Learning Output Kernels with Block Coordinate Descent

By Francesco Dinuzzo, Cheng Soon Ong, Peter Gehler, Gianluigi Pillonetto. 2011

98 citations recorded by the source corpus.

Subfields: Optimization & Training, Statistical Learning Theory

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Citations in the corpus

A Survey on Multi-Task Learning (2017, background): “Problem (21) can also been interpreted from the perspective of reproducing kernel Hilbert spaces for vector-valued functions [85], [86], [87], [88].”
Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Łojasiewicz Condition (2016, methodology): “Invexity was first introduced by Hanson [1981], and has been used in the context of learning output kernels [Dinuzzo et al., 2011]. Craven and Glover [1985] show that a smooth f is invex if and only if every stationary point of f is a global minimum. Since the PL inequality implies that all stationa”
Forward and Reverse Gradient-Based Hyperparameter Optimization (2017, background): “In Table 4, we report comparative results obtained with two state-of-the-art multitask learning methods (Dinuzzo et al. (2011) and Jawanpuria et al. (2015)) on the CIFAR-10 dataset.”
Multiple Operator-valued Kernel Learning (2012, background): “It should be pointed out that in a recent work [10], the problem of learning the output kernel was formulated as an optimization problem over the cone of positive semidefinite matrices, and a block-coordinate descent method was proposed to solve it.”
Operator-valued Kernels for Learning from Functional Response Data (2015, background): “output structure. In this context, learning the operatorvalued kernel would be interesting to nd the right model of dependencies between outputs. Recent works in this direction includes the papers of Dinuzzo et al. (2011), Kadri et al. (2012), Sindhwani et al. (2013) and Lim et al. (2015), but furth”
Learning Triggering Kernels for Multi-dimensional Hawkes Processes (2013, background): “Its learning has been addressed extensively in recent literature where one tries to learn a better positive definite kernel by combining several positive definite kernels (Cortes et al., 2012; Argyriou et al., 2006; Bach, 2008; Dinuzzo et al., 2011; Sonnenburg et al., 2006).”
Multilabel relationship learning (2013, methodology): “A recent study on learning an output kernel in [Dinuzzo et al. 2011; Dinuzzo and Fukumizu 2011] has the same objective as our method.”
Efficient Output Kernel Learning for Multiple Tasks (2015, methodology): “The formulation in (6) is similar to [9, 17, 18].”
Convex Deep Learning via Normalized Kernels (2014, background): “A key idea is to show that this totally corrective update can be accomplished with considerably improved efficiency through the use of block coordinate descent [35].”
Learning multiple visual tasks while discovering their structure (2015, methodology): “Then, the sequence itself is convergent and is minimizing by continuity.”
Convex Learning of Multiple Tasks and their Structure (2015, methodology): “Exploiting the theory of reproducing kernel Hilbert spaces for vector-valued functions (RKHSvv) [25], we consider and analyze a ﬂexible regularization framework, within which a variety of previously proposed approaches can be recovered as special cases, see e.g. [19, 24, 26, 37, 14, 31].”
Cross-Domain Object Recognition Via Input-Output Kernel Analysis (2013, methodology): “More details on RKHSs of vector-valued functions could be found in [16], [17], [30].”
Input Output Kernel Regression (2016, background): “…angle of their universality (Caponnetto et al. (2008); Carmeli et al. (2010)) and developed in di ↵ erent contexts such as structured classiﬁcation (Dinuzzo et al., 2011), functional regression (Kadri et al., 2010), link prediction (Brouard et al., 2011) or semi-supervised learning (Minh and…”