Universal Multi-Task Kernels

By Andrea Caponnetto, Charles A. Micchelli, Massimiliano Pontil, Yiming Ying. 2008

167 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Control and Systems Engineering, Statistical Learning Theory

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “Second, it improves the performance analysis of conditional mean embedding as one has access to a rich theory of vector-valued regression (Micchelli and Pontil 2005, Carmeli et al. 2006, Caponnetto and De Vito 2007, Caponnetto et al. 2008).”
Conditional mean embeddings as regressors (2012, background): “thearXiv:1205.4656v2 [cs.LG] 24 Jul 2012 Conditional mean embeddings as regressors ory of vector-valued regression (Micchelli & Pontil, 2005; Carmeli et al., 2006; Caponnetto & De Vito, 2007; Caponnetto et al., 2008). We demonstrate the utility of this connection by providing novel character”
Universality, Characteristic Kernels and RKHS Embedding of Measures (2010, background): “In addition, Carmeli et al. (2010, Remark 4.1) showed that k being cc-universal is equivalent to it being universal in the sense of Micchelli et al. (2006) and Caponnetto et al.”
Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributions (2016, background): “…learning community gradually introduced more and more variants of universal kernels (Steinwart, 2001; Micchelli et al., 2006; Carmeli et al., 2006; Caponnetto et al., 2008), but instead of also introducing variants of characteristic kernels, it stuck to the original deﬁnition given by Fukumizu et…”
Vector Field Learning via Spectral Filtering (2010, background): “In this section, we briefly review some matrix valued kernels for vector fields learning - see [25,26,27].”
Semi-supervised Penalized Output Kernel Regression for Link Prediction (2011, unknown): “Deﬁnition 1 (Operator-valued kernel (Senkene & Tempel’man, 1973; Caponnetto et al., 2008)) .”
Learning Output Kernels with Block Coordinate Descent (2011, background): “…kernel can be decomposed as the product of a scalar kernel and a positive semidefinite kernel matrix that represents the similarity between the output components, a structure that has been considered in a variety of works, (Evgeniou et al., 2005; Caponnetto et al., 2008; Baldassarre et al., 2010).”
Learning the coordinate gradients (2011, background): “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].”
Multi-output learning via spectral filtering (2012, methodology): “In fact, if the kernel is universal (Caponnetto et al. 2008) such an assumption can be dropped and (universal) Bayes consistency can be proven with similar techniques (Caponnetto 2006).”
Robust generalised Bayesian inference for intractable likelihoods (2021, unknown): “(2006); Caponnetto et al. (2008); Carmeli et al. (2010). For simplicity we start with the scalar-valued case and define a scalar-valued kernel: Definition 2 (Scalar-valued kernel).”
Efficient Output Kernel Learning for Multiple Tasks (2015, background): “The multi-task kernel on input and output is assumed to be decoupled as the product of a scalar kernel and the output kernel, which is a positive semidefinite matrix [1, 13, 14, 15].”
Elastic-net regularization in learning theory (2008, background): “Other examples of applications in an infinite-dimensional setting are given in [31].”
Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality (2012, background): “◦ We specialize our framework to the class of separable kernels [1] which are of interest due to their universality [9], conceptual simplicity and potential for scalability.”
A Generalized Kernel Approach to Structured Output Learning (2012, methodology): “We now provide a few definitions related to operatorvalued kernels and their associated RKHSs that are used in the paper (see (Micchelli & Pontil, 2005; Caponnetto et al., 2008; Álvarez et al., 2012) for more details).”
Universality , Characteristic Kernels and RKHS Embedding of Measures (2011, background): “…space and the type of approximation, various notions of universality— c-universality (Steinwart, 2001), cc-universality (Micchelli et al., 2006; Caponnetto et al., 2008), c 0 -universality (Carmeli et al., 2010; Sriperumbudur et al., 2010a) and L p -universality (Steinwart and Christmann,…”
Operator-valued Kernels for Learning from Functional Response Data (2015, methodology): “However, it is also interesting to explore these kernels from a feature space point of view (Schölkopf et al., 1999; Caponnetto et al., 2008).”