System identification: theory for the user
System identification: theory for the user
Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
Regularization theory and neural networks architectures
Neural Computation
An introduction to infinite-dimensional linear systems theory
An introduction to infinite-dimensional linear systems theory
The nature of statistical learning theory
The nature of statistical learning theory
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Bayesian Classification With Gaussian Processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Introduction to Variational Methods for Graphical Models
Machine Learning
A Tutorial on Support Vector Machines for Pattern Recognition
Data Mining and Knowledge Discovery
A tutorial on support vector regression
Statistics and Computing
On Learning Vector-Valued Functions
Neural Computation
Estimating the Support of a High-Dimensional Distribution
Neural Computation
Gaussian Processes for Classification: Mean-Field Algorithms
Neural Computation
Local distance preservation in the GP-LVM through back constraints
ICML '06 Proceedings of the 23rd international conference on Machine learning
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
A tutorial on spectral clustering
Statistics and Computing
Graph Laplacians and their Convergence on Random Neighborhood Graphs
The Journal of Machine Learning Research
Semi-Supervised Learning
Efficient approximate Regularized Least Squares by Toeplitz matrix
Pattern Recognition Letters
Two new graph kernels and applications to chemoinformatics
GbRPR'11 Proceedings of the 8th international conference on Graph-based representations in pattern recognition
People re-identification by graph kernels methods
GbRPR'11 Proceedings of the 8th international conference on Graph-based representations in pattern recognition
A graph-kernel method for re-identification
ICIAR'11 Proceedings of the 8th international conference on Image analysis and recognition - Volume Part I
Two new graphs kernels in chemoinformatics
Pattern Recognition Letters
Multi-resolutive sparse approximations of d-dimensional data
Computer Vision and Image Understanding
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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.