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).
By Cl\'ement L. Canonne, Yash Pote, Jonathan Scarlett, Joy Qiping Yang
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.
By Guangjian Zhang
arXiv:2608. 04288v1 Announce Type: new Abstract: Calibration requires a predictor to be unbiased after conditioning on its own predictions.
By Jiuyao Lu, Krishnakumar Balasubramanian, Aleksandr Podkopaev, Shiva Prasad Kasiviswanathan
arXiv:2610.08277v1 Announce Type: cross
Abstract: Deciding whether two samples come from the same distribution is a classical problem in statistics, and generative transport offers a new way to appro...
By Eshant English, Kenji Fukumizu, Taiji Suzuki
arXiv:2609. 20883v1 Announce Type: new Abstract: 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 $O(n^{-1/\Theta(d)})$, though shown to be minimax optimal.
By Saumya Goyal, Barnab\'as P\'oczos
The paper develops a nonparametric empirical Bayes approach for estimating sums of functions of observable and unobservable variables in Poisson mixture models, using regular and coarsened minimum‑distance estimation of the mixing distribution. It proves large‑sample guarantees that the plug‑in estimates converge to the oracle Bayes estimate, achieving nearly parametric rates when the mixing distribution has finite support. Finite‑sample analyses are provided for two specific sums—total intensity below a threshold and the number of units exceeding latent intensity—along with minimax regret bounds and conditions for bounded regret.
By Stefano Favaro, Sandra Fortini, Soham Jana
arXiv:2608. 06337v1 Announce Type: cross Abstract: A monotone adversary observes an i.
By Anay Mehrotra
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).
By Gautam Kamath
The paper compares the parallelism capabilities of three diffusion large language model paradigms—masked, uniform, and Gaussian diffusion. It proves that uniform and Gaussian diffusion can sample with a number of forward passes scaling with the dual total correlation of the distribution, potentially much less than the context length, whereas masked diffusion may require more passes. The study establishes a provable separation in parallelism, showing that masked diffusion’s critical windows are asymptotically narrower than those of the other two approaches.
By Sitan Chen, Liye Wang
arXiv:2610.07655v1 Announce Type: cross
Abstract: Discrete diffusion models have emerged as a practically successful framework for generative modeling on discrete product spaces, yet their statistica...
By Dongsun Yoon, Saptarshi Chakraborty
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.
By Buu Phan, Lester Mackey, David Alvarez-Melis
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.
By Mark Bun, Rathin Desai, Renato Ferreira Pinto Jr