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In this paper we study multi-task kernel ridge regression and try to understand when the multi-task procedure performs better than the single-task one, in terms of averaged quadratic risk. In order to do so, we compare the risks of the estimators with perfect calibration, the emph{oracle risk}. We are able to give explicit settings, favorable to the multi-task procedure, where the multi-task oracle performs better than the single-task one. In situations where the multi-task procedure is conjectured to perform badly, we also show the oracle does so. We then complete our study with simulated examples, where we can compare both oracle risks in more natural situations. A consequence of our result is that the multi-task ridge estimator has a lower risk than any single-task estimator, in favorable situations.
In this paper we study the kernel multiple ridge regression framework, which we refer to as multi-task regression, using penalization techniques. The theoretical analysis of this problem shows that the key element appearing for an optimal calibration
In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The optimal conv
We consider a sparse multi-task regression framework for fitting a collection of related sparse models. Representing models as nodes in a graph with edges between related models, a framework that fuses lasso regressions with the total variation penal
We propose statistical inferential procedures for panel data models with interactive fixed effects in a kernel ridge regression framework.Compared with traditional sieve methods, our method is automatic in the sense that it does not require the choic
Regularization is an essential element of virtually all kernel methods for nonparametric regression problems. A critical factor in the effectiveness of a given kernel method is the type of regularization that is employed. This article compares and co