Artificial Intelligence
Algorithmic complexity bounds on future prediction errors
Information and Computation
On semimeasures predicting Martin-Löf random sequences
Theoretical Computer Science
Information Processing Letters
Nonstochastic bandits: Countable decision set, unbounded costs and reactive environments
Theoretical Computer Science
Consistency of discrete Bayesian learning
Theoretical Computer Science
Leading strategies in competitive on-line prediction
Theoretical Computer Science
On calibration error of randomized forecasting algorithms
Theoretical Computer Science
On universal transfer learning
Theoretical Computer Science
Sequential predictions based on algorithmic complexity
Journal of Computer and System Sciences
Randomness behaviour in blum universal static complexity spaces
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
Asymptotic non-learnability of universal agents with computable horizon functions
Theoretical Computer Science
On Potential Cognitive Abilities in the Machine Kingdom
Minds and Machines
Universal knowledge-seeking agents
Theoretical Computer Science
The Journal of Machine Learning Research
| Hi-index | 754.84 |
In 1964 the author proposed as an explication of {em a priori} probability the probability measure induced on output strings by a universal Turing machine with unidirectional output tape and a randomly coded unidirectional input tape. Levin has shown that iftilde{P}'_{M}(x)is an unnormalized form of this measure, andP(x)is any computable probability measure on strings,x, thentilde{P}'_{M}geqCP(x)whereCis a constant independent ofx. The corresponding result for the normalized form of this measure,P'_{M}, is directly derivable from Willis' probability measures on nonuniversal machines. If the conditional probabilities ofP'_{M}are used to approximate those ofP, then the expected value of the total squared error in these conditional probabilities is bounded by-(1/2) ln C. With this error criterion, and when used as the basis of a universal gambling scheme,P'_{M}is superior to Cover's measurebast. WhenHastequiv -log_{2} P'_{M}is used to define the entropy of a rmite sequence, the equationHast(x,y)= Hast(x)+H^{ast}_{x}(y)holds exactly, in contrast to Chaitin's entropy definition, which has a nonvanishing error term in this equation.