Spectral Algorithms for Supervised Learning

By L. Lo Gerfo, Lorenzo Rosasco, Francesca Odone, Ernesto De Vito, Alessandro Verri. 2008

172 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

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In Computational Mechanics

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Citations in the corpus

Vector Field Learning via Spectral Filtering (2010, methodology): “We present the class of regularized kernel methods under study, referring to [2,22] for the scalar case.”
Beyond Least-Squares: Fast Rates for Regularized Empirical Risk Minimization through Self-Concordance (2019, unknown): “…in order: (a) the obtained rate is the same as least-squares and minimax optimal [8, 35, 5], (b) the fact that regularized ERM is adaptive to the regularity of the function up to r = 1 / 2 is a byproduct of Tikhonov regularization as already shown for the least-squares case by Gerfo et al. [14].”
Less is More: Nyström Computational Regularization (2015, unknown): “Such an assumption is natural in view of using techniques such as (4), which can be seen as a form of spectral filtering, that estimate stable solutions by discarding the contribution of small eigenvalues [27].”
Generalization Properties of Learning with Random Features (2016, background): “This approach is classical in inverse problems [18] and has been proposed and analyzed in [25, 5] for machine learning.”
Kernel ridge vs. principal component regression: Minimax bounds and the qualification of regularization operators (2017, methodology): “This has been observed previously by other researchers; others have even noted that Tikhonov regularization (KRR) saturates, while spectral cut-off regularization (KPCR) does not (Mathé, 2005; Bauer et al., 2007; Lo Gerfo et al., 2008).”
Multi-output learning via spectral filtering (2012, methodology): “There are few algorithms for which the regularization path can be easily computed, among which SVM for classification (Hastie et al. 2004) and regression (Gunter and Zhu 2006; Wang et al. 2008) and regularization with the lasso penalty (Efron et al. 2004).”
Simple and Effective Regularization Methods for Training on Noisily Labeled Data with Generalization Guarantee (2019, background): “It was shown to perform comparably to early-stopped gradient descent (Bauer et al., 2007; Gerfo et al., 2008; Raskutti et al., 2014; Wei et al., 2017).”
Learning Sets with Separating Kernels (2012, methodology): “In the following sections, we will show that spectral regularization [3, 31, 43] can be used to learn the support efﬁciently from the data.”
Data-driven calibration of linear estimators with minimal penalties (2009, methodology): “ers [31, 16], that is, Aw,α = diag((1 −(kα/w))+ , k = 1...n) for some parameters w,α > 0. This example matches case (i) in Proposition 1. • Linear spectral methods for statistical inverse problems [10, 26], such as spectral cut-oﬀ (or principal components regression) and ℓ2-boosting. • Symmetrize”