FAIRM: Learning invariant representations for algorithmic fairness and domain generalization with minimax optimality

Machine learning methods often assume that the test data have the same distribution as the training data. However, this assumption may not hold due to multiple levels of heterogeneity in applications, raising issues in algorithmic fairness and domain generalization. In this work, we address the problem of fair and generalizable machine learning by invariant principles. We propose a training environment-based oracle, FAIRM, which has desirable fairness and domain generalization properties under a diversity-type condition. We then provide an empirical FAIRM with finite-sample theoretical guarantees under weak distributional assumptions. We then develop efficient algorithms to realize FAIRM in linear models and demonstrate the nonasymptotic performance with minimax optimality. We evaluate our method in numerical experiments with synthetic data and MNIST data and show that it outperforms its counterparts.

Multi-dimensional domain generalization with low-rank structures

In conventional statistical and machine learning methods, it is typically assumed that the test data are identically distributed with the training data. However, this assumption does not always hold, especially in applications where the target population are not well-represented in the training data. This is a notable issue in health-related studies, where specific ethnic populations may be underrepresented, posing a significant challenge for researchers aiming to make statistical inferences about these minority groups. In this work, we present a novel approach to addressing this challenge in linear regression models. We organize the model parameters for all the sub-populations into a tensor. By studying a structured tensor completion problem, we can achieve robust domain generalization, i.e., learning about sub-populations with limited or no available data. Our method novelly leverages the structure of group labels and it can produce more reliable and interpretable generalization results. We establish rigorous theoretical guarantees for the proposed method and demonstrate its minimax optimality. To validate the effectiveness of our approach, we conduct extensive numerical experiments and a real data study focused on education level prediction for multiple ethnic groups, comparing our results with those obtained using other existing methods.

Transferred Q-learning

We consider $Q$-learning with knowledge transfer, using samples from a target reinforcement learning (RL) task as well as source samples from different but related RL tasks. We propose transfer learning algorithms for both batch and online $Q$-learning with offline source studies. The proposed transferred $Q$-learning algorithm contains a novel re-targeting step that enables vertical information-cascading along multiple steps in an RL task, besides the usual horizontal information-gathering as transfer learning (TL) for supervised learning. We establish the first theoretical justifications of TL in RL tasks by showing a faster rate of convergence of the $Q$ function estimation in the offline RL transfer, and a lower regret bound in the offline-to-online RL transfer under certain similarity assumptions. Empirical evidences from both synthetic and real datasets are presented to back up the proposed algorithm and our theoretical results.

Improving Out-of-Distribution Robustness via Selective Augmentation

Machine learning algorithms typically assume that training and test examples are drawn from the same distribution. However, distribution shift is a common problem in real-world applications and can cause models to perform dramatically worse at test time. In this paper, we specifically consider the problems of domain shifts and subpopulation shifts (eg. imbalanced data). While prior works often seek to explicitly regularize internal representations and predictors of the model to be domain invariant, we instead aim to regularize the whole function without restricting the model's internal representations. This leads to a simple mixup-based technique which learns invariant functions via selective augmentation called LISA. LISA selectively interpolates samples either with the same labels but different domains or with the same domain but different labels. We analyze a linear setting and theoretically show how LISA leads to a smaller worst-group error. Empirically, we study the effectiveness of LISA on nine benchmarks ranging from subpopulation shifts to domain shifts, and we find that LISA consistently outperforms other state-of-the-art methods.

Targeting Underrepresented Populations in Precision Medicine: A Federated Transfer Learning Approach

The limited representation of minorities and disadvantaged populations in large-scale clinical and genomics research has become a barrier to translating precision medicine research into practice. Due to heterogeneity across populations, risk prediction models are often found to be underperformed in these underrepresented populations, and therefore may further exacerbate known health disparities. In this paper, we propose a two-way data integration strategy that integrates heterogeneous data from diverse populations and from multiple healthcare institutions via a federated transfer learning approach. The proposed method can handle the challenging setting where sample sizes from different populations are highly unbalanced. With only a small number of communications across participating sites, the proposed method can achieve performance comparable to the pooled analysis where individual-level data are directly pooled together. We show that the proposed method improves the estimation and prediction accuracy in underrepresented populations, and reduces the gap of model performance across populations. Our theoretical analysis reveals how estimation accuracy is influenced by communication budgets, privacy restrictions, and heterogeneity across populations. We demonstrate the feasibility and validity of our methods through numerical experiments and a real application to a multi-center study, in which we construct polygenic risk prediction models for Type II diabetes in AA population.

Transfer Learning in Large-scale Gaussian Graphical Models with False Discovery Rate Control

Transfer learning for high-dimensional Gaussian graphical models (GGMs) is studied with the goal of estimating the target GGM by utilizing the data from similar and related auxiliary studies. The similarity between the target graph and each auxiliary graph is characterized by the sparsity of a divergence matrix. An estimation algorithm, Trans-CLIME, is proposed and shown to attain a faster convergence rate than the minimax rate in the single study setting. Furthermore, a debiased Trans-CLIME estimator is introduced and shown to be element-wise asymptotically normal. It is used to construct a multiple testing procedure for edge detection with false discovery rate control. The proposed estimation and multiple testing procedures demonstrate superior numerical performance in simulations and are applied to infer the gene networks in a target brain tissue by leveraging the gene expressions from multiple other brain tissues. A significant decrease in prediction errors and a significant increase in power for link detection are observed.

Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality

This paper considers the estimation and prediction of a high-dimensional linear regression in the setting of transfer learning, using samples from the target model as well as auxiliary samples from different but possibly related regression models. When the set of "informative" auxiliary samples is known, an estimator and a predictor are proposed and their optimality is established. The optimal rates of convergence for prediction and estimation are faster than the corresponding rates without using the auxiliary samples. This implies that knowledge from the informative auxiliary samples can be transferred to improve the learning performance of the target problem. In the case that the set of informative auxiliary samples is unknown, we propose a data-driven procedure for transfer learning, called Trans-Lasso, and reveal its robustness to non-informative auxiliary samples and its efficiency in knowledge transfer. The proposed procedures are demonstrated in numerical studies and are applied to a dataset concerning the associations among gene expressions. It is shown that Trans-Lasso leads to improved performance in gene expression prediction in a target tissue by incorporating the data from multiple different tissues as auxiliary samples.