Universal Artificial Intelligence: Sequential Decisions Based On Algorithmic Probability
Universal Artificial Intelligence: Sequential Decisions Based On Algorithmic Probability
Prediction, Learning, and Games
Prediction, Learning, and Games
On the possibility of learning in reactive environments with arbitrary dependence
Theoretical Computer Science
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
On Finding Predictors for Arbitrary Families of Processes
The Journal of Machine Learning Research
On the Relation between Realizable and Nonrealizable Cases of the Sequence Prediction Problem
The Journal of Machine Learning Research
| Hi-index | 0.00 |
The problem is sequence prediction in the following setting. A sequence x1, ..., xn, ... of discrete-valued observations is generated according to some unknown probabilistic law (measure) μ. After observing each outcome, it is required to give the conditional probabilities of the next observation. The measure μ belongs to an arbitrary class C of stochastic processes. We are interested in predictors ρ whose conditional probabilities converge to the "true" μ-conditional probabilities if any μ ε C is chosen to generate the data. We show that if such a predictor exists, then a predictor can also be obtained as a convex combination of a countably many elements of C. In other words, it can be obtained as a Bayesian predictor whose prior is concentrated on a countable set. This result is established for two very different measures of performance of prediction, one of which is very strong, namely, total variation, and the other is very weak, namely, prediction in expected average Kullback-Leibler divergence.