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.
arXiv:2609.23789v1 Announce Type: new Abstract: Modern conditional generative models face significant challenges when learning complex covariate dependencies. While sufficient dimension reduction (SD...
arXiv:2608. 15121v1 Announce Type: cross Abstract: Sufficient dimension reduction (SDR) seeks the minimal subspace of the predictors that captures the full conditional distribution of the response, which is known as the central subspace (CS).
arXiv:2607. 16725v1 Announce Type: cross Abstract: Conditional generative modeling remains a challenging problem in semi-supervised settings where labeled data is scarce but unlabeled samples are abundant.
arXiv:2607. 12833v1 Announce Type: cross Abstract: Circular data, representing angles or directions, are frequently encountered in computer vision, biology, geology, and meteorology.
The paper introduces Conditional-Independence-Regularized Distributional Autoencoders, a framework for learning low-dimensional representations of mixed-type data that includes both numerical and categorical variables. It uses an energy-score objective for numerical variables, a likelihood objective for categorical variables, and an auxiliary conditional independence regularization term to capture dependencies between variable types. The authors provide theoretical analysis and demonstrate that the method improves categorical distribution recovery, achieves competitive overall conditional distribution recovery, and preserves mixed-type dependence structure on synthetic and real-world datasets.
The paper investigates diffusion models trained in a lazy high‑dimensional regime, extending benign overfitting theory to generative settings. By analyzing denoising score matching in a vector‑valued RKHS with an inner‑product kernel, the authors derive exact risk trajectories under gradient flow when the number of samples scales proportionally with dimensionality. These trajectories reveal three distinct phases—spectral generalization, noise‑dominated interpolation, and empirical Bayes memorization—whose interplay shapes the distribution of generated samples.
arXiv:2603.05575v2 Announce Type: replace-cross Abstract: We study prediction-powered conditional inference in the setting where labeled data are scarce, unlabeled covariates are abundant, and a blac...
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.
arXiv:2510.17072v2 Announce Type: replace Abstract: Regression with non-Euclidean responses---e.g., probability distributions, networks, symmetric positive-definite matrices, and compositions---has b...
arXiv:2609.13917v1 Announce Type: new Abstract: Energy-Based Models (EBMs) provide a flexible framework for generative modeling by learning an energy landscape that assigns low energy values to reali...
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. As these models proliferate, practitioners often face multiple plausible generators whose performance can vary with the task, data, or input condition.
arXiv:2609.01410v1 Announce Type: cross Abstract: Generative data augmentation is widely used to mitigate class imbalance, yet its theoretical effect on downstream generalization remains poorly under...