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The Bayesian framework is a well-studied and successful framework for inductive reasoning, which includes hypothesis testing and confirmation, parameter estimation, sequence prediction, classification, and regression.
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Théorie analytique des probabilités
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Theory of Probability
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A formal theory of inductive inference: Parts 1 and 2
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P. Gács · 1974
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Laws of information conservation (non-growth) and aspects of the foundation of probability theory
L. A. Levin · 1974
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A theory of program size formally identical to information theory
G. J. Chaitin · 1975
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On the complexity of finite sequences
A. Lempel and J. Ziv · 1976
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Complexity-based induction systems: Comparisons and convergence theorems
R. J. Solomonoff · 1978
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Reference posterior distributions for Bayesian inference (with discussion)
J. M. Bernardo · 1979
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On the relation between descriptional complexity and algorithmic probability
P. Gács · 1983
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A universal prior for integers and estimation by minimum description length
J. J. Rissanen · 1983
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A. P. Dawid · 1984
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Stochastic Complexity in Statistical Inquiry
J. J. Rissanen · 1989
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Information-theoretic asymptotics of Bayes methods
B. S. Clarke and A. R. Barron · 1990
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Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory
J. Earman · 1993
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The selection of prior distributions by formal rules
R. E. Kass and L. Wasserman · 1996
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Inferences from multinomial data: learning about a bag of marbles
P. Walley · 1996
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Optimality of universal Bayesian prediction for general loss and alphabet
M. Hutter · 2003
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Probability Theory: The Logic of Science
E. T. Jaynes · 2003
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Universal convergence of semimeasures on individual random sequences
M. Hutter and An. A. Muchnik · 2004
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Universal Artificial Intelligence: Sequential Decisions based on Algorithmic Probability
M. Hutter · 2004
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Probability captures the logic of scientific confirmation
P. Maher · 2004
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On the convergence speed of MDL predictions for Bernoulli sequences
J. Poland and M. Hutter · 2004
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M. Li and P. M. B. Vitányi · 1997
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No free lunch theorems for optimization
D. H. Wolpert and W. G. Macready · 1997
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Laplace’s law of succession and universal encoding
R. E. Krichevskiy · 1998
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Universal prediction
N. Merhav and M. Feder · 1998
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The Nature of Statistical Learning Theory
V. N. Vapnik · 1999
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New error bounds for Solomonoff prediction
M. Hutter · 2001
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Optimal ordered problem solver
J. Schmidhuber · 2004
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Monotone conditional complexity bounds on future prediction errors
A. Chernov and M. Hutter · 2005
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Clustering by compression
R. Cilibrasi and P. M. B. Vitányi · 2005
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Statistical and Inductive Inference by Minimum Message Length
C. S. Wallace · 2005
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Similarity of objects and the meaning of words
R. Cilibrasi and P. M. B. Vitányi · 2006
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On generalized computable universal priors and their convergence
M. Hutter · 2006
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Stationary algorithmic probability
Markus Müller · 2006
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MDL convergence speed for Bernoulli sequences
J. Poland and M. Hutter · 2006
Later among the works it cites.
Algorithmic complexity bounds on future prediction errors
A. Chernov, M. Hutter, and J. Schmidhuber · 2007
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