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Bias-Corrected Data Synthesis for Imbalanced Learning

Pengfei Lyu, Zhengchi Ma, Linjun Zhang, Anru R. Zhang

TL;DR

This work tackles imbalanced classification by introducing a bias-corrected data-synthesis framework that compensates for distribution mismatch between synthetic and true minority data. The core idea is to estimate minority bias via majority information and correct the augmented loss with a bias-transfer term, yielding a bias-corrected loss $L^{\rm bc}$ that improves predictive accuracy and estimation stability. The authors provide non-asymptotic risk and parameter-estimation bounds, establish conditions under which bias correction outperforms standard synthetic augmentation, and demonstrate robustness across tasks, including multi-task learning and causal inference via ATE estimation. Empirical validation on simulations and MNIST corroborates that bias correction consistently enhances performance, especially when synthetic generators Devise biased minority samples, highlighting practical impact for real-world imbalanced settings.

Abstract

Imbalanced data, where the positive samples represent only a small proportion compared to the negative samples, makes it challenging for classification problems to balance the false positive and false negative rates. A common approach to addressing the challenge involves generating synthetic data for the minority group and then training classification models with both observed and synthetic data. However, since the synthetic data depends on the observed data and fails to replicate the original data distribution accurately, prediction accuracy is reduced when the synthetic data is naively treated as the true data. In this paper, we address the bias introduced by synthetic data and provide consistent estimators for this bias by borrowing information from the majority group. We propose a bias correction procedure to mitigate the adverse effects of synthetic data, enhancing prediction accuracy while avoiding overfitting. This procedure is extended to broader scenarios with imbalanced data, such as imbalanced multi-task learning and causal inference. Theoretical properties, including bounds on bias estimation errors and improvements in prediction accuracy, are provided. Simulation results and data analysis on handwritten digit datasets demonstrate the effectiveness of our method.

Bias-Corrected Data Synthesis for Imbalanced Learning

TL;DR

This work tackles imbalanced classification by introducing a bias-corrected data-synthesis framework that compensates for distribution mismatch between synthetic and true minority data. The core idea is to estimate minority bias via majority information and correct the augmented loss with a bias-transfer term, yielding a bias-corrected loss that improves predictive accuracy and estimation stability. The authors provide non-asymptotic risk and parameter-estimation bounds, establish conditions under which bias correction outperforms standard synthetic augmentation, and demonstrate robustness across tasks, including multi-task learning and causal inference via ATE estimation. Empirical validation on simulations and MNIST corroborates that bias correction consistently enhances performance, especially when synthetic generators Devise biased minority samples, highlighting practical impact for real-world imbalanced settings.

Abstract

Imbalanced data, where the positive samples represent only a small proportion compared to the negative samples, makes it challenging for classification problems to balance the false positive and false negative rates. A common approach to addressing the challenge involves generating synthetic data for the minority group and then training classification models with both observed and synthetic data. However, since the synthetic data depends on the observed data and fails to replicate the original data distribution accurately, prediction accuracy is reduced when the synthetic data is naively treated as the true data. In this paper, we address the bias introduced by synthetic data and provide consistent estimators for this bias by borrowing information from the majority group. We propose a bias correction procedure to mitigate the adverse effects of synthetic data, enhancing prediction accuracy while avoiding overfitting. This procedure is extended to broader scenarios with imbalanced data, such as imbalanced multi-task learning and causal inference. Theoretical properties, including bounds on bias estimation errors and improvements in prediction accuracy, are provided. Simulation results and data analysis on handwritten digit datasets demonstrate the effectiveness of our method.

Paper Structure

This paper contains 30 sections, 6 theorems, 125 equations, 4 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Our Contribution
  4. Methodology
  5. Bias Correction with Synthetic Data
  6. Multi-Task Imbalanced Learning
  7. Average Treatment Effect Estimation
  8. Theoretical Properties
  9. Bias Correction for Risk Functions
  10. Bias Correction for Multi-Task Learning
  11. Average Treatment Effect Estimation
  12. Simulation Studies
  13. Mean Shift Model
  14. Non-linear Classification
  15. Sigmoid Bernoulli Model
  16. ...and 15 more sections

Key Result

Proposition 1

Suppose Assumption asmp_transformation holds and there exists $0 < c_1 < c_2 < 1/2$ such that $c_1 \leq n_1/n \leq c_2$. Then for any $\alpha\in(0,1)$, with probability at least $1-\alpha$, Specifically, when $n_1^* = O(n_0 - n_1)$, $\tilde{n}_1 = n_1^* = O(n_0 - n_1)$, $n_{0c} = n_1^* = O(n_0 - n_1)$ and $\tilde{n}_0 = n_1^* = O(n_0 - n_1)$, the result can be written as follows: For any $\alpha

Figures (4)

  • Figure 1: A pictorial illustration of imbalanced learning based on raw data, synthetic augmentation and bias correction.
  • Figure 2: Distribution and $F_\beta$ score for four non-linear classification settings.
  • Figure 3: Square Root MSE for ATE Estimation of Three Methods across Four Distributions of Covariates $\bm X$.
  • Figure 4: Seven metrics (Recall, Precision, Accuracy, Fowlkes-Mallows score (FM), F1-score, Matthews Correlation Coefficient (MCC), and Jaccard index) for the three methods applied to the MNIST dataset (digits 0-4). Results are shown for binary classification of digit 1 (top panel) and digit 4 (bottom panel), treated as minority classes.

Theorems & Definitions (12)

  • Proposition 1
  • Proposition 2
  • Theorem 3.1
  • Theorem 3.2
  • Remark 1
  • Theorem 3.3
  • Corollary 1
  • proof
  • proof
  • proof
  • ...and 2 more