Universal Bounds for Self-Normalized Kullback-Leibler Estimation
This work studies an entropy-based estimator of Kullback-Leibler (KL) divergence constructed from normalized importance weights. We prove a universal finite-sample bound showing that its expectation can exceed the target-proposal KL divergence by at most $\log 2$ for any sample size. We then characterize the KL divergence between the distribution induced by importance-weighted resampling and the proposal, showing that it is upper bounded by both the expectation of the entropy-based estimator and the target-proposal KL divergence. Importantly, these bounds require neither bounded importance weights nor finite higher moments. We apply these results to test-time alignment of generative model...
| Authors | Buu Phan, Lester Mackey, David Alvarez-Melis |
|---|---|
| Primary category | stat.ML |
| Published | 9 October 2026 |
| Last updated at source | 9 October 2026 |
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