Smart Multi-Task Bregman Clustering and Multi-Task Kernel Clustering

AAAI Conferences

Multitask Bregman Clustering (MBC) alternatively updates clusters and learns relationship between clusters of different tasks, and the two phases boost each other. However, the boosting does not always have positive effect, it may also cause negative effect. Another issue of MBC is that it cannot deal with nonlinear separable data. In this paper, we show that MBC's process of using cluster relationship to boost the updating clusters phase may cause negative effect, i.e., cluster centroid may be skewed under some conditions. We propose a smart multi-task Bregman clustering (S-MBC) algorithm which identifies negative effect of the boosting and avoids the negative effect if it occurs. We then extend the framework of S-MBC to a smart multi-task kernel clustering (S-MKC) framework to deal with nonlinear separable data. We also propose a specific implementation of the framework which could be applied to any Mercer kernel. Experimental results confirm our analysis, and demonstrate the superiority of our proposed methods.


Multi-Stage Multi-Task Feature Learning

Neural Information Processing Systems

Multi-task sparse feature learning aims to improve the generalization performance by exploiting the shared features among tasks. It has been successfully applied to many applications including computer vision and biomedical informatics. In this paper, we propose a non-convex formulation for multi-task sparse feature learning based on a novel regularizer. To solve the non-convex optimization problem, we propose a Multi-Stage Multi-Task Feature Learning (MSMTFL) algorithm. Moreover, we present a detailed theoretical analysis showing that MSMTFL achieves a better parameter estimation error bound than the convex formulation.


Probabilistic Multi-Task Feature Selection

Neural Information Processing Systems

Recently, some variants of the $l_1$ norm, particularly matrix norms such as the $l_{1,2}$ and $l_{1,\infty}$ norms, have been widely used in multi-task learning, compressed sensing and other related areas to enforce sparsity via joint regularization. In this paper, we unify the $l_{1,2}$ and $l_{1,\infty}$ norms by considering a family of $l_{1,q}$ norms for $1 q\le\infty$ and study the problem of determining the most appropriate sparsity enforcing norm to use in the context of multi-task feature selection. Based on this probabilistic interpretation, we develop a probabilistic model using the noninformative Jeffreys prior. We also extend the model to learn and exploit more general types of pairwise relationships between tasks. For both versions of the model, we devise expectation-maximization (EM) algorithms to learn all model parameters, including $q$, automatically.


Multi-Task Multi-View Clustering for Non-Negative Data

AAAI Conferences

Multi-task clustering and multi-view clustering have severally found wide applications and received much attention in recent years. Nevertheless, there are many clustering problems that involve both multi-task clustering and multi-view clustering, i.e., the tasks are closely related and each task can be analyzed from multiple views. In this paper, for non-negative data (e.g., documents), we introduce a multi-task multi-view clustering (MTMVC) framework which integrates within-view-task clustering, multi-view relationship learning and multi-task relationship learning. We then propose a specific algorithm to optimize the MTMVC framework. Experimental results show the superiority of the proposed algorithm over either multi-task clustering algorithms or multi-view clustering algorithms for multi-task clustering of multi-view data.


Multi-Task Learning and Algorithmic Stability

AAAI Conferences

In this paper, we study multi-task algorithms from the perspective of the algorithmic stability. We give a definition of the multi-task uniform stability, a generalization of the conventional uniform stability, which measures the maximum difference between the loss of a multi-task algorithm trained on a data set and that of the multi-task algorithm trained on the same data set but with a data point removed in each task. In order to analyze multi-task algorithms based on multi-task uniform stability, we prove a generalized McDiarmid's inequality which assumes the difference bound condition holds by changing multiple input arguments instead of only one in the conventional McDiarmid's inequality. By using the generalized McDiarmid's inequality as a tool, we can analyze the generalization performance of general multi-task algorithms in terms of the multi-task uniform stability. Moreover, as applications, we prove generalization bounds of several representative regularized multi-task algorithms.