arXiv Statistics ML

A data-driven Fourier-mixture neural-network method for density estimation

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.

arXiv Machine Learning

Aug 24

Amortized Bandwidth Learning for Kernel Density Estimation under Logarithmic Score

The paper introduces an amortized learning framework for selecting bandwidths in kernel density estimation by optimizing the logarithmic score across a distribution of tasks. It uses a truncated-and-renormalized bounded-support formulation and affine standardization to achieve stable learning and transferability across different intervals. Experiments on Gaussian samples, a multi-family benchmark, and randomized Gaussian mixtures demonstrate that the learned selector outperforms traditional methods such as Silverman’s rule, Sheather–Jones, and least‑squares cross‑validation, especially for small or heterogeneous samples.

By Junyi Liang, Hailiang Du

benchmarks

arXiv Machine Learning

Jun 15

Recursively Trained Diffusion Models: Limiting Collapse Distribution and Spectral Characterization

arXiv:2606. 13796v1 Announce Type: cross Abstract: Recursive training of generative models on their own outputs can lead to model collapse, a compounding drift away from the true data distribution.

By Na\"il B. Khelifa, Richard E. Turner, Ramji Venkataramanan

diffusion

arXiv Machine Learning

Jun 26

Learning from a Biased Sample

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

safety

arXiv Machine Learning

Jun 5

Gradient-Flow Optimization as Dynamic Random-Effects Inference: Testing and Early Stopping with Applications to Deep Learning

arXiv:2605. 27991v2 Announce Type: replace-cross Abstract: Gradient-flow optimization is usually viewed as an algorithmic procedure for minimizing empirical loss, with training duration selected by validation or heuristic early-stopping rules.

By Minhao Yao, Ruoyu Wang, Xihong Lin, Lin Liu, Zhonghua Liu

arXiv Machine Learning

Jun 9

Dendrograms of Mixing Measures for Softmax-Gated Gaussian Mixture of Experts: Consistency Without Model Sweeps

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 Machine Learning

Aug 4

Augmented Inverse Hybrid Weighting: Robust Inference under Deterministic and Random Distribution Shifts

arXiv:2608. 00701v1 Announce Type: cross Abstract: Reweighting source samples to match a target covariate distribution is a standard response to distribution shift when generalizing evidence from one population to another.

By Ying Jin, Ying Jin, Dominik Rothenh\"ausler

safety

arXiv Machine Learning

Sep 10

DDPM Score Matching and Distribution Learning

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

diffusion multimodal

arXiv Machine Learning

Jul 7

Optimal Mixture-of-Experts Model Averaging for Conditional Generative Models

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

arXiv Machine Learning

Jun 17

Learning from Biased and Costly Data Sources: Minimax-optimal Data Collection under a Budget

arXiv:2602. 17894v2 Announce Type: replace-cross Abstract: Data collection is a critical component of modern statistical and machine learning pipelines, particularly when data must be gathered from multiple heterogeneous sources to study a target population of interest.

By Michael O. Harding, Vikas Singh, Kirthevasan Kandasamy

arXiv Machine Learning

Jun 24

Target-Aware Linear Regression Under Distribution Shift

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

benchmarks safety

arXiv Statistics ML

Sep 2

Deep Skew-t Mixture Models

arXiv:2609.00773v1 Announce Type: cross Abstract: High-dimensional clustering is challenging when component distributions are both heavy-tailed and directionally asymmetric. We propose a deep skew-$t...

By Jinran Wu, You-Gan Wang, Geoffrey J. McLachlan

benchmarks

arXiv Machine Learning

Aug 12

A Joint-Distribution Route to Fair Representations with Continuous Sensitive Attributes

arXiv:2608. 10470v1 Announce Type: new Abstract: Fair representation learning with a continuous sensitive attribute $S$ requires a representation $Z$ that is statistically independent of $S$.

By Yijin Ni, Xiaoming Huo

safety

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