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Feature Extraction for Universal Hypothesis Testing via Rank-constrained Optimization
This paper concerns the construction of tests for universal hypothesis
testing problems, in which the alternate hypothesis is poorly modeled and the
observation space is large. The mismatched universal test is a feature-based
technique for this purpose. In prior work it is shown that its
finite-observation performance can be much better than the (optimal) Hoeffding
test, and good performance depends crucially on the choice of features. The
contributions of this paper include: 1) We obtain bounds on the number of
\epsilon distinguishable distributions in an exponential family. 2) This
motivates a new framework for feature extraction, cast as a rank-constrained
optimization problem. 3) We obtain a gradient-based algorithm to solve the
rank-constrained optimization problem and prove its local convergence.Comment: 5 pages, 4 figures, submitted to ISIT 201
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