25 research outputs found
Conic Multi-Task Classification
Traditionally, Multi-task Learning (MTL) models optimize the average of
task-related objective functions, which is an intuitive approach and which we
will be referring to as Average MTL. However, a more general framework,
referred to as Conic MTL, can be formulated by considering conic combinations
of the objective functions instead; in this framework, Average MTL arises as a
special case, when all combination coefficients equal 1. Although the advantage
of Conic MTL over Average MTL has been shown experimentally in previous works,
no theoretical justification has been provided to date. In this paper, we
derive a generalization bound for the Conic MTL method, and demonstrate that
the tightest bound is not necessarily achieved, when all combination
coefficients equal 1; hence, Average MTL may not always be the optimal choice,
and it is important to consider Conic MTL. As a byproduct of the generalization
bound, it also theoretically explains the good experimental results of previous
relevant works. Finally, we propose a new Conic MTL model, whose conic
combination coefficients minimize the generalization bound, instead of choosing
them heuristically as has been done in previous methods. The rationale and
advantage of our model is demonstrated and verified via a series of experiments
by comparing with several other methods.Comment: Accepted by European Conference on Machine Learning and Principles
and Practice of Knowledge Discovery in Databases (ECMLPKDD)-201
Mistake Bounds for Binary Matrix Completion
We study the problem of completing a binary matrix in an online learning setting.On each trial we predict a matrix entry and then receive the true entry. We propose a Matrix Exponentiated Gradient algorithm [1] to solve this problem. We provide a mistake bound for the algorithm, which scales with the margin complexity [2, 3] of the underlying matrix. The bound suggests an interpretation where each row of the matrix is a prediction task over a finite set of objects, the columns. Using this we show that the algorithm makes a number of mistakes which is comparable up to a logarithmic factor to the number of mistakes made by the Kernel Perceptron with an optimal kernel in hindsight. We discuss applications of the algorithm to predicting as well as the best biclustering and to the problem of predicting the labeling of a graph without knowing the graph in advance
Consistent Multitask Learning with Nonlinear Output Relations
Key to multitask learning is exploiting relationships between different tasks
to improve prediction performance. If the relations are linear, regularization
approaches can be used successfully. However, in practice assuming the tasks to
be linearly related might be restrictive, and allowing for nonlinear structures
is a challenge. In this paper, we tackle this issue by casting the problem
within the framework of structured prediction. Our main contribution is a novel
algorithm for learning multiple tasks which are related by a system of
nonlinear equations that their joint outputs need to satisfy. We show that the
algorithm is consistent and can be efficiently implemented. Experimental
results show the potential of the proposed method.Comment: 25 pages, 1 figure, 2 table
Meta-learning with Stochastic Linear Bandits
We investigate meta-learning procedures in the setting of stochastic linear
bandits tasks. The goal is to select a learning algorithm which works well on
average over a class of bandits tasks, that are sampled from a
task-distribution. Inspired by recent work on learning-to-learn linear
regression, we consider a class of bandit algorithms that implement a
regularized version of the well-known OFUL algorithm, where the regularization
is a square euclidean distance to a bias vector. We first study the benefit of
the biased OFUL algorithm in terms of regret minimization. We then propose two
strategies to estimate the bias within the learning-to-learn setting. We show
both theoretically and experimentally, that when the number of tasks grows and
the variance of the task-distribution is small, our strategies have a
significant advantage over learning the tasks in isolation