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# Linear Latent Force Models Using Gaussian Processes

Mauricio A. Álvarez, David Luengo, Neil D. Lawrence, 35(11):2693-2705, 2013.

#### Abstract

Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data driven modelling with a physical model of the system. We show how different, physically-inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology and geostatistics.

#### Cite this Paper

BibTeX

```
@InProceedings{pmlr-v-alvarez-llfm13,
title = {Linear Latent Force Models Using Gaussian Processes},
author = {Mauricio A. Álvarez and David Luengo and Neil D. Lawrence},
pages = {2693--2705},
year = {},
editor = {},
volume = {35},
number = {11},
url = {http://inverseprobability.com/publications/alvarez-llfm13.html},
abstract = {Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data driven modelling with a physical model of the system. We show how different, physically-inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology and geostatistics.}
}
```

Endnote

```
%0 Conference Paper
%T Linear Latent Force Models Using Gaussian Processes
%A Mauricio A. Álvarez
%A David Luengo
%A Neil D. Lawrence
%B
%C Proceedings of Machine Learning Research
%D
%E
%F pmlr-v-alvarez-llfm13
%I PMLR
%J Proceedings of Machine Learning Research
%P 2693--2705
%R 10.1109/TPAMI.2013.86
%U http://inverseprobability.com
%V
%N 11
%W PMLR
%X Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data driven modelling with a physical model of the system. We show how different, physically-inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology and geostatistics.
```

RIS

```
TY - CPAPER
TI - Linear Latent Force Models Using Gaussian Processes
AU - Mauricio A. Álvarez
AU - David Luengo
AU - Neil D. Lawrence
BT -
PY -
DA -
ED -
ID - pmlr-v-alvarez-llfm13
PB - PMLR
SP - 2693
DP - PMLR
EP - 2705
DO - 10.1109/TPAMI.2013.86
L1 -
UR - http://inverseprobability.com/publications/alvarez-llfm13.html
AB - Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data driven modelling with a physical model of the system. We show how different, physically-inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology and geostatistics.
ER -
```

APA

`Álvarez, M.A., Luengo, D. & Lawrence, N.D.. (). Linear Latent Force Models Using Gaussian Processes. `*, in PMLR* (11):2693-2705

#### Related Material

BibTeX

```
@InProceedings{/alvarez-llfm13,
title = {Linear Latent Force Models Using Gaussian Processes},
author = {Mauricio A. Álvarez and David Luengo and Neil D. Lawrence},
pages = {2693--2705},
year = {},
editor = {},
volume = {35},
number = {11},
url = {http://inverseprobability.com/publications/alvarez-llfm13.html},
abstract = {Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data driven modelling with a physical model of the system. We show how different, physically-inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology and geostatistics.}
}
```

Endnote

```
%0 Conference Paper
%T Linear Latent Force Models Using Gaussian Processes
%A Mauricio A. Álvarez
%A David Luengo
%A Neil D. Lawrence
%B
%C Proceedings of Machine Learning Research
%D
%E
%F /alvarez-llfm13
%I PMLR
%J Proceedings of Machine Learning Research
%P 2693--2705
%R 10.1109/TPAMI.2013.86
%U http://inverseprobability.com
%V
%N 11
%W PMLR
%X Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data driven modelling with a physical model of the system. We show how different, physically-inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology and geostatistics.
```

RIS

```
TY - CPAPER
TI - Linear Latent Force Models Using Gaussian Processes
AU - Mauricio A. Álvarez
AU - David Luengo
AU - Neil D. Lawrence
BT -
PY -
DA -
ED -
ID - /alvarez-llfm13
PB - PMLR
SP - 2693
DP - PMLR
EP - 2705
DO - 10.1109/TPAMI.2013.86
L1 -
UR - http://inverseprobability.com/publications/alvarez-llfm13.html
AB - Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data driven modelling with a physical model of the system. We show how different, physically-inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology and geostatistics.
ER -
```

APA

`Álvarez, M.A., Luengo, D. & Lawrence, N.D.. (). Linear Latent Force Models Using Gaussian Processes. `*, in PMLR* (11):2693-2705