Value Regularization and Fenchel Duality

By Ryan M. Rifkin, Ross A. Lippert. 2007

90 citations recorded by the source corpus.

How researchers see this paper

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

Citations in the corpus

Convex Functions: Constructions, Characterizations and Counterexamples (2010, unknown): “It would be hard to exaggerate the ubiquity of Fenchel duality as a tool in diverse fields [299] such as mechanics [195], machine learning [365], mathematical economics [300], statistical fitting algorithms [56], in addition to many others discussed in the text.”
On the Dual Formulation of Boosting Algorithms (2009, methodology): “In [23], a similar idea has been used to derive different duals of kernel methods, which leads to the so-called value regularization.”
Learning from Conditional Distributions via Dual Kernel Embeddings (2016, background): “e function is also proper, convex and lower semicontinuous. More improtantly, the (‘;‘) are dual to each other, i.e., (‘) = ‘, which is known as Fenchel duality (Hiriart-Urruty and Lemarechal, 2012; Rifkin and Lippert, 2007). Therefore, we can represent the ‘by its convex conjugate as , ‘(v) = sup u”
Convex Deep Learning via Normalized Kernels (2014, background): “This is essentially the value regularization framework [28].”
Differentiable Sparse Coding (2008, background): “L1 regularization provides sparse solutions because its Fenchel dual [13] is the max function, meaning only the most useful basis vectors participate in the reconstruction.”
Toward Supervised Anomaly Detection (2014, background): “Fenchel duality for machine learning has been pioneered by Rifkin and Lippert (2007) under the assumption of full-rank kernels.”
Differential Sparse Coding (2008, background): “L 1 regularization provides sparse solutions because its Fenchel dual [13] is the max function, meaning only the most useful basis vectors participate in the reconstruction.”