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Convex quantization preserves logconcavity

Pol del Aguila PlaAleix Boquet-PujadasJoakim Jald\'en
Jun 2022
摘要
Much like convexity is key to variational optimization, a logconcavedistribution is key to amenable statistical inference. Quantization is oftendisregarded when writing likelihood models: ignoring the limitations ofphysical detectors. This begs the questions: would including quantizationpreclude logconcavity, and, are the true data likelihoods logconcave? We showthat the same simple assumption that leads to logconcave continuous datalikelihoods also leads to logconcave quantized data likelihoods, provided thatconvex quantization regions are used.
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