Abstract
We consider here an universal predictor based on pattern matching. For a given string x1, x2…, xn, the predictor will guess the next symbol xn+1 in such a way that the prediction error tends to zero as n →∞ provided the string x n1 = x1, x2, …, xn, is generated by a mixing source. We shall prove that the rate of convergence of the prediction error is 0(n-ε) for any ε > 0. In this preliminary version, we only prove our results for memoryless sources and a sketch for mixing sources. However, we indicate that our algorithm can predict equally successfully the next k symbols as long as k= 0(1).
1 This work was supported by Purdue Grant GIFG-9919.
2 Additional support by the ESPRIT Basic Research Action No. 7141 (ALcom II).
3 This author was additionally supported by NSF Grants NCR-9415491 and C-CR-9804760.
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References
P. Algoet, Universal Schemes for Prediction, Gambling and Portfolio Selection, Ann. Prob, 20, 901–941, 1992.
T.M. Cover and J.A. Thomas, Elements of Information Theory,John Wiley&Sons, New York (1991).
A. Ehrenfeucht and J. Mycielski, A Pseudorandom Sequence —How Random Is It? Amer. Math. Monthly,99, 373–375, 1992
M. Feder, N. Merhav, and M. Gutman, Universal Prediction of Individual Sequences, IEEE Trans. Information Theory,38, 1258–1270, 1992.
P. Jacquet, Average Case Analysis of Pattern Matching Predictor, INRIA TR, 1999.
J. Kieffer, Prediction and Information Theory, preprint, 1998.
K. Marton and P. Shields, The Positive-Divergence and Blowing-up Properties, Israel J. Math,80, 331–348 (1994).
N. Merhav, M. Feder, and M. Gutman, Some Properties of Sequential Predictors for Binary Markov Sources, IEEE Trans. Information Theory, 39, 887–892, 1993.
N. Merhav, M. Feder, Universal Prediction, IEEE Trans. Information Theory, 44, 2124–2147, 1998.
G. Moravi, S. Yakowitz, and P. Algoet, Weak Convergent Nonparametric Forecasting of Stationary Time Series, IEEE Trans. Information Theory
J. Rissanen, Complexity of Strings in the Class of Markov Sources, IEEE Trans. Information Theory, 30, 526–532, 1984.
J. Rissanen, Universal Coding, Information, Prediction, and Estimation, IEEE Trans. Information Theory,30, 629–636, 1984.
B. Ryabko, Twice-Universal Coding, Problems of Information Transmission, 173–177, 1984.
B. Ryabko, Prediction of Random Sequences and Universal Coding, Problems of Information Transmission, 24, 3–14, 1988.
B. Ryabko, The Complexity and Effectiveness of Prediction Algorithms, J. Complexity,10, 281–295, 1994.
C. Shannon, Prediction and Entropy of Printed English, Bell System Tech. J, 30, 50–64, 1951.
W. Szpankowski, A Generalized Suffix Tree and Its (Un)Expected Asymptotic Behaviors, SIAM J. Compt, 22, 1176–1198, 1993.
W. Szpankowski, Average Case Analysis of Algorithms on Sequences, John Wiley & Sons, New York 2000 (to appear).
J. Vitter and P. Krishnan, Optimal Prefetching via Data Compression, J. ACM,43, 771–793, 1996.
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Jacquet, P., Szpankowski, W., Apostol, I. (2000). An Universal Predictor Based on Pattern Matching: Preliminary results 1 . In: Gardy, D., Mokkadem, A. (eds) Mathematics and Computer Science. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8405-1_7
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DOI: https://doi.org/10.1007/978-3-0348-8405-1_7
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