Topics in matrix analysis
Machine Learning - Special issue on inductive transfer
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Task clustering and gating for bayesian multitask learning
The Journal of Machine Learning Research
Learning Multiple Tasks with Kernel Methods
The Journal of Machine Learning Research
Learning Bounds for Kernel Regression Using Effective Data Dimensionality
Neural Computation
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
A Framework for Learning Predictive Structures from Multiple Tasks and Unlabeled Data
The Journal of Machine Learning Research
Convex multi-task feature learning
Machine Learning
Data-driven Calibration of Penalties for Least-Squares Regression
The Journal of Machine Learning Research
Recovering sparse signals with a certain family of nonconvex penalties and DC programming
IEEE Transactions on Signal Processing
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In this paper we study the kernel multiple ridge regression framework, which we refer to as multitask regression, using penalization techniques. The theoretical analysis of this problem shows that the key element appearing for an optimal calibration is the covariance matrix of the noise between the different tasks. We present a new algorithm to estimate this covariance matrix, based on the concept of minimal penalty, which was previously used in the single-task regression framework to estimate the variance of the noise. We show, in a non-asymptotic setting and under mild assumptions on the target function, that this estimator converges towards the covariance matrix. Then plugging this estimator into the corresponding ideal penalty leads to an oracle inequality. We illustrate the behavior of our algorithm on synthetic examples.