Heterogeneous multitask learning with joint sparsity constraints
نویسندگان
چکیده
Multitask learning addresses the problem of learning related tasks whose information on parameters is assumed to be shared with each other. Previous approaches usually deal with homogeneous tasks such as a set of regression tasks only or a set of classification tasks only. In this paper, we consider the problem of learning multiple related tasks, where tasks consist of predicting both continuous and discrete outputs from a common set of input variables that lie in a high-dimensional space. All of the tasks are related in the sense that they share the same set of relevant input variables, but the amount of influence of each input on different outputs may vary. We formulate this problem as a combination of linear regressions and logistic regressions, and model the joint sparsity as L1/L∞ or L1/L2 norm of the model parameters. Among several possible applications, our approach addresses an important open problem in genetic association mapping, where the goal is to discover genetic markers that influence multiple correlated traits jointly. In our experiments, we demonstrate our method in the setting of association mapping, using simulated and asthma datasets, and show that our method can effectively recover the relevant inputs with respect to all of the tasks.
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