# Infinite Predictor Subspace Models for Multitask Learning

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Piyush Rai,
Hal Daumé III
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Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:613-620, 2010.

#### Abstract

Given several related learning tasks, we propose a nonparametric Bayesian model that captures task relatedness by assuming that the task parameters (i.e., predictors) share a latent subspace. More specifically, the intrinsic dimensionality of the task subspace is not assumed to be known a priori. We use an infinite latent feature model to automatically infer this number (depending on and limited by only the number of tasks). Furthermore, our approach is applicable when the underlying task parameter subspace is inherently sparse, drawing parallels with l1 regularization and LASSO-style models. We also propose an augmented model which can make use of (labeled, and additionally unlabeled if available) inputs to assist learning this subspace, leading to further improvements in the performance. Experimental results demonstrate the efficacy of both the proposed approaches, especially when the number of examples per task is small. Finally, we discuss an extension of the proposed framework where a nonparametric mixture of linear subspaces can be used to learn a manifold over the task parameters, and also deal with the issue of negative transfer from unrelated tasks.

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