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Theoretically Guaranteed Distribution Adaptable Learning

Chao Xu, Xijia Tang, Guoqing Liu, Yuhua Qian, Chenping Hou

TL;DR

Encoding Feature Marginal Distribution Information (EFMDI) broke the limitations of optimal transport to characterize the environmental changes and enable model reuse across diverse data distributions and can enhance the reusable and evolvable properties of DAL in accommodating evolving distributions.

Abstract

In many open environment applications, data are collected in the form of a stream, which exhibits an evolving distribution over time. How to design algorithms to track these evolving data distributions with provable guarantees, particularly in terms of the generalization ability, remains a formidable challenge. To handle this crucial but rarely studied problem and take a further step toward robust artificial intelligence, we propose a novel framework called Distribution Adaptable Learning (DAL). It enables the model to effectively track the evolving data distributions. By Encoding Feature Marginal Distribution Information (EFMDI), we broke the limitations of optimal transport to characterize the environmental changes and enable model reuse across diverse data distributions. It can enhance the reusable and evolvable properties of DAL in accommodating evolving distributions. Furthermore, to obtain the model interpretability, we not only analyze the generalization error bound of the local step in the evolution process, but also investigate the generalization error bound associated with the entire classifier trajectory of the evolution based on the Fisher-Rao distance. For demonstration, we also present two special cases within the framework, together with their optimizations and convergence analyses. Experimental results over both synthetic and real-world data distribution evolving tasks validate the effectiveness and practical utility of the proposed framework.

Theoretically Guaranteed Distribution Adaptable Learning

TL;DR

Encoding Feature Marginal Distribution Information (EFMDI) broke the limitations of optimal transport to characterize the environmental changes and enable model reuse across diverse data distributions and can enhance the reusable and evolvable properties of DAL in accommodating evolving distributions.

Abstract

In many open environment applications, data are collected in the form of a stream, which exhibits an evolving distribution over time. How to design algorithms to track these evolving data distributions with provable guarantees, particularly in terms of the generalization ability, remains a formidable challenge. To handle this crucial but rarely studied problem and take a further step toward robust artificial intelligence, we propose a novel framework called Distribution Adaptable Learning (DAL). It enables the model to effectively track the evolving data distributions. By Encoding Feature Marginal Distribution Information (EFMDI), we broke the limitations of optimal transport to characterize the environmental changes and enable model reuse across diverse data distributions. It can enhance the reusable and evolvable properties of DAL in accommodating evolving distributions. Furthermore, to obtain the model interpretability, we not only analyze the generalization error bound of the local step in the evolution process, but also investigate the generalization error bound associated with the entire classifier trajectory of the evolution based on the Fisher-Rao distance. For demonstration, we also present two special cases within the framework, together with their optimizations and convergence analyses. Experimental results over both synthetic and real-world data distribution evolving tasks validate the effectiveness and practical utility of the proposed framework.

Paper Structure

This paper contains 28 sections, 9 theorems, 71 equations, 8 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. The DAL Problem
  3. Notations and Problem Setting
  4. The DAL framework
  5. Transport Model Reuse
  6. Optimal Transport Between Feature Domains
  7. Evolving Cost Matrix Calculation
  8. Manifold Regularization
  9. Theoretical Analysis
  10. Generalization Ability of DAL
  11. Discussion
  12. Model Reuse Improves the Bound
  13. Manifold Regularization Improves the Bound
  14. Framework Implementations
  15. Two Illustrations
  16. ...and 13 more sections

Key Result

Lemma 1

Let $\bm{\mathcal{L}}$ be the family of loss function associated to $\bm{\mathcal{F}}$, i.e., $\bm{\mathcal{L} }= \left\{ {{\bm{x}} \to \ell(f(\bm{x}),\bm{y}),f \in \bm{\mathcal{F}}} \right\}$. Suppose the loss function is $B$-bounded, then, for any $\delta$ > 0, with probability at least $1-\delta$ where ${\hat{\mathfrak{R}}}(\bm{\mathcal{L}})$ is empirical Rademacher complexity of loss function

Figures (8)

  • Figure 1: Illustration for Data Distribution Evolving Streaming Learning. In environment monitoring task, the data distribution might be evolving gradually in the streaming data.
  • Figure 2: Illustration for a local step in the evolving stage.
  • Figure 3: Illustration of the EFMDI and Transport Model Reuse
  • Figure 4: Experimental results of DAL and representative comparison methods on a toy example. As depicted in the first row, encompasses four distinct classification tasks characterized by diverse data distributions. The following three rows correspond to the classification results of the two comparison methods and DAL. Task 0 represents the initiation stage and involves fully labeled data for training the source model. Note that Task 0 is the starting stage and all methods stand at the same starting line (Source model Result).
  • Figure 5: The influence of evolving data distribution on the performance of each model.
  • ...and 3 more figures

Theorems & Definitions (10)

  • Lemma 1: Generalization Error Bound
  • Lemma 2: Rademacher Vector Contraction Inequality DBLP:journals/corr/Maurer16
  • Lemma 3: Kahane-Khintchine inequality 1994On
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Definition 1: Fisher-Rao distance 2021Information
  • Proposition 1
  • Proposition 2
  • Proposition 3