Near-Optimal Hypothesis Testing via Convex Optimization
summary
Constructs tests by solving a finite convex optimization that maximizes affinity between two convex parameter sets in an exponential family and yields a detector equal to half log-likelihood ratio; the optimal value is the single‑sample error bound whose K‑sample error equals that value^K. Assumes a good observation scheme (Gaussian, Poisson, finite or IID product exponential families) so the semi‑infinite problem becomes tractable. Test is provably near‑optimal: achieving the same risk needs at most a constant (~2) factor more samples.
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chapters (11)
- 0:00Introduction
- 0:25Foundational results in non-parametric stats
- 3:40Descriptive vs operational results
- 4:45Building detectors
- 9:27Convex optimization formulation
- 12:40Good observation teams
- 17:50Main result for hypothesis testing
- 21:09Gaussian and Poisson schemes
- 21:52Multiple hypotheses testing
- 26:02Signal processing applications
- 26:50Q&A
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