35 research outputs found

    Inductive reasoning and Kolmogorov complexity

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    AbstractReasoning to obtain the “truth” about reality, from external data, is an important, controversial, and complicated issue in man's effort to understand nature. (Yet, today, we try to make machines do this.) There have been old useful principles, new exciting models, and intricate theories scattered in vastly different areas including philosophy of science, statistics, computer science, and psychology. We focus on inductive reasoning in correspondence with ideas of R. J. Solomonoff. While his proposals result in perfect procedures, they involve the noncomputable notion of Kolmogorov complexity. In this paper we develop the thesis that Solomonoff's method is fundamental in the sense that many other induction principles can be viewed as particular ways to obtain computable approximations to it. We demonstrate this explicitly in the cases of Gold's paradigm for inductive inference, Rissanen's minimum description length (MDL) principle, Fisher's maximum likelihood principle, and Jaynes' maximum entropy principle. We present several new theorems and derivations to this effect. We also delimit what can be learned and what cannot be learned in terms of Kolmogorov complexity, and we describe an experiment in machine learning of handwritten characters. We also give an application of Kolmogorov complexity in Valiant style learning, where we want to learn a concept probably approximately correct in feasible time and examples

    Information theory : proceedings of the 1990 IEEE international workshop, Eindhoven, June 10-15, 1990

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    Information theory : proceedings of the 1990 IEEE international workshop, Eindhoven, June 10-15, 1990

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    The Monge array--an abstraction and its applications

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1991.Includes bibliographical references (p. 211-219).by James KIimbrough Park.Ph.D

    Computational learning theory : new models and algorithms

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1989.Includes bibliographical references (leaves 116-120).by Robert Hal Sloan.Ph.D

    PCD

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    Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Page 96 blank. Cataloged from PDF version of thesis.Includes bibliographical references (p. 87-95).The security of systems can often be expressed as ensuring that some property is maintained at every step of a distributed computation conducted by untrusted parties. Special cases include integrity of programs running on untrusted platforms, various forms of confidentiality and side-channel resilience, and domain-specific invariants. We propose a new approach, proof-carrying data (PCD), which sidesteps the threat of faults and leakage by reasoning about properties of a computation's output data, regardless of the process that produced it. In PCD, the system designer prescribes the desired properties of a computation's outputs. Corresponding proofs are attached to every message flowing through the system, and are mutually verified by the system's components. Each such proof attests that the message's data and all of its history comply with the prescribed properties. We construct a general protocol compiler that generates, propagates, and verifies such proofs of compliance, while preserving the dynamics and efficiency of the original computation. Our main technical tool is the cryptographic construction of short non-interactive arguments (computationally-sound proofs) for statements whose truth depends on "hearsay evidence": previous arguments about other statements. To this end, we attain a particularly strong proof-of-knowledge property. We realize the above, under standard cryptographic assumptions, in a model where the prover has blackbox access to some simple functionality - essentially, a signature card.by Alessandro Chiesa.M.Eng

    Teaching, learning, and exploration

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994.Includes bibliographical references (p. 81-85).by Yiqun Yin.Ph.D
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