Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912409541672960 |
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| author | Boutoille, Guillaume Pagès, Gilles |
| author_facet | Boutoille, Guillaume Pagès, Gilles |
| contents | In this paper we revisit the exsistence theorem for $L^r$-optimal quantization, $r\ge 2$, with respect to a Bregman divergence: we establish the existence of optimal quantizaers under lighter assumptions onthe strictly convex function which generates the divergence, espcially in the quadratic case ($r=2$). We then prove a uniqueness theorem ``à la Trushkin'' in one dimension for strongly unimodal distributions and divergences gerated by strictly convex functions whiose thire dervative is either stictly $\log$-convex or $\log$-concave. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01746 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Boutoille, Guillaume Pagès, Gilles Probability In this paper we revisit the exsistence theorem for $L^r$-optimal quantization, $r\ge 2$, with respect to a Bregman divergence: we establish the existence of optimal quantizaers under lighter assumptions onthe strictly convex function which generates the divergence, espcially in the quadratic case ($r=2$). We then prove a uniqueness theorem ``à la Trushkin'' in one dimension for strongly unimodal distributions and divergences gerated by strictly convex functions whiose thire dervative is either stictly $\log$-convex or $\log$-concave. |
| title | Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited |
| topic | Probability |
| url | https://arxiv.org/abs/2506.01746 |