Optimal random quantisers for spherically symmetric distributions
Zador's celebrated theorem is a cornerstone of optimal quantisation: it establishes both the weak limit of the empirical distribution of an optimal $n$-point quantiser in $R^d$ and the decay rate of the associated $L_s$-mean quantisation error. In large dimension, however, observing this asymptotic behaviour requires an astronomically large sample size. We prove that, for spherically symmetric target distributions, optimisation over all spherically symmetric distributions is a convex problem and derive an equivalence theorem that both characterises global optimality and yields a constructive algorithm. We show that, for moderate $n$, random quantisers uniformly distributed on a sphere of ...
| Authors | Luc Pronzato, Anatoly Zhigljavsky |
|---|---|
| Primary category | math.ST |
| Published | 8 October 2026 |
| Last updated at source | 8 October 2026 |
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