilian and M. Naor. On the Complexity of Statistical Reasoning. In Proceedings, Israeli Symposium on Theory of Computing and Systems, pages 209{ 217, 1995.
Zero Knowledge and the Chromatic Number - Feige, Kilian (1996) (90 citations) Self-citation (Kilian) (Correct)
....provide a direct reduction from ff(G) to (G) Instead, it is based on randomized versions of PCPs (RPCPs) introduced in [11] Zero knowledge PCPs are a subfamily of randomized PCPs. Indeed, some of the randomized PCPs we use are in fact zero knowledge PCPs. Similar PCPs were previously used in [25] to show the hardness of certain probabilistic inference problems. In its simpler form, our reduction has the following structure: Simple hardness results for (G) 1. Reduce the problem of approximating max 3SAT to approximating the acceptance probability in a randomized PCP for max 3SAT. 2. ....
J. Kilian and M. Naor. On the Complexity of Statistical Reasoning. In Proceedings, Israeli Symposium on Theory of Computing and Systems, pages 209--217, 1995.
Probabilistically Checkable Proofs with Zero Knowledge - Kilian, Petrank, Tardos (1997) Self-citation (Kilian) (Correct)
....greater than U . Robust PCPs and the hardness of approximation Our motivation for this investigation is primarily philosophical. However, it is worth noting that constructions for robust PCPs, or variants thereof have been used to prove results on the hardness of approximation. Kilian and Naor [8] directly use robust PCPs to establish the strongest known hardness of approximation results for certain problems in statistical inference. Feige and Kilian [4] use PCPs inspired by robust PCPs, though with slightly weaker properties, to show the strongest known results for approximating the ....
J. Kilian and M. Naor. On the Complexity of Statistical Reasoning. In Proceedings, Israeli Symposium on Theory of Computing and Systems, pages 209--217, 1995.
The Weizmann Workshop on Probabilistic Proof Systems - Feige, (Eds.) (1994) (Correct)
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J. Kilian, M. Naor. "On the complexity of statistical reasoning."
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