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We develop adaptive schemes for bidirectional modeling of unknown discrete stationary sources. These algorithms can be applied to statistical inference problems such as noncausal universal discrete denoising that exploit bidirectional dependencies. Efficient algorithms for constructing those models are developed and we compare their performance to that of… (More)

The risk return relation is a staple of modern finance. When risk is measured by volatility, it is well known that option prices convey risk. In a parametric Marko-vian setting, risk-neutral transition probabilities can also be determined from option prices. Recently, Ross has shown that real-world transition probabilities of a Marko-vian state variable can… (More)

Erasure entropy rate (introduced recently by Verdu and Weissman) differs from Shannon's entropy rate in that the conditioning occurs with respect to both the past and the future, as opposed to only the past (or the future). In this paper, universal algorithms for estimating erasure entropy rate are proposed based on the basic and extended context-tree… (More)

Erasure entropy rate differs from Shannon's entropy rate in that the conditioning occurs with respect to both the past and the future, as opposed to only the past (or the future). In this paper, consistent universal algorithms for estimating erasure entropy rate are proposed based on the basic and extended context-tree weighting (CTW) algorithms. Simulation… (More)

A source <i>X</i> goes through an erasure channel whose output is <i>Z</i>. The goal is to compress losslessly <i>X</i> when the compressor knows <i>X</i> and <i>Z</i> and the decompressor knows <i>Z</i>. We propose a universal algorithm based on context-tree weighting (CTW), parameterized by a memory-length parameter. We show that if the erasure channel is… (More)

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