Multitask learning aims at solving a set of related tasks simultaneously, by exploiting the shared knowledge for improving the performance on individual tasks. Hence, an important aspect of multitask learning is to understand the similarities within a set of tasks. Previous works have incorporated this similarity information explicitly (e.g., weighted loss for each task) or implicitly (e.g., adversarial loss for feature adaptation), for achieving good empirical performances. However, the theoretical motivations for adding task similarity knowledge are often missing or incomplete. In this paper, we give a different perspective from a theoretical point of view to understand this practice. We first provide an upper bound on the generalization error of multitask learning, showing the benefit of explicit and implicit task similarity knowledge. We systematically derive the bounds based on two distinct task similarity metrics: H divergence and Wasserstein distance. From these theoretical results, we revisit the Adversarial Multi-task Neural Network, proposing a new training algorithm to learn the task relation coefficients and neural network parameters iteratively. We assess our new algorithm empirically on several benchmarks, showing not only that we find interesting and robust task relations, but that the proposed approach outperforms the baselines, reaffirming the benefits of theoretical insight in algorithm design.
Some survey papers @cite_10 @cite_1 @cite_2 have made a broad and detailed presentation of the general MTL. More specifically related to our work, on the practical side, we note several approaches that use tasks relationship to improve empirical performances: solve a convex optimization problem in the original space or Reproducing Kernel Hilbert-Space to extract tasks relationships, propose probabilistic models through construction of a task covariance matrix or estimate the multitask likelihood from a deep Bayes model. On the theoretical side, analyze the weighted sum loss algorithm and its applications in online learning, active learning and transductive learning. Moreover, analyze generalization error of representation-based approaches, and analyze the algorithmic stability in MTL.
@cite_1 @cite_10 @cite_2
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When we have several related tasks, solving them simultaneously is shown to be more effective than solving them individually. This approach is called multi-task learning (MTL) and has been studied extensively. Existing approaches to MTL often treat all the tasks as uniformly related to each other and the relatedness of the tasks is controlled globally. For this reason, the existing methods can lead to undesired solutions when some tasks are not highly related to each other, and some pairs of related tasks can have significantly different solutions. In this paper, we propose a novel MTL algorithm that can overcome these problems. Our method makes use of a task network, which describes the relation structure among tasks. This allows us to deal with intricate relation structures in a systematic way. Furthermore, we control the relatedness of the tasks locally, so all pairs of related tasks are guaranteed to have similar solutions. We apply the above idea to support vector machines (SVMs) and show that the optimization problem can be cast as a second order cone program, which is convex and can be solved efficiently. The usefulness of our approach is demonstrated through simulations with protein super-family classification and ordinal regression problems. 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 task relationships. In particular, we consider a joint estimation problem of the task relationship structure and the individual task parameters, which is solved using alternating minimization. The task relationship structure learning component builds on recent advances in structure learning of Gaussian graphical models based on sparse estimators of the precision (inverse covariance) matrix. We illustrate the effectiveness of the proposed model on a variety of synthetic and benchmark datasets for regression and classification. We also consider the problem of combining climate model outputs for better projections of future climate, with focus on temperature in South America, and show that the proposed model outperforms several existing methods for the problem. 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 exible Gaussian copula models that relaxes the Gaussian marginal assumption is also proposed. We illustrate the effectiveness of the proposed model on a variety of synthetic and benchmark data sets for regression and classification. 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. Multiple task learning (MTL) is becoming popular due to its theoretical advances and empirical successes. The key idea of MTL is to explore the hidden relationships among multiple tasks to enhance learning performance. Recently, many MTL algorithms have been developed and applied to various problems such as feature selection and kernel learning. However, most existing methods highly relied on certain assumptions of the task relationships. For instance, several works assumed that there is a major task group and several outlier tasks, and used a decomposition approach to identify the group structure and outlier tasks simultaneously. In this paper, we adopt a more general formulation for MTL without making specific structure assumptions. Instead of performing model decomposition, we directly impose an elastic-net regularization with a mixture of the structure and outlier penalties and formulate the objective as an unconstrained convex problem. To derive the optimal solution efficiently, we propose to use an Iteratively Reweighted Least Square (IRLS) method with a preconditioned conjugate gradient, which is computationally affordable for high dimensional data. Extensive experiments are conducted over both synthetic and real data, and comparisons with several state-of-the-art algorithms clearly show the superior performance of the proposed method.