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Credit Attribution and Stable Compression

Roi Livni, Shay Moran, Kobbi Nissim, Chirag Pabbaraju

TL;DR

This work examines the expressive power of these stability notions within the PAC learning framework, provides a comprehensive characterization of learnability for algorithms adhering to these principles, and proposes new definitions of Differential Privacy that weaken the stability guarantees for a designated subset of datapoints.

Abstract

Credit attribution is crucial across various fields. In academic research, proper citation acknowledges prior work and establishes original contributions. Similarly, in generative models, such as those trained on existing artworks or music, it is important to ensure that any generated content influenced by these works appropriately credits the original creators. We study credit attribution by machine learning algorithms. We propose new definitions--relaxations of Differential Privacy--that weaken the stability guarantees for a designated subset of $k$ datapoints. These $k$ datapoints can be used non-stably with permission from their owners, potentially in exchange for compensation. Meanwhile, the remaining datapoints are guaranteed to have no significant influence on the algorithm's output. Our framework extends well-studied notions of stability, including Differential Privacy ($k = 0$), differentially private learning with public data (where the $k$ public datapoints are fixed in advance), and stable sample compression (where the $k$ datapoints are selected adaptively by the algorithm). We examine the expressive power of these stability notions within the PAC learning framework, provide a comprehensive characterization of learnability for algorithms adhering to these principles, and propose directions and questions for future research.

Credit Attribution and Stable Compression

TL;DR

This work examines the expressive power of these stability notions within the PAC learning framework, provides a comprehensive characterization of learnability for algorithms adhering to these principles, and proposes new definitions of Differential Privacy that weaken the stability guarantees for a designated subset of datapoints.

Abstract

Credit attribution is crucial across various fields. In academic research, proper citation acknowledges prior work and establishes original contributions. Similarly, in generative models, such as those trained on existing artworks or music, it is important to ensure that any generated content influenced by these works appropriately credits the original creators. We study credit attribution by machine learning algorithms. We propose new definitions--relaxations of Differential Privacy--that weaken the stability guarantees for a designated subset of datapoints. These datapoints can be used non-stably with permission from their owners, potentially in exchange for compensation. Meanwhile, the remaining datapoints are guaranteed to have no significant influence on the algorithm's output. Our framework extends well-studied notions of stability, including Differential Privacy (), differentially private learning with public data (where the public datapoints are fixed in advance), and stable sample compression (where the datapoints are selected adaptively by the algorithm). We examine the expressive power of these stability notions within the PAC learning framework, provide a comprehensive characterization of learnability for algorithms adhering to these principles, and propose directions and questions for future research.
Paper Structure (13 sections, 9 theorems, 39 equations, 1 figure)

This paper contains 13 sections, 9 theorems, 39 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Definitions and Examples
  3. Algorithms with Credit Attribution.
  4. Main Theorems
  5. Generalization.
  6. Technical Background and Proofs
  7. Upper Bound: PAC learnability implies $(\varepsilon=\delta=0)$-counterfactual credit attribution learning
  8. Lower Bound: A dichotomy for sample DP-compression
  9. Bounded boosting of empirical measure
  10. Conclusion
  11. Acknowledgements
  12. Supplementary Proofs
  13. A DP sample compression scheme based on Randomized Response

Key Result

Theorem 1

Let $\mathcal{C}$ be a concept class with VC dimension $\mathtt{VC}(\mathcal{C}) = d < \infty$, and let $\alpha, \beta$ denote the error and confidence parameters. Then, there exists an $(\varepsilon=0, \delta=0)$-CCA learning rule $M$ that learns $\mathcal{C}$ with sample complexity $n=O\left(\frac

Figures (1)

  • Figure 1: Support Vector Machine (SVM) as an $(\varepsilon=\delta=0)$-counterfactual credit attributor: The SVM algorithm identifies a maximum-margin separating hyperplane, which is defined by the subsample of the support vectors. Any input point which is not a support vector does not influence the output: even if it is removed from the input sample, the output hyperplane does not change.

Theorems & Definitions (31)

  • Definition 1: Counterfactual Credit Attribution
  • Example 2.1: Stable Sample Compression nikita2017optimalbousquet2020proper
  • Definition 2: Semi-Differentially Private Mechanism
  • Remark 1
  • Definition 3: Sample DP-Compression Scheme
  • Example 2.2: Randomized Response
  • Theorem 1: PAC Learning with Credit Attribution $=$ PAC Learning
  • Theorem 2: Sublinear Sample DP-Compression $=$ DP Learning
  • Theorem 3
  • Definition 4: CCA PAC learning rule
  • ...and 21 more