Learning Correlative and Personalized Structure for Online Multi-Task Classification

Abstract

Multi-Task Learning (MTL) can enhance the classifier's generalization performance by learning multiple related tasks simultaneously. Conventional MTL works under the offline or batch learning setting and suffers from the expensive training cost together with the poor scalability. To address such inefficiency issues, online learning technique has been applied to solve MTL problems. However, most existing algorithms for online MTL constrain task relatedness into a presumed structure via a single weight matrix, a strict restriction that does not always hold in practice. In this paper, we propose a general online MTL framework that overcomes this restriction by decomposing the weight matrix into two components: the first component captures the correlative structure among tasks in a low-rank subspace, and the second component identifies the personalized patterns for the outlier tasks. A projected gradient scheme is devised to learn such components adaptively. Theoretical analysis shows that the proposed algorithm can achieve a sub-linear regret with respect to the best linear model in hindsight. Experimental investigation on a number of real-world datasets also verifies the efficacy of our approach.

Robust Online Multi-Task Learning with Correlative and Personalized Structures

“…Although the composite problem (11) can be solved by [49], the composite function with linear constraints has not been investigated to solve the MTL problem. We employ a projected gradient scheme [50], [51] to optimize this problem with both smooth and nonsmooth terms.…”

“…We employ a projected gradient scheme [50], [51] to optimize this problem with both smooth and nonsmooth terms. Specifically, by substituting (12) into (11) and omitting the terms unrelated to U and V , the problem can be rewritten as a projected gradient schema,…”

“…After updating the model in each round, the current input will be discarded. As a result, online learning algorithms are efficient and scalable, and have been successfully applied to a number of MTL applications [7], [8], [9], [10], [11].…”

Robust Cost-Sensitive Learning for Recommendation with Implicit Feedback

“…For the first limitation (imbalanced classes), cost-sensitive learning [11] and positive-unlabeled matrix completion algorithms [13] have been proposed to exploit an asymmetric cost of error from positive and unlabeled samples. For the second limitation (outlier estimation), robust matrix decomposition algorithm [14] has been developed to detect the outliers and learn basis from the recovered subspace, and it showed success in different applications, including system identification [10], multi-task learning [47], [44], PCA [8] and graphical modeling [9]. Although each aforementioned algorithm, e.g.…”