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Federated Prediction-Powered Inference from Decentralized Data

Ping Luo, Xiaoge Deng, Ziqing Wen, Tao Sun, Dongsheng Li

TL;DR

Fed-PPI unites federated learning with Prediction-Powered Inference to enable statistically valid conclusions from decentralized, private data without data sharing. The framework defines aggregation rules, imputed gradients, and empirical rectifiers to produce prediction-powered confidence intervals for convex and nonconvex estimands, with concrete algorithms for mean, quantile, logistic, and linear regression. Theoretical guarantees (finite-sample and asymptotic) and extensive experiments across real tasks and simulations demonstrate that Fed-PPI delivers intervals with valid coverage close to centralized analyses, while accommodating data heterogeneity and unlabeled data. This approach addresses data silos and privacy concerns, with practical impact for diverse scientific domains relying on collaborative yet privacy-preserving inference.

Abstract

In various domains, the increasing application of machine learning allows researchers to access inexpensive predictive data, which can be utilized as auxiliary data for statistical inference. Although such data are often unreliable compared to gold-standard datasets, Prediction-Powered Inference (PPI) has been proposed to ensure statistical validity despite the unreliability. However, the challenge of `data silos' arises when the private gold-standard datasets are non-shareable for model training, leading to less accurate predictive models and invalid inferences. In this paper, we introduces the Federated Prediction-Powered Inference (Fed-PPI) framework, which addresses this challenge by enabling decentralized experimental data to contribute to statistically valid conclusions without sharing private information. The Fed-PPI framework involves training local models on private data, aggregating them through Federated Learning (FL), and deriving confidence intervals using PPI computation. The proposed framework is evaluated through experiments, demonstrating its effectiveness in producing valid confidence intervals.

Federated Prediction-Powered Inference from Decentralized Data

TL;DR

Fed-PPI unites federated learning with Prediction-Powered Inference to enable statistically valid conclusions from decentralized, private data without data sharing. The framework defines aggregation rules, imputed gradients, and empirical rectifiers to produce prediction-powered confidence intervals for convex and nonconvex estimands, with concrete algorithms for mean, quantile, logistic, and linear regression. Theoretical guarantees (finite-sample and asymptotic) and extensive experiments across real tasks and simulations demonstrate that Fed-PPI delivers intervals with valid coverage close to centralized analyses, while accommodating data heterogeneity and unlabeled data. This approach addresses data silos and privacy concerns, with practical impact for diverse scientific domains relying on collaborative yet privacy-preserving inference.

Abstract

In various domains, the increasing application of machine learning allows researchers to access inexpensive predictive data, which can be utilized as auxiliary data for statistical inference. Although such data are often unreliable compared to gold-standard datasets, Prediction-Powered Inference (PPI) has been proposed to ensure statistical validity despite the unreliability. However, the challenge of `data silos' arises when the private gold-standard datasets are non-shareable for model training, leading to less accurate predictive models and invalid inferences. In this paper, we introduces the Federated Prediction-Powered Inference (Fed-PPI) framework, which addresses this challenge by enabling decentralized experimental data to contribute to statistically valid conclusions without sharing private information. The Fed-PPI framework involves training local models on private data, aggregating them through Federated Learning (FL), and deriving confidence intervals using PPI computation. The proposed framework is evaluated through experiments, demonstrating its effectiveness in producing valid confidence intervals.
Paper Structure (51 sections, 15 theorems, 78 equations, 8 figures, 1 table, 4 algorithms)

This paper contains 51 sections, 15 theorems, 78 equations, 8 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries and Definitions
  4. Convex Estimation
  5. Aggregation weights
  6. Imputed gradient
  7. Empirical rectifier
  8. Actual Estimate
  9. Aggregation Weights
  10. Imputed gradient
  11. Empirical rectifier
  12. Beyond Convex Estimation
  13. Imputed gradient
  14. Empirical rectifier
  15. Algorithms
  16. ...and 36 more sections

Key Result

Theorem 1

Suppose that the convex estimation problem is nondegenerate as in convex-solution. Fix $\alpha \in (0,1)$ and $\Delta(\theta) \in (0,\alpha)$. Suppose that, for any $\theta \in \mathbb{R}^d$, we can construct $\mathcal{T}_{\alpha-\delta}$ and $\mathcal{R}_\delta(\theta)$ satisfying Let $\mathcal{C}_\alpha^{PP}=\{\theta:0\in\mathcal{R}_\delta(\theta)+\mathcal{T}_{\alpha-\delta}(\theta)\}$, where $

Figures (8)

  • Figure 1: Systems for prediction-powered inference in FL; The upper half of the figure represents the traditional FL training process, while the lower half depicts the Prediction-Powered Inference process and parameters aggregation on the client side.
  • Figure 2: Comparison of prediction-powered confidence interval at Client 1-5, FL aggregation and Centralized data. Each row is a different application. Column 1 provides an introduction to the application, while columns 2-4 present Case 1-3 as outlined in Section \ref{['subsec-set']}. In each figure, the prediction-powered confidence intervals at clients 1-5 are represented by blue gradient bars, with lighter shades indicating higher confidence levels.
  • Figure 3: Prediction-powered confidence intervals with different partition. The rows represent scenarios from Case 1 to Case 3, and the columns represent two different total dataset partition: [4:1:1:1:1] and [1:1:1:1:4].
  • Figure 4: Prediction-powered confidence intervals with 20 clients in Case 1. Each subplot corresponds to a real task.
  • Figure : FL-prediction-powered mean estimation
  • ...and 3 more figures

Theorems & Definitions (23)

  • Theorem 1: Convex estimation
  • Theorem 2: Convex estimation: asymptotic version
  • Theorem 3: General risk minimization: finite population
  • Proposition 1: Mean estimation
  • Proposition 2: Quantile estimation
  • Proposition 3: Logistic regression
  • Proposition 4: Linear regression
  • Proposition 5
  • proof
  • Theorem 1
  • ...and 13 more