Mapping functional equations to the topology of Networks yields a natural interpolation method for time series data


Contact
Lars.Kindermann [ at ] awi.de

Abstract

Typically machine learning methods attempt to construct from some limited amount of data a more general model which extends the range of application beyond the available examples. Many methods specifically attempt to be purely data driven, assuming, that everything is contained in the data. On the other hand, there often exists additional abstract knowledge about the system to be modeled, but there is no obvious method how to combine these two domains. We propose the calculus of functional equations as an appropriate language to describe many relations in a way that is more general than a typical parameterized model, but allows to be more specific about the setting than using an universal approximation scheme like neural networks. Symmetries, conservation laws, and concepts like determinism can be expressed this way. Many of these functional equations can be translated into specific network structures and topologies, which will constrain the possible input-output relations of the network to the solution space of the equations. This results in less data that is necessary for training and may lead to more general results, too, that can be derived from the model. As an example, a natural method for inter- or extrapolation of time series is derived, which does not use any fixed interpolation scheme but is automatically constructed from the knowledge/assumption that the data series is generated by an underlying deterministic dynamical system.



Item Type
Inbook
Authors
Divisions
Primary Division
Programs
Primary Topic
Peer revision
Peer-reviewed
Publication Status
Published
Eprint ID
34684
Cite as
Kindermann, L. and Lewandowski, A. (2013): Mapping functional equations to the topology of Networks yields a natural interpolation method for time series data / H. Glotin and Y. LeCun (editors) , In: Neural information processing scaled for bioacoustics - from neurons to big data, Proceedings of Neural Information Processing Scaled for Bioacoustics: from neurons to Big Data, Tahoe Lake, Nevada, USA, NIPS Int. Conf., ISBN: 979-10-90821-04-0 .


Download
[img]
Preview
PDF
NIPS2013-Kindermann-Paper.pdf

Download (178kB) | Preview
Cite this document as:
[img]
Preview
PDF
NIPS2013-Kindermann-Slides.pdf

Download (1MB) | Preview
Cite this document as:

Share

Research Platforms
N/A

Campaigns


Actions
Edit Item Edit Item