Timezone: »

 
Poster
Duality in RKHSs with Infinite Dimensional Outputs: Application to Robust Losses
Pierre Laforgue · Alex Lambert · Luc Brogat-Motte · Florence d'Alche-Buc

Tue Jul 14 01:00 PM -- 01:45 PM & Wed Jul 15 01:00 AM -- 01:45 AM (PDT) @ Virtual
in Poster Session 7 »

Operator-Valued Kernels (OVKs) and associated vector-valued Reproducing Kernel Hilbert Spaces provide an elegant way to extend scalar kernel methods when the output space is a Hilbert space. Although primarily used in finite dimension for problems like multi-task regression, the ability of this framework to deal with infinite dimensional output spaces unlocks many more applications, such as functional regression, structured output prediction, and structured data representation. However, these sophisticated schemes crucially rely on the kernel trick in the output space, so that most of previous works have focused on the square norm loss function, completely neglecting robustness issues that may arise in such surrogate problems. To overcome this limitation, this paper develops a duality approach that allows to solve OVK machines for a wide range of loss functions. The infinite dimensional Lagrange multipliers are handled through a Double Representer Theorem, and algorithms for \epsilon-insensitive losses and the Huber loss are thoroughly detailed. Robustness benefits are emphasized by a theoretical stability analysis, as well as empirical improvements on structured data applications.

Keywords: Convex Optimization · Kernel Methods · Structured Prediction · General Machine Learning Techniques
[ Slides] 

Author Information

Pierre Laforgue (Télécom Paris)
Alex Lambert (Télécom ParisTech)
Luc Brogat-Motte (Télécom Paris)
Florence d'Alche-Buc (Télécom ParisTech, Université Paris-Saclay,Paris, France)

More from the Same Authors