arXiv:2605. 23225v2 Announce Type: replace-cross Abstract: We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given samples from two unknown distributions $p,q$ and a parameter $\varepsilon \in(0,1/2]$, between $p=q$ and $|H(p)-H(q)| \geq \varepsilon$ (where $H$ denotes the Shannon entropy).
The paper presents tight bounds for equivalence testing using non‑adaptive conditional samples. It shows that determining whether two unknown distributions are identical or ε‑far in total variation distance requires ∫Θ((log n)/ε²) queries. Consequently, the query complexity for uniformity, identity, and equivalence testing with non‑adaptive conditional samples is ∫Θ(log n).
arXiv:2606. 27349v3 Announce Type: replace-cross Abstract: How different are several probability distributions from one another?
arXiv:2607. 15645v1 Announce Type: cross Abstract: Motivated by the challenge of testing distributions over high-dimensional or continuous domains, we study distribution testing with respect to bounded classes of distinguishers.
arXiv:2610. 26944v2 Announce Type: replace Abstract: Strict replicability requires two independent training samples, processed with the same random seed, to produce exactly the same hypothesis.
arXiv:2607. 16966v1 Announce Type: cross Abstract: Estimating entropy from samples is fundamental in information theory and property testing.
arXiv:2608. 04288v1 Announce Type: new Abstract: Calibration requires a predictor to be unbiased after conditioning on its own predictions.
The paper introduces an entropy-based estimator for Kullback-Leibler divergence that uses normalized importance weights. It establishes a universal finite-sample bound, proving that the estimator’s expectation can exceed the true target‑proposal KL divergence by no more than λ2, regardless of sample size. Additionally, it shows that the KL divergence between the distribution produced by importance‑weighted resampling and the proposal is bounded by both the estimator’s expectation and the target‑proposal KL divergence, without requiring bounded weights or finite higher moments. The authors apply these theoretical results to test‑time alignment of generative models via Soft Best‑of‑N sampling and to relative entropy coding, yielding finite‑sample policy‑divergence guarantees and moment‑free bounds on coding cost.
arXiv:2609.13703v1 Announce Type: cross Abstract: In the best-arm identification problem, we are given $n$ stochastic arms with unknown means and wish to identify the arm with the largest mean with p...
arXiv:2607. 24732v1 Announce Type: cross Abstract: Motivated by learning from heterogeneous and overlapping data providers, we study a stylized model of distribution learning from restricted conditional samples.
arXiv:2608. 06262v1 Announce Type: new Abstract: Model evaluations may fix all tests before observing any responses or select later tests using earlier responses.
arXiv:2507. 12843v3 Announce Type: replace Abstract: Are two distributions close to each other with statistical significance?
arXiv:2610. 26944v1 Announce Type: cross Abstract: Under the quantifier $\exists A\,\forall D$, where the realizable distribution and its marginal are unknown, we determine the finite-class sample-complexity exponent for strict replicability: two independent samples and one shared seed must produce identical functions.