EPFL | Biomedical Imaging Group | Preserved Logconcavity

Convex Quantization Preserves Logconcavity

P. del Aguila Pla, A. Boquet-Pujadas, J. Jaldén

IEEE Signal Processing Letters, vol. 29, pp. 2697–2701, December 2022.

A logconcave likelihood is as important to proper statistical inference as a convex cost function is important to variational optimization. Quantization is often disregarded when writing likelihood models, ignoring the limitations of the physical detectors used to collect the data. These two facts call for the question: would including quantization in likelihood models preclude logconcavity? are the true data likelihoods logconcave? We provide a general proof that the same simple assumption that leads to logconcave continuous-data likelihoods also leads to logconcave quantized-data likelihoods, provided that convex quantization regions are used.

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AUTHOR="del Aguila Pla, P. and Boquet-Pujadas, A. and Jald{\'{e}}n, J.",
TITLE="Convex Quantization Preserves Logconcavity",
JOURNAL="{IEEE} Signal Processing Letters",
YEAR="2022",
volume="29",
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pages="2697--2701",
month="December",
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