arXiv:2605. 13092v2 Announce Type: replace-cross Abstract: Density estimation in high-dimensional settings is an important and challenging statistical problem.
arXiv:2511. 05924v4 Announce Type: replace Abstract: Estimating probability density and its score from samples remains a core problem in generative modeling, Bayesian inference, and kinetic theory.
BayesNDE is a neural density estimator that uses Bayesian generative modeling to estimate densities without relying on invertible networks or Jacobian-determinant calculations. It constructs an adaptive proposal for each observation by inferring a sample-specific latent posterior, and then applies bridge sampling to combine proposal samples with separate posterior samples for density estimation. Experiments on synthetic datasets show improved density estimation and structure recovery, while real-world applications demonstrate better anomaly detection.
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.
arXiv:2607. 07671v1 Announce Type: new Abstract: Probabilistic circuits (PCs) can model complex joint distributions while supporting exact and efficient computation of many inference queries.
arXiv:2609.15785v1 Announce Type: cross Abstract: We study density ratio estimation and importance-weighted regression under target shift with continuous outputs. Under target shift, the conditional...
arXiv:2607. 10068v1 Announce Type: new Abstract: Implicit neural representations (INRs) offer compact encoding of volumes, but as lossy approximators, inevitably have prediction errors.
arXiv:2606. 29925v1 Announce Type: new Abstract: As deep learning models are increasingly deployed in high-stakes applications, providing well-calibrated uncertainty estimates has become as critical as achieving high predictive accuracy.
arXiv:2605. 25811v2 Announce Type: replace-cross Abstract: We study counterfactual distribution learning for high-dimensional outcomes whose laws may concentrate near lower-dimensional structure.
arXiv:2402. 13425v3 Announce Type: replace-cross Abstract: It is becoming increasingly common in regression to train neural networks that model the entire distribution even if only the mean is required for prediction.
Sufficiently Reduced Distributional Regression (SRDR) is a generative approach that merges conditional distribution estimation with nonlinear sufficient dimension reduction (SDR). By framing SDR as a risk minimization problem using strictly proper scoring rules, SRDR jointly learns a dimension reduction map and a generative prediction model through minimization of the energy score, which can be estimated via sampling. The method extends to multi‑environment data and classification, and theoretical results show convergence of estimated conditional distributions in energy distance, implying asymptotic sufficiency. In experiments on CT slice localization, superconductivity data, and digit classification, SRDR recovers low‑dimensional sufficient structure and matches or surpasses state‑of‑the‑art nonlinear SDR methods in representation quality and predictive performance.
The paper introduces BROT, a two‑step approach for estimating optimal transport maps. First, it computes the unregularized OT plan, then fits a deep neural network to the resulting barycentric targets using least‑squares regression. The authors prove that, under standard regularity conditions, BROT achieves the minimax convergence rate when the true OT map is Lipschitz, and demonstrate its effectiveness on synthetic data, images, and downstream tasks such as single‑cell perturbation prediction and unsupervised domain adaptation.
arXiv:2602. 13362v2 Announce Type: replace-cross Abstract: A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty.