# Support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise

@inproceedings{Steinwart2007SupportVM, title={Support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise}, author={Ingo Steinwart and Marian Anghel}, year={2007} }

We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamical system from a noisy observation of the present state. Our main result shows, for example, that support vector machines (SVMs) using Gaussian RBF kernels can learn the best forecaster from a sequence of noisy observations if (a) the unknown observational noise process is bounded and has a summable α-mixing rate and (b) the unknown ergodic dynamical system is defined by a Lipschitz continuous… CONTINUE READING

Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

#### Topics from this paper.

#### Citations

##### Publications citing this paper.

SHOWING 1-10 OF 14 CITATIONS

## On the need for structure modelling in sequence prediction

VIEW 7 EXCERPTS

CITES METHODS & BACKGROUND

HIGHLY INFLUENCED

## Embeddings and Prediction of Dynamical Time Series

VIEW 4 EXCERPTS

CITES BACKGROUND & METHODS

HIGHLY INFLUENCED

## A Bernstein-type Inequality for Some Mixing Processes and Dynamical Systems with an Application to Learning

VIEW 3 EXCERPTS

CITES METHODS & BACKGROUND

## Statistical learning of kernel-based methods for non-i.i.d. observations

VIEW 3 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## Gibbs posterior convergence and the thermodynamic formalism.

VIEW 1 EXCERPT

CITES BACKGROUND

## MACRO: A Meta-Algorithm for Conditional Risk Minimization

VIEW 1 EXCERPT

CITES BACKGROUND

## Learning Theory for Conditional Risk Minimization

VIEW 1 EXCERPT

## Empirical risk minimization and complexity of dynamical models

VIEW 1 EXCERPT

CITES BACKGROUND

## Kernel Density Estimation for Dynamical Systems

VIEW 1 EXCERPT

CITES BACKGROUND

## Variational analysis of inference from dynamical systems

VIEW 2 EXCERPTS

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 44 REFERENCES

## Learning from dependent observations

VIEW 5 EXCERPTS

## Decay of correlations for non H

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Introduction to strong mixing conditions

VIEW 2 EXCERPTS

## Denoising Deterministic Time Series

VIEW 3 EXCERPTS

## Function Classes That Approximate the Bayes Risk

VIEW 2 EXCERPTS