News
15 Sep, 2017. The slide file was uploaded
Title
Solomonoff’s universal induction, or algorithmic probability
Type
Invited talk at SIG-AGI
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slide
Solomonoff’s universal induction, or algorithmic probability
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Turing degree
News
5-7 Aug, 2017. Summer School of mathematical foundations
Title
Turing degree
Type
A lecture at summer school of mathematical foundations (in Japanese)
Download
A resume in Japanese can be downloaded from the website.
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Relation between the rate of convergence of strong law of large numbers and the rate of concentration of Bayesian prior in game-theoretic probability
News
8 Aug, 2017. Online
28 July 2017. accepted by SPA
Title
Relation between the rate of convergence of strong law of large numbers and the rate of concentration of Bayesian prior in game-theoretic probability
(with R. Sato and A. Takemura)
Type
Full paper
Journal
Stochastic Processes and their Applications
The page at SPA
Abstract
We study the behavior of the capital process of a continuous Bayesian mixture of fixed proportion
betting strategies in the one-sided unbounded forecasting game in game-theoretic probability. We
establish the relation between the rate of convergence of the strong law of large numbers in the selfnormalized
form and the rate of divergence to infinity of the prior density around the origin. In
particular we present prior densities ensuring the validity of Erdos–Feller–Kolmogorov–Petrowsky ˝
law of the iterated logarithm.
download
arXiv
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Null-additivity in the theory of algorithmic randomness
News
Gave up for publication.
Rejected.
Title
Null-additivity in the theory of algorithmic randomness
Type
Full paper
Journal
Abstract
download
additive
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Berry’s paradox
News
22 Apr, 2016. The slide file was uploaded
Title
Berry’s paradox
Type
Freshman seminar at math department of Meiji University
Download
Slide in Japanese
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Random numbers
News
22 Apr, 2016. The slide file was uploaded
Title
Random numbers
Type
A talk at a high school
Download
Slide (in Japanese)
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Can one compute a more random set uniformly?
News
24 Mar, 2016. The slide file was uploaded
Title
Can one compute a more random set uniformly?
Type
A talk at a meeting of Mathematical Society of Japan
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mathsoc
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An Introduction to statistics
News
24 Mar, 2016. The slide file was uploaded
Title
An Introduction to statistics
Type
A talk to junior-high students
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junior
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Randomness of randomness deficiency
News
26 Feb, 2016. The slide file was uploaded
Title
Randomness of randomness deficiency
Type
A talk in a seminar with Suzuki lab
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slide
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Randomness notions in Muchnik and Medvedev degrees
News
26 Feb, 2016. The slide file was uploaded
Title
Randomness notions in Muchnik and Medvedev degrees
Type
A talk in Dagstuhl seminar on “Computability Theory”
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slide
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