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- W2952905692 abstract "The Bayesian framework is ideally suited for induction problems. The probability of observing $x_t$ at time $t$, given past observations $x_1...x_{t-1}$ can be computed with Bayes' rule if the true distribution $mu$ of the sequences $x_1x_2x_3...$ is known. The problem, however, is that in many cases one does not even have a reasonable estimate of the true distribution. In order to overcome this problem a universal distribution $xi$ is defined as a weighted sum of distributions $mu_iinM$, where $M$ is any countable set of distributions including $mu$. This is a generalization of Solomonoff induction, in which $M$ is the set of all enumerable semi-measures. Systems which predict $y_t$, given $x_1...x_{t-1}$ and which receive loss $l_{x_t y_t}$ if $x_t$ is the true next symbol of the sequence are considered. It is proven that using the universal $xi$ as a prior is nearly as good as using the unknown true distribution $mu$. Furthermore, games of chance, defined as a sequence of bets, observations, and rewards are studied. The time needed to reach the winning zone is bounded in terms of the relative entropy of $mu$ and $xi$. Extensions to arbitrary alphabets, partial and delayed prediction, and more active systems are discussed." @default.
- W2952905692 created "2019-06-27" @default.
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- W2952905692 date "2001-01-21" @default.
- W2952905692 modified "2023-09-27" @default.
- W2952905692 title "General Loss Bounds for Universal Sequence Prediction" @default.
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