Kernels for Multi--task Learning

By Charles A. Micchelli, Massimiliano Pontil. 2004

171 citations recorded by the source corpus.

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Citations in the corpus

Kernels for Vector-Valued Functions: a Review (2011, methodology): “Following [64, 91], we can define a regularizer that, in addition to a standard regularization on the single components, forces stronger or weaker similarity between them through a givenD×D positive weight matrix M,”
Monitoring Land-Cover Changes: A Machine-Learning Perspective (2016, background): “For example, in scenarios where graph-based representations are used to show the relationships among tasks, where the vertices of the graph are the tasks and the edges between the vertices denote relationships among the tasks, graph-based regularization techniques have been explored for multitask le”
Smart Multitask Bregman Clustering and Multitask Kernel Clustering (2015, methodology): “…prior distribution in hierarchical Bayesian models [Bakker and Heskes 2003], exploiting kernel-based methods with regularization [Evgeniou and Pontil 2004; Evgeniou et al. 2005; Micchelli and Pontil 2004], sharing the parameters of Gaussian process [Bonilla et al. 2007; Lawrence and Platt 2004].”
Learning the Shared Subspace for Multi-task Clustering and Transductive Transfer Classification (2009, background): “This motivates multi-task learning [10] [11] [12] [13] [14] [15].”
Revisiting Stein's paradox: multi-task averaging (2014, background): “In this paper we do just that: apply this regularizer to mean estimation, show that this special case enables new and useful analytic results, and demonstrate its performance with simulated and real data.”
Multi-Task Learning via Conic Programming (2007, methodology): “Our experiments demonstrate that the proposed method is also useful in the ordinal regression scenarios and tends to outperform existing approaches [9, 8]”
Accurate interatomic force fields via machine learning with covariant kernels (2016, background): “Here, we show how Vectorial Gaussian Process (VGP) [29, 30] regression provides a more natural framework for force learning, where the correct vector behaviour of forces under symmetry transformations can be obtained by using a new family of vector kernels of co-variant nature.”
Vector Field Learning via Spectral Filtering (2010, background): “A regularizer that forces stronger or weaker similarity between the components [29] is defined as”
Convex Learning of Multiple Tasks and their Structure (2015, methodology): “Finally, the second term in ( P ) follows by observing that, for all f ∈ H of the form f ( ) = =1 k ( x i , · ) Ac i , the squared norm can be written as f 2 H = ni,j k ( x i , x j ) c ⊤ i Ac j = tr ( AC ⊤ KC ) where C ∈ R n × T is the matrix with i -th row corresponding to the co-efﬁcient vector c…”
Multi-Task Averaging (2011, background): “However, a stronger statement can be made: Theorem: If γ ≥ 0, 0 ≤ Ars ∞ for all r, s and 0 σ 2 t Nt ∞ for all t, then the MTA estimates {Y ∗t } given in (3) are a convex combination of the task sample averages {Ȳt}.”
Multi-Task Multi-View Clustering (2016, background): “For example, the tasks for clustering the web pages from four universities are four related tasks.”
Block Variable Selection in Multivariate Regression and High-dimensional Causal Inference (2010, methodology): “Multivariate Regression may be viewed as th e classical precursor to many modern techniques in machine learning such as multi-task learning [15, 16, 1] and structured output prediction [18, 10, 22].”
Learning the coordinate gradients (2011, methodology): “The above contributions rely on very recent developments from machine learning: multi-task learning [5, 20, 21] and multiple kernel learning with sparse regularization (aka nonparametric group lasso) [3, 16, 30].”
A Gang of Bandits (2013, methodology): “, [8, 17, 12] and a version of the linear bandit algorithm described and analyzed in [1].”
A Literature Survey on Domain Adaptation of Statistical Classifiers (2007, methodology): “There have been many studies on multi-task learning [Caruana, 1997, Ben-David and Schuller, 2003, Micchelli and Pontil, 2005, Xue et al., 2007].”
Operator-valued Kernels for Learning from Functional Response Data (2015, background): “Moreover, their extension to matrixvalued kernels has helped to bring additional improvements in learning vector-valued functions (Micchelli and Pontil, 2005a; Reisert and Burkhardt, 2007; Caponnetto and De Vito, 2006).”
Multi-output learning via spectral filtering (2012, methodology): “Remark 1 In multi-task learning (Evgeniou et al. 2005; Caponnetto et al. 2008; Micchelli and Pontil 2004) the goal is to learn several correlated scalar problems simultaneously.”