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CORR
2008
Springer

Information In The Non-Stationary Case

13 years 3 months ago
Information In The Non-Stationary Case
Information estimates such as the "direct method" of Strong et al. (1998) sidestep the difficult problem of estimating the joint distribution of response and stimulus by instead estimating the difference between the marginal and conditional entropies of the response. While this is an effective estimation strategy, it tempts the practitioner to ignore the role of the stimulus and the meaning of mutual information. We show here that, as the number of trials increases indefinitely, the direct (or "plug-in") estimate of marginal entropy converges (with probability 1) to the entropy of the time-averaged conditional distribution of the response, and the direct estimate of the conditional entropy converges to the time-averaged entropy of the conditional distribution of the response. Under joint stationarity and ergodicity of the response and stimulus, the difference of these quantities converges to the mutual information. When the stimulus is deterministic or non-stationa...
Vincent Q. Vu, Bin Yu, Robert E. Kass
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where CORR
Authors Vincent Q. Vu, Bin Yu, Robert E. Kass
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