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Estimating a probability using finite memory

  • Extended Abstract
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 158)

Abstract

Let {Xi i=1 } be a sequence of independent Bernoulli random variables with probability p that X i =1 and probability q=1 − p that X i =0 for all i≥1. We consider time-invariant finite-memory (i.e., finite-state) estimation procedures for the parameter p which take X1, ... as an input sequence. In particular, we describe an n-state deterministic estimation procedure that can estimate p with mean-square error O(log n/n) and an n-state probabilistic estimation procedure that can estimate p with mean-square error O(1/n). We prove that the O(1/n) bound is optimal to within a constant factor. In addition, we show that linear estimation procedures are just as powerful (up to the measure of mean-square error) as arbitrary estimation procedures. The proofs are based on the Markov Chain Tree Theorem.

Keywords

IEEE Transaction Estimation Procedure Learn Automaton Underlying Graph Deterministic Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Extended Abstract
    • 1
  1. 1.Frank Thomson Leighton and Ronald L. Rivest Mathematics Department and Laboratory for Computer ScienceMassachusetts Institute of TechnologyCambridge

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