Wasserstein-Cram\'er-Rao Theory of Unbiased Estimation
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The paper investigates preference elicitation under the Bradley‑Terry‑Luce model, focusing on estimating an unknown partworth vector from pairwise queries that satisfy a joint identifiability condition. It derives minimax lower bounds and shows that the canonical maximum likelihood estimator (MLE) exists, is unique, and achieves near‑optimal error rates once the sample size exceeds a design‑dependent threshold, without requiring compactness constraints or external regularizers. The analysis decomposes the estimation error into a linear stochastic term, a second‑order bias, and a higher‑order remainder, providing a unified non‑asymptotic theory for parametric utility elicitation.
arXiv:2609.40193v1 Announce Type: new Abstract: We establish near-linear accuracy bounds for the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA). The target is $\pi\propto e^{-f-g}$, w...
arXiv:2609. 20749v1 Announce Type: cross Abstract: Location estimation exhibits markedly different finite-sample behavior across noise distributions: regular families typically yield root-\(n\) rates, whereas compactly supported laws may admit faster, boundary-driven rates.
arXiv:2602. 04272v2 Announce Type: replace-cross Abstract: The Importance-Weighted Evidence Lower Bound (IW-ELBO) has emerged as an effective objective for variational inference (VI), tightening the standard ELBO and mitigating the mode-seeking behaviour.
arXiv:2201. 01973v3 Announce Type: replace-cross Abstract: The problem of linear predictions has been extensively studied for the past century under pretty generalized frameworks.
The paper investigates quantile distributional policy evaluation by approximating the return distribution under a policy with a quantile Bellman fixed point. It constructs an estimator from an empirical Markov decision process and derives non‑asymptotic error bounds in Wasserstein distances, achieving root‑n rates that are independent of the quantile resolution for a wide range of Wasserstein orders. The authors also characterize the exact local asymptotic minimax risk and show that their estimator attains this optimal rate, while examining how the risk depends on resolution in simple state‑space examples.