mlsanityData to 14 Oct 2026

A Likelihood Based Approach to Distribution Regression Using Conditional Deep Generative Models

arXiv 2410.02025 ↗First posted 2 Oct 2024math.ST cs.AI cs.LGcited by 4

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Abstract (arXiv)

In this work, we explore the theoretical properties of conditional deep generative models under the statistical framework of distribution regression where the response variable lies in a high-dimensional ambient space but concentrates around a potentially lower-dimensional manifold. More specifically, we study the large-sample properties of a likelihood-based approach for estimating these models. Our results lead to the convergence rate of a sieve maximum likelihood estimator (MLE) for estimating the conditional distribution (and its devolved counterpart) of the response given predictors in the Hellinger (Wasserstein) metric. Our rates depend solely on the intrinsic dimension and smoothness of the true conditional distribution. These findings provide an explanation of why conditional deep generative models can circumvent the curse of dimensionality from the perspective of statistical foundations and demonstrate that they can learn a broader class of nearly singular conditional distributions. Our analysis also emphasizes the importance of introducing a small noise perturbation to the data when they are supported sufficiently close to a manifold. Finally, in our numerical studies, we demonstrate the effective implementation of the proposed approach using both synthetic and real-world datasets, which also provide complementary validation to our theoretical findings.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 25 of its 72 references that are in the map. First posted on arXiv 2 Oct 2024.

Builds on

25 of 72 references.

References · 25

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13 more
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 2.

4 papers.

  1. 2025GDR-learners: Orthogonal Learning of Generative Models for Potential Outcomescited by 1
  2. 2025Nonparametric estimation of conditional probability distributions using a generative approach based on conditional push-forward neural networkscited by 1
  3. 2026Causality-Encoded Diffusion Models for Interventional Sampling and Edge Inferencecited by 0
  4. 2026Extended Wasserstein-GAN Approach to Causal Distribution Learning: Density-Free Estimation and Minimax Optimalitycited by 0