Zijian Guo

Xin Xiong, Zijian Guo, Tianxi Cai

Many existing transfer learning methods rely on leveraging information from source data that closely resembles the target data. However, this approach often overlooks valuable knowledge that may be present in different yet potentially related auxiliary samples. When dealing with a limited amount of target data and a diverse range of source models, our paper introduces a novel approach, Distributionally Robust Optimization for Transfer Learning (TransDRO), that breaks free from strict similarity constraints. TransDRO is designed to optimize the most adversarial loss within an uncertainty set, defined as a collection of target populations generated as a convex combination of source distributions that guarantee excellent prediction performances for the target data. TransDRO effectively bridges the realms of transfer learning and distributional robustness prediction models. We establish the identifiability of TransDRO and its interpretation as a weighted average of source models closest to the baseline model. We also show that TransDRO achieves a faster convergence rate than the model fitted with the target data. Our comprehensive numerical studies and analysis of multi-institutional electronic health records data using TransDRO further substantiate the robustness and accuracy of TransDRO, highlighting its potential as a powerful tool in transfer learning applications.

Yihong Gu, Cong Fang, Yang Xu et al. · princeton

Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as ICP [Peters et al., 2016] and EILLS [Fan et al., 2024] that can attain sample-efficient estimation are based on exponential time algorithms. In this paper, we show that such a problem is intrinsically hard in computation: the decision problem, testing whether a non-trivial prediction-invariant solution exists across two environments, is NP-hard even for the linear causal relationship. In the world where P$\neq$NP, our results imply that the estimation error rate can be arbitrarily slow using any computationally efficient algorithm. This suggests that pursuing causality is fundamentally harder than detecting associations when no prior assumption is pre-offered. Given there is almost no hope of computational improvement under the worst case, this paper proposes a method capable of attaining both computationally and statistically efficient estimation under additional conditions. Furthermore, our estimator is a distributionally robust estimator with an ellipse-shaped uncertain set where more uncertainty is placed on spurious directions than invariant directions, resulting in a smooth interpolation between the most predictive solution and the causal solution by varying the invariance hyper-parameter. Non-asymptotic results and empirical applications support the claim.

Jue Hou, Zijian Guo, Tianxi Cai

Risk modeling with EHR data is challenging due to a lack of direct observations on the disease outcome, and the high dimensionality of the candidate predictors. In this paper, we develop a surrogate assisted semi-supervised-learning (SAS) approach to risk modeling with high dimensional predictors, leveraging a large unlabeled data on candidate predictors and surrogates of outcome, as well as a small labeled data with annotated outcomes. The SAS procedure borrows information from surrogates along with candidate predictors to impute the unobserved outcomes via a sparse working imputation model with moment conditions to achieve robustness against mis-specification in the imputation model and a one-step bias correction to enable interval estimation for the predicted risk. We demonstrate that the SAS procedure provides valid inference for the predicted risk derived from a high dimensional working model, even when the underlying risk prediction model is dense and the risk model is mis-specified. We present an extensive simulation study to demonstrate the superiority of our SSL approach compared to existing supervised methods. We apply the method to derive genetic risk prediction of type-2 diabetes mellitus using a EHR biobank cohort.