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Bridging Algorithmic Information Theory and Machine Learning: A New Approach to Kernel Learning
Physica A: Statistical Mechanics and its Applications, 2023Machine Learning (ML) and Algorithmic Information Theory (AIT) look at Complexity from different points of view. We explore the interface between AIT and Kernel Methods (that are prevalent in ML) by adopting an AIT perspective on the problem of learning ...
B. Hamzi, Marcus Hutter, H. Owhadi
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Algorithmic Information Theory for Physicists and Natural Scientists
, 2020This book has been written in the hope that readers will be able to absorb the key ideas behind algorithmic information theory so that they are in a better position to access the mathematical developments and to apply the ideas to their own areas of ...
S. Devine
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Algorithmic Information Theory and Undecidability
Synthese, 2000Chaitin has proven that the halting probability \(\Omega=\sum\{2^{-|p|}\mid p\text{\;halts}\}\) of a universal Turing machine is not computable, and, moreover, that any recursively axiomatizable theory enables us to determine only finitely many digits of \(\Omega\).
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On the algorithmic foundation of information theory
IEEE Transactions on Information Theory, 1979The information content of binary sequences is defined by minimal program complexity measures and is related to computable martingales. The equivalence of the complexity approach and the martingale approach after restriction to effective random tests is used to establish generalized source coding theorems and converses.
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The application of algorithmic information theory to noisy patterned strings
Complexity, 2006S. Devine
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A statistical mechanical interpretation of algorithmic information theory
SpringerBriefs in Mathematical Physics, 2008We develop a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities, such as free energy, energy, statistical mechanical entropy, and specific heat, into algorithmic information ...
K. Tadaki
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Algorithmic Information Theory
1993Algorithmic information theory uses the notion of algorithm to measure the amount of information in a finite object. The corresponding definition was suggested in 1960s by Ray Solomonoff, Andrei Kolmogorov, Gregory Chaitin and others: the amount of information in a finite object, or its complexity, was defined as the minimal length of a program that ...
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Analytic algorithmics, combinatorics, and information theory
IEEE Information Theory Workshop, 2005., 2005Analytic information theory aims at studying problems of information theory using analytic techniques of computer science and combinatorics. Following Hadamard's and Knuth's precept, we tackle these problems by complex analysis methods such as generating functions, Mellin transform, Fourier series, saddle point method, analytic poissonization and de ...
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A consistency algorithm based on information theory
Mathematical Population Studies, 1994"This paper provides a geometric-mean solution to the consistency problem of multidimensional demographic projection models, based on the constrained minimization of an entropy function. A comparison with the existing harmonic-mean solution yields many similarities and almost no differences....However, one major advantage of the geometric mean is that
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