Sufficient dimension reduction improves conditional generative models
Belted Engression: Sufficient Dimension Reduction for Generative Distributional Regression
Machine LearningArtificial Intelligence
Summary
Conditional generative models try to create new data based on input features but often struggle when these inputs are complex. The authors present Belted Engression, a method that smartly compresses the input information before generating new data. This approach uses a structural bottleneck in the model to ensure only the essential information is passed along, making the model more efficient. Their work also includes mathematical proofs showing the method works well and tests confirming it predicts distributions accurately while using fewer parameters.
What this means in practice
- •For machine learning engineers: Build more efficient generative models that handle complex inputs with fewer parameters and better distributional accuracy.
- •For data science teams: Improve predictive modeling for tasks involving complex covariates by compressing input data without losing essential distributional information.
Authors
Wenxi Tan, Bing Li, Lingzhou Xue
Abstract
Modern conditional generative models face significant challenges when learning complex covariate dependencies. While sufficient dimension reduction (SDR) provides a principled approach to compress these dependencies, traditional SDR frameworks were not formulated for conditional generation. To bridge this gap, we propose Belted Engression, a unified and architecturally parameter-efficient framework for generative distributional regression. Our approach establishes an end-to-end compress-then-generate paradigm driven by sufficient representation learning, embedding a structural bottleneck into the generative architecture. Theoretically, we prove that the standard SDR condition is equivalent to a law-preserving generative factorization, which is achieved at the global optimum of the population Belted Engression objective. Furthermore, by uncovering a localized Bernstein-type control for the energy-score loss, we establish finite-sample convergence rates that are sharper than those of existing results. We also prove that this belted architecture is strictly smaller, operating with an asymptotically vanishing parameter count relative to the unstructured baseline. Extensive simulations and real-world applications demonstrate that Belted Engression achieves superior distributional prediction and SDR recovery with fewer trainable parameters.