Loading [a11y]/accessibility-menu.js
Entropy property testing with finitely many errors | IEEE Conference Publication | IEEE Xplore

Entropy property testing with finitely many errors


Abstract:

Let P be a class of distributions over natural numbers, and A be a subset of ℝ+. We study the problem of deciding, using i.i.d. samples X1,X2,... from an unknown p ∈ P, w...Show More

Abstract:

Let P be a class of distributions over natural numbers, and A be a subset of ℝ+. We study the problem of deciding, using i.i.d. samples X1,X2,... from an unknown p ∈ P, whether the entropy H(p) is in A or not. The decision is updated based on every new observation Xn-we are interested in decision rules that make only finitely many errors no matter what the underlying source is. We give necessary and sufficient conditions on the class P and A that can be decided with only finitely many errors. We show for example that such rules exist for testing the rationality of entropy within a given interval, for testing if the entropy falls in an interval of form (a,b], but no such decision rule exists to determine if the entropy is finite or if the entropy falls in an interval of form [a,b]. In the process, we also highlight the conceptual foundation this framework shares with regularization.
Date of Conference: 21-26 June 2020
Date Added to IEEE Xplore: 24 August 2020
ISBN Information:

ISSN Information:

Conference Location: Los Angeles, CA, USA

References

References is not available for this document.