Belted Engression: Sufficient Dimension Reduction for Generative Distributional Regression

arXiv:2609.23789 · cs.LG, cs.AI, math.ST, stat.ME, stat.ML, stat.TH · Submitted 2026-09-20 · Read on arXiv

cs.LG, cs.AI, math.ST, stat.ME, stat.ML, stat.TH

Submitted: 2026-09-20

Updated: 2026-09-20

Comments: 32 pages, 6 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Empirical Coverage — 9× in this paper · explained in 2 episodes
• Representation Learning — 9× in this paper · explained in 2 episodes
• Generative Model — 6× in this paper · explained in 2 episodes
• Generative Models — 5× in this paper · explained in 2 episodes
• Accuracy — 3× in this paper · explained in 1 episode
• Generative Modeling — 3× in this paper · explained in 3 episodes
• Robustness — 3× in this paper · explained in 5 episodes
• Parameter Efficiency — 2× in this paper · explained in 3 episodes
• Theoretical Guarantees — 2× in this paper · explained in 2 episodes
• Activation Function — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Heteroscedasticity — 1× in this paper · explained in 2 episodes
• Loss Function — 1× in this paper · explained in 2 episodes
• Neural Network Approximation — 1× in this paper · explained in 2 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Structural Constraints — 1× in this paper · explained in 2 episodes
• Variational Bayes — 1× in this paper · explained in 2 episodes

Sources

• Neural Generative Distributional Regression
• Error Analysis of Neural-Network-Based Engression
• Theoretical Analysis of Engression and Reverse Markov Engression
• Distributional Principal Autoencoders
• On Conditional Stochastic Interpolation for Generative Nonlinear Sufficient Dimension Reduction

Related papers

• Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
• AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
• Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
• Convergence issues in Relational Concept Analysis based on AOC-posets
• Beliefs Beyond Posteriors: Local-Consistency Optimisation for Bayesian Neural Networks
• Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks