# LEARNING WITH INFINITELY MANY KERNELS VIA SEMI-INFINITE PROGRAMMING

@inproceedings{Weber2008LEARNINGWI, title={LEARNING WITH INFINITELY MANY KERNELS VIA SEMI-INFINITE PROGRAMMING}, author={G Weber}, year={2008} }

Abstract: In recent years, learning methods are desirable because of their reliability and efficiency in real-world problems. We propose a novel method to find infinitely many kernel combinations for learning problems with the help of infinite and semi-infinite optimization regarding all elements in kernel space. This will provide to study variations of combinations of kernels when considering heterogeneous data in real-world applications. Looking at all infinitesimally fine convex combinations…

## 15 Citations

### MODELLING OF KERNEL MACHINES BY INFINITE AND SEMI‐INFINITE PROGRAMMING

- Computer Science, Mathematics
- 2009

This work proposes a novel method of “infinite” kernel combinations for learning problems with the help of infinite and semi‐infinite programming regarding all elements in kernel space.

### On numerical optimization theory of infinite kernel learning

- Computer ScienceJ. Glob. Optim.
- 2010

The results show that the new algorithm called “infinite” kernel learning (IKL) on heterogenous data sets improves the classifaction accuracy efficiently on heterogeneous data compared to classical one-kernel approaches.

### Non-Sparse Regularization and Efficient Training with Multiple Kernels

- Computer ScienceArXiv
- 2010

Improvements in MKL have finally made MKL fit for deployment to practical applications: MKL now has a good chance of improving the accuracy (over a plain sum kernel) at an affordable computational cost.

### Non-Sparse Regularization for Multiple Kernel Learning

- Computer Science
- 2010

Empirical applications of p-norm MKL to three real-world problems from computational biology show that non-sparse MKL achieves accuracies that go beyond the state-of-the-art.

### Norm Multiple Kernel Learning

- Computer Science
- 2011

Empirical applications of lp-norm MKL to three real-world problems from computational biology show that non-sparse MKL achieves accuracies that surpass the state-of-the-art, and two efficient interleaved optimization strategies for arbitrary norms are developed.

### ` p-Norm Multiple Kernel Learning

- Computer Science
- 2008

P-norm MKL to three real-world problems from computational biology show that non-sparse MKL achieves accuracies that surpass the state-of-the-art, and two efficient interleaved optimization strategies for arbitrary norms are developed.

### Learning with infinitely many features

- Computer ScienceMachine Learning
- 2012

A principled framework for learning with infinitely many features, situations that are usually induced by continuously parametrized feature extraction methods, and it is shown that using Fourier-based features, it is possible to perform approximate infinite kernel learning.

### Optimality Conditions for Convex Semi-infinite Programming Problems with Finitely Representable Compact Index Sets

- MathematicsJournal of Optimization Theory and Applications
- 2017

In the present paper, we analyze a class of convex semi-infinite programming problems with arbitrary index sets defined by a finite number of nonlinear inequalities. The analysis is carried out by…

### Optimality Conditions for Convex Semi-infinite Programming Problems with Finitely Representable Compact Index Sets

- MathematicsJ. Optim. Theory Appl.
- 2017

This paper analyzes a class of convex semi-infinite programming problems with arbitrary index sets defined by a finite number of nonlinear inequalities by employing the constructive approach, which relies on the notions of immobile indices and their immobility orders.

### Multiple Kernel Learning Algorithms

- Computer ScienceJ. Mach. Learn. Res.
- 2011

Overall, using multiple kernels instead of a single one is useful and it is believed that combining kernels in a nonlinear or data-dependent way seems more promising than linear combination in fusing information provided by simple linear kernels, whereas linear methods are more reasonable when combining complex Gaussian kernels.

## References

SHOWING 1-10 OF 26 REFERENCES

### Multiple kernel learning, conic duality, and the SMO algorithm

- Computer ScienceICML
- 2004

Experimental results are presented that show that the proposed novel dual formulation of the QCQP as a second-order cone programming problem is significantly more efficient than the general-purpose interior point methods available in current optimization toolboxes.

### Large Scale Multiple Kernel Learning

- Computer ScienceJ. Mach. Learn. Res.
- 2006

It is shown that the proposed multiple kernel learning algorithm can be rewritten as a semi-infinite linear program that can be efficiently solved by recycling the standard SVM implementations, and generalize the formulation and the method to a larger class of problems, including regression and one-class classification.

### Linear Semi-Infinite Optimization

- Mathematics
- 1998

MODELLING. Modelling with the Primal Problem. Modelling with the Dual Problem. LINEAR SEMI-INFINITE SYSTEMS. Alternative Theorems. Consistency. Geometry. Stability. THEORY OF LINEAR SEMI-INFINITE…

### An Introduction to Support Vector Machines and Other Kernel-based Learning Methods

- Computer Science
- 2000

This is the first comprehensive introduction to Support Vector Machines (SVMs), a new generation learning system based on recent advances in statistical learning theory, and will guide practitioners to updated literature, new applications, and on-line software.

### Pattern Analysis for the Prediction of Eukoryatic Pro-peptide Cleavage Sites ?

- Computer Science
- 2007

An application that will allow the prediction of the pro-peptide cleavage site of fungal extracellular proteins which display mostly a monobasic or dibasic processing site is developed and a novel approach that simultaneously performs model selection together with the test of accuracy and testing confidence levels is introduced.

### Charakterisierung struktureller stabilit at in der nichtlinearen optimierung

- Augustinus publishing house (now: Mainz publishing house)
- 1992