Sparse Priors for Efficient Distribution Learning
Despite the widespread use and success of generative AI techniques today, theoretical guarantees on learning a distribution supported in $d$ dimensions from $n$ samples degrade as $O(n^{-1/Θ(d)})$, though shown to be minimax optimal. We hypothesize that present bounds are too pessimistic because smoothness assumptions are not enough to capture the structure of distributions that often appear in real applications. Consequently, we introduce the class of sparse priors and define the "Sparse Dimension" as a measure of sparsity of a prior over the space of all distributions. We show that distribution learning under a $k$-sparse prior achieves a Bayesian risk lower bound of $Ω(\sqrt{k/n})$ und...
| Authors | Saumya Goyal, Barnabás Póczos |
|---|---|
| Primary category | cs.LG |
| Published | 16 September 2026 |
| Last updated at source | 16 September 2026 |
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