The paper addresses the challenge of estimating joint probability distributions in high-dimensional settings by factorizing them autoregressively and using nonparametric conditional estimators. It establishes theoretical convergence bounds that link the difficulty of joint estimation to the hardest factor in the factorization, especially when conditional estimators adapt to sparsity in an undirected dependence graph. Empirical results show that an autoregressive estimator built with parallel gradient boosting achieves competitive performance on simulated and real datasets, even without optimizing factorization order.
By R\'emy Chapelle (CB, EVDG, CESP)
arXiv:2606. 30372v1 Announce Type: new Abstract: Quantitative research across the social and behavioral sciences depends on human subject experiments that are expensive, slow, and subject to sampling bias.
By Haobo Yang
arXiv:2606. 22775v2 Announce Type: replace-cross Abstract: Distribution shift between training and deployment is a pervasive challenge for modern AI systems.
By Zhewen Hou, Tian Zheng
arXiv:2510. 12744v2 Announce Type: replace-cross Abstract: We develop a unified statistical framework for softmax-gated Gaussian mixture of experts (SGMoE) that addresses three long-standing obstacles in parameter estimation and model selection: (i) non-identifiability of gating parameters up to common translations, (ii) intrinsic gate-expert interactions that induce coupled differential relations in the likelihood, and (iii) the tight numerator-denominator coupling in the softmax-induced conditional density.
By Do Tien Hai, Trung Nguyen Mai, TrungTin Nguyen, Nhat Ho, Binh T. Nguyen, Christopher Drovandi
arXiv:2209. 01754v5 Announce Type: replace-cross Abstract: The empirical risk minimization approach to data-driven decision making requires access to training data drawn under the same conditions as those that will be faced when the decision rule is deployed.
By Roshni Sahoo, Lihua Lei, Stefan Wager
arXiv:2606. 25188v1 Announce Type: new Abstract: Efficient uncertainty quantification (UQ) is essential for trustworthy large-scale learning.
By Kun Jin, James Harrison, Jiawei Li, Sihan Liu, Jiayi Liu, Randolph Linderman, Yuening Li, Arnab Bhadury, Sourabh Prakash Bansod, Liang Liu, Jasper Snoek
arXiv:2504.05161v2 Announce Type: replace-cross
Abstract: Score estimation is the backbone of score-based generative models (SGMs), especially denoising diffusion probabilistic models (DDPMs). A key...
By Sinho Chewi, Alkis Kalavasis, Anay Mehrotra, Omar Montasser
arXiv:2607. 04360v1 Announce Type: cross Abstract: Conditional generative models have emerged as powerful tools for sampling from target conditional distributions, driving substantial advances across a wide range of scientific and applied domains.
By Shijin Gong, Baihua He, Xinyu Zhang
The paper introduces a model‑agnostic inference framework for partially identified causal effects that leverages covariate information without requiring discrete covariates or accurate conditional distribution estimates. Using duality theory for optimal transport, the method delivers uniformly valid inference in randomized experiments, is doubly robust in observational settings, achieves asymptotic unbiasedness when nuisance parameters converge semiparametrically, and allows multiplier‑bootstrap selection of covariates and models while remaining computationally efficient. Empirical applications show the approach consistently narrows identified sets and confidence intervals without imposing extra structural assumptions.
By Wenlong Ji, Lihua Lei, Asher Spector
The paper introduces a data‑driven Fourier‑trained neural‑network estimator for fixed‑horizon probability densities, using a positive Gaussian–Laplace mixture with a closed‑form characteristic function. Training occurs directly in Fourier space, enabling non‑negativity and unit‑mass preservation while handling both i.i.d. and resampling‑based pseudo‑sampling data. The authors provide theoretical error bounds, a multidimensional extension, and demonstrate competitive empirical performance against Expectation–Maximization, especially on heavy‑tailed targets.
By Duy-Minh Dang, Volter Entoma
The paper introduces a framework that combines deep generative models with symbolic regression to estimate symbolic expressions for unnormalized probability density functions directly from observed samples. By incorporating domain-specific priors—such as interaction ranges and a set of primitive functions—the method can factorize large distributions and remain tractable. Experiments demonstrate its effectiveness on multivariate toy distributions and on lattice models from computational physics, including the XY model and φ⁴ theory, where it produces compact symbolic approximations of the Hamiltonian across scales.
By Vikas Kanaujia, Riyansha Singh, Shashank Sharma, Vipul Arora
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