Unified Transfer Learning Models for High-Dimensional Linear Regression

Transfer learning plays a key role in modern data analysis when: (1) the target data are scarce but the source data are sufficient; (2) the distributions of the source and target data are heterogeneous. This paper develops an interpretable unified transfer learning model, termed as UTrans, which can detect both transferable variables and source data. More specifically, we establish the estimation error bounds and prove that our bounds are lower than those with target data only. Besides, we propose a source detection algorithm based on hypothesis testing to exclude the nontransferable data. We evaluate and compare UTrans to the existing algorithms in multiple experiments. It is shown that UTrans attains much lower estimation and prediction errors than the existing methods, while preserving interpretability. We finally apply it to the US intergenerational mobility data and compare our proposed algorithms to the classical machine learning algorithms.

Integrative Clustering of Multi-View Data by Nonnegative Matrix Factorization

Learning multi-view data is an emerging problem in machine learning research, and nonnegative matrix factorization (NMF) is a popular dimensionality-reduction method for integrating information from multiple views. These views often provide not only consensus but also diverse information. However, most multi-view NMF algorithms assign equal weight to each view or tune the weight via line search empirically, which can be computationally expensive or infeasible without any prior knowledge of the views. In this paper, we propose a weighted multi-view NMF (WM-NMF) algorithm. In particular, we aim to address the critical technical gap, which is to learn both view-specific and observation-specific weights to quantify each view's information content. The introduced weighting scheme can alleviate unnecessary views' adverse effects and enlarge the positive effects of the important views by assigning smaller and larger weights, respectively. In addition, we provide theoretical investigations about the convergence, perturbation analysis, and generalization error of the WM-NMF algorithm. Experimental results confirm the effectiveness and advantages of the proposed algorithm in terms of achieving better clustering performance and dealing with the corrupted data compared to the existing algorithms.