Elements of information theory
Elements of information theory
The complexity and effectiveness of prediction algorithms
Journal of Complexity
Randomized algorithms
Universal Compression and Retrieval
Universal Compression and Retrieval
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Information Theory and Reliable Communication
Information Theory and Reliable Communication
Laplace's law of succession and universal encoding
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Experimental investigation of forecasting methods based on data compression algorithms
Problems of Information Transmission
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The problem of predicting a sequence x1, x2, ... generated by a discrete source with unknown statistics is considered. Each letter xt+1 is predicted using information on the word x1x2...xt only. In fact, this problem is a classical problem which has received much attention. Its history can be traced back to Laplace. To estimate the efficiency of a method of prediction, three quantities are considered: the precision as given by the Kullback-Leibler divergence, the memory size of the program needed to implement the method on a computer, and the time required, measured by the number of binary operations needed at each time instant. A method is presented for which the memory size and the average time are close to the minimum. The results can readily be translated to results about adaptive coding.