A Theory for Conditional Generative Modeling on Multiple Data Sources

2025-02-20

AI Summary

This paper addresses the theoretical analysis challenge in multi-source conditional generative modeling. It systematically investigates how inter-source similarity and model expressivity affect distribution estimation error. We derive the first bracketing-number-based error bound for multi-source conditional maximum likelihood estimation, proving theoretically that when sources are sufficiently similar and the model is expressive enough, joint multi-source training yields a strictly tighter estimation error bound than single-source training—where generalization performance improves synergistically with both the number of sources and their pairwise similarity. Our analysis encompasses conditional Gaussian estimation, autoregressive models, and flexible energy-based models, and integrates average total variation distance. Extensive synthetic and real-data experiments validate the theoretical predictions, and open-source code ensures reproducibility. The core contribution is establishing a unified statistical learning framework for multi-source conditional generation and, for the first time, quantifying the collaborative gain from multi-source integration from a rigorous statistical perspective.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models
• Natural Language Processing: Generation

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

The success of large generative models has driven a paradigm shift, leveraging massive multi-source data to enhance model capabilities. However, the interaction among these sources remains theoretically underexplored. This paper takes the first step toward a rigorous analysis of multi-source training in conditional generative modeling, where each condition represents a distinct data source. Specifically, we establish a general distribution estimation error bound in average total variation distance for conditional maximum likelihood estimation based on the bracketing number. Our result shows that when source distributions share certain similarities and the model is expressive enough, multi-source training guarantees a sharper bound than single-source training. We further instantiate the general theory on conditional Gaussian estimation and deep generative models including autoregressive and flexible energy-based models, by characterizing their bracketing numbers. The results highlight that the number of sources and similarity among source distributions improve the advantage of multi-source training. Simulations and real-world experiments validate our theory. Code is available at: url{https://github.com/ML-GSAI/Multi-Source-GM}.

Problem

• Analyzes multi-source training in conditional generative modeling
• Establishes error bounds for conditional maximum likelihood estimation
• Validates theory with simulations and real-world experiments

Innovation

• Multi-source conditional generative modeling
• Bracketing number for error estimation
• Deep generative models analysis