Localized Lasso for High-Dimensional Regression

We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function defined by local sparse models, one at each data point. We introduce sample-wise network regularization to borrow strength across the models, and sample-wise exclusive group sparsity (a.k.a., $\ell_{1,2}$ norm) to introduce diversity into the choice of feature sets in the local models. The local models are interpretable in terms of similarity of their sparsity patterns. The cost function is convex, and thus has a globally optimal solution. Moreover, we propose a simple yet efficient iterative least-squares based optimization procedure for the localized Lasso, which does not need a tuning parameter, and is guaranteed to converge to a globally optimal solution. The solution is empirically shown to outperform alternatives for both simulated and genomic personalized medicine data

Deep Multi-view Learning to Rank

We study the problem of learning to rank from multiple information sources. Though multi-view learning and learning to rank have been studied extensively leading to a wide range of applications, multi-view learning to rank as a synergy of both topics has received little attention. The aim of the paper is to propose a composite ranking method while keeping a close correlation with the individual rankings simultaneously. We present a generic framework for multi-view subspace learning to rank (MvSL2R), and two novel solutions are introduced under the framework. The first solution captures information of feature mappings from within each view as well as across views using autoencoder-like networks. Novel feature embedding methods are formulated in the optimization of multi-view unsupervised and discriminant autoencoders. Moreover, we introduce an end-to-end solution to learning towards both the joint ranking objective and the individual rankings. The proposed solution enhances the joint ranking with minimum view-specific ranking loss, so that it can achieve the maximum global view agreements in a single optimization process. The proposed method is evaluated on three different ranking problems, i.e. university ranking, multi-view lingual text ranking and image data ranking, providing superior results compared to related methods.Comment: Published at IEEE TKD

Scalable Machine Learning Methods for Massive Biomedical Data Analysis.

Modern data acquisition techniques have enabled biomedical researchers to collect and analyze datasets of substantial size and complexity. The massive size of these datasets allows us to comprehensively study the biological system of interest at an unprecedented level of detail, which may lead to the discovery of clinically relevant biomarkers. Nonetheless, the dimensionality of these datasets presents critical computational and statistical challenges, as traditional statistical methods break down when the number of predictors dominates the number of observations, a setting frequently encountered in biomedical data analysis. This difficulty is compounded by the fact that biological data tend to be noisy and often possess complex correlation patterns among the predictors. The central goal of this dissertation is to develop a computationally tractable machine learning framework that allows us to extract scientifically meaningful information from these massive and highly complex biomedical datasets. We motivate the scope of our study by considering two important problems with clinical relevance: (1) uncertainty analysis for biomedical image registration, and (2) psychiatric disease prediction based on functional connectomes, which are high dimensional correlation maps generated from resting state functional MRI.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111354/1/takanori_1.pd