Multi-task Sparse Structure Learning With Gaussian Copula Models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously. While sometimes the underlying task relationship structure is known, often the structure needs to be estimated from data at hand. In this paper, we present a novel family of models for MTL, applicable to regression and classification problems, capable of learning the structure of tasks relationship. In particular, we consider a joint estimation problem of the tasks relationship structure and the individual task parameters, which is solved using alternating minimization. The task relationship revealed by structure learning is founded on recent advances in Gaussian graphical models endowed with sparse estimators of the precision (inverse covariance) matrix. An extension to include flexible Gaussian copula models that relaxes the Gaussian marginal assumption is also proposed. We illustrate the e ff ectiveness of the proposed model on a variety of synthetic and benchmark data sets for regression and classi fi cation. We also consider the problem of combining Earth System Model (ESM) outputs for better projections of future climate, with focus on projections of temperature by combining ESMs in South and North America, and show that the proposed model outperforms several existing methods for the problem.17NSF [IIS-1029711, IIS-0916750, IIS-0953274, CNS-1314560, IIS-1422557, CCF-1451986, IIS-1447566]NASA [NNX12AQ39A]IBMYahooCNPqCNPq, BrazilConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Learning Sparse Sharing Architectures for Multiple Tasks

Most existing deep multi-task learning models are based on parameter sharing, such as hard sharing, hierarchical sharing, and soft sharing. How choosing a suitable sharing mechanism depends on the relations among the tasks, which is not easy since it is difficult to understand the underlying shared factors among these tasks. In this paper, we propose a novel parameter sharing mechanism, named \emph{Sparse Sharing}. Given multiple tasks, our approach automatically finds a sparse sharing structure. We start with an over-parameterized base network, from which each task extracts a subnetwork. The subnetworks of multiple tasks are partially overlapped and trained in parallel. We show that both hard sharing and hierarchical sharing can be formulated as particular instances of the sparse sharing framework. We conduct extensive experiments on three sequence labeling tasks. Compared with single-task models and three typical multi-task learning baselines, our proposed approach achieves consistent improvement while requiring fewer parameters.Comment: Accepted by AAAI 202

Localized Sparse Incomplete Multi-view Clustering

Incomplete multi-view clustering, which aims to solve the clustering problem on the incomplete multi-view data with partial view missing, has received more and more attention in recent years. Although numerous methods have been developed, most of the methods either cannot flexibly handle the incomplete multi-view data with arbitrary missing views or do not consider the negative factor of information imbalance among views. Moreover, some methods do not fully explore the local structure of all incomplete views. To tackle these problems, this paper proposes a simple but effective method, named localized sparse incomplete multi-view clustering (LSIMVC). Different from the existing methods, LSIMVC intends to learn a sparse and structured consensus latent representation from the incomplete multi-view data by optimizing a sparse regularized and novel graph embedded multi-view matrix factorization model. Specifically, in such a novel model based on the matrix factorization, a l1 norm based sparse constraint is introduced to obtain the sparse low-dimensional individual representations and the sparse consensus representation. Moreover, a novel local graph embedding term is introduced to learn the structured consensus representation. Different from the existing works, our local graph embedding term aggregates the graph embedding task and consensus representation learning task into a concise term. Furthermore, to reduce the imbalance factor of incomplete multi-view learning, an adaptive weighted learning scheme is introduced to LSIMVC. Finally, an efficient optimization strategy is given to solve the optimization problem of our proposed model. Comprehensive experimental results performed on six incomplete multi-view databases verify that the performance of our LSIMVC is superior to the state-of-the-art IMC approaches. The code is available in https://github.com/justsmart/LSIMVC.Comment: Published in IEEE Transactions on Multimedia (TMM). The code is available at Github https://github.com/justsmart/LSIMV