Please note that eDoc will be permanently shut down in the first quarter of 2021!      Home News About Us Contact Contributors Disclaimer Privacy Policy Help FAQ

Home
Search
Quick Search
Advanced
Fulltext
Browse
Collections
Persons
My eDoc
Session History
Login
Name:
Password:
Documentation
Help
Support Wiki
Direct access to
document ID:


          Institute: MPI für biologische Kybernetik     Collection: Biologische Kybernetik     Display Documents



ID: 419964.0, MPI für biologische Kybernetik / Biologische Kybernetik
Kernels, Regularization and Differential Equations
Authors:Steinke, F.; Schölkopf, B.
Date of Publication (YYYY-MM-DD):2008-11
Title of Journal:Pattern Recognition
Volume:41
Issue / Number:11
Start Page:3271
End Page:3286
Audience:Not Specified
Intended Educational Use:No
Abstract / Description:Many common machine learning methods such as Support Vector Machines or Gaussian process
inference make use of positive definite kernels, reproducing kernel Hilbert spaces, Gaussian processes, and
regularization operators. In this work these objects are presented in a general, unifying framework, and
interrelations are highlighted.
With this in mind we then show how linear stochastic differential equation models can be incorporated
naturally into the kernel framework. And vice versa, many kernel machines can be interpreted in terms of
differential equations. We focus especially on ordinary differential equations, also known as dynamical
systems, and it is shown that standard kernel inference algorithms are equivalent to Kalman filter methods
based on such models.
In order not to cloud qualitative insights with heavy mathematical machinery, we restrict ourselves to finite
domains, implying that differential equations are treated via their corresponding finite difference equations.
External Publication Status:published
Document Type:Article
Communicated by:Holger Fischer
Affiliations:MPI f�r biologische Kybernetik/Empirical Inference (Dept. Sch�lkopf)
Identifiers:LOCALID:5251
URL:http://www.sciencedirect.com/science?_ob=MImg&_ima...
The scope and number of records on eDoc is subject to the collection policies defined by each institute - see "info" button in the collection browse view.