Multi-output learning via spectral filtering

By Luca Baldassarre, Lorenzo Rosasco, Annalisa Barla, Alessandro Verri. 2012

67 citations recorded by the source corpus.

In this paper we study a class of regularized kernel methods for multi-output learning which are based on filtering the spectrum of the kernel matrix. The considered methods include Tikhonov regularization as a special case, as well as interesting alternatives such as vector-valued extensions of L2 boosting and other iterative schemes. Computational properties are discussed for various examples of kernels for vector-valued functions and the benefits of iterative techniques are illustrated. Generalizing previous results for the scalar case, we show a finite sample bound for the excess risk of the obtained estimator, which allows to prove consistency both for regression and multi-category classification. Finally, we present some promising results of the proposed algorithms on artificial and real data.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Mathematical Physics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computer Vision and Pattern Recognition

In Mathematical Physics

Citations in the corpus

Kernels for Vector-Valued Functions: a Review (2011, background): “In fact, computing the divergence of a linear combination of its columns, ∇ ⊤ (Φ( u ) c ) , with c ∈ R p , it is possible to show that [7] where the last equality follows applying the product rule of the gradient, the fact that the coefﬁcient vector c does not depend upon u and the equality a ⊤ aa…”
Operator-valued Kernels for Learning from Functional Response Data (2015, background): “Since this seminal work, it has been demonstrated that these kernels and their associated spaces are capable of solving various other learning problems such as multiple output learning (Baldassarre et al., 2012), manifold regularization (Minh and Sindhwani, 2011), structured output prediction (Broua”
Input Output Kernel Regression (2016, methodology): “In the remainder of this section we propose to derive models based on on a simple but powerful family of operator-values kernels (OVK) based on scalar-valued kernels, called decomposable kernels or separable kernels (´Alvarez et al., 2012; Baldassarre et al., 2012).”
A survey on multi‐output regression (2015, methodology): “2013 Baldassarre et al.(44) 2012 Evgeniou and Pontil(45) 2004 Kernel methods Evgeniou et al.”
Machine learning approaches for improving condition-based maintenance of naval propulsion plants (2016, methodology): “Although several approaches, such as the ones based on multi-task learning(44) or transfer learning,(45) can be applied to training models in the MO framework, the most effective solution often consists in decomposing the MO dataset into m SO problems.(46,47) In addition to allow simplifying the pre”