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# Variational inference for Student-$t$ models: Robust Bayesian interpolation and generalised component analysis

Michael E. Tipping, Neil D. Lawrence, 69:123-141, 2005.

#### Abstract

We demonstrate how a variational approximation scheme enables effective inference of key parameters in probabilisitic signal models which employ the Student-t distribution. Using the two scenarios of previous termrobustnext term interpolation and independent component analysis (ICA) as examples, we illustrate the key feature of the approach: that the form of the noise distribution in the interpolation case, and the source distributions in the ICA case, can be inferred from the data concurrent with all other model parameters.

#### Cite this Paper

BibTeX

```
@InProceedings{pmlr-v-tipping-variational05,
title = {Variational inference for Student-$t$ models: Robust Bayesian interpolation and generalised component analysis},
author = {Michael E. Tipping and Neil D. Lawrence},
pages = {123--141},
year = {},
editor = {},
volume = {69},
url = {http://inverseprobability.com/publications/tipping-variational05.html},
abstract = {We demonstrate how a variational approximation scheme enables effective inference of key parameters in probabilisitic signal models which employ the Student-t distribution. Using the two scenarios of previous termrobustnext term interpolation and independent component analysis (ICA) as examples, we illustrate the key feature of the approach: that the form of the noise distribution in the interpolation case, and the source distributions in the ICA case, can be inferred from the data concurrent with all other model parameters.}
}
```

Endnote

```
%0 Conference Paper
%T Variational inference for Student-$t$ models: Robust Bayesian interpolation and generalised component analysis
%A Michael E. Tipping
%A Neil D. Lawrence
%B
%C Proceedings of Machine Learning Research
%D
%E
%F pmlr-v-tipping-variational05
%I PMLR
%J Proceedings of Machine Learning Research
%P 123--141
%U http://inverseprobability.com
%V
%W PMLR
%X We demonstrate how a variational approximation scheme enables effective inference of key parameters in probabilisitic signal models which employ the Student-t distribution. Using the two scenarios of previous termrobustnext term interpolation and independent component analysis (ICA) as examples, we illustrate the key feature of the approach: that the form of the noise distribution in the interpolation case, and the source distributions in the ICA case, can be inferred from the data concurrent with all other model parameters.
```

RIS

```
TY - CPAPER
TI - Variational inference for Student-$t$ models: Robust Bayesian interpolation and generalised component analysis
AU - Michael E. Tipping
AU - Neil D. Lawrence
BT -
PY -
DA -
ED -
ID - pmlr-v-tipping-variational05
PB - PMLR
SP - 123
DP - PMLR
EP - 141
L1 -
UR - http://inverseprobability.com/publications/tipping-variational05.html
AB - We demonstrate how a variational approximation scheme enables effective inference of key parameters in probabilisitic signal models which employ the Student-t distribution. Using the two scenarios of previous termrobustnext term interpolation and independent component analysis (ICA) as examples, we illustrate the key feature of the approach: that the form of the noise distribution in the interpolation case, and the source distributions in the ICA case, can be inferred from the data concurrent with all other model parameters.
ER -
```

APA

`Tipping, M.E. & Lawrence, N.D.. (). Variational inference for Student-$t$ models: Robust Bayesian interpolation and generalised component analysis. `*, in PMLR* :123-141

#### Related Material

BibTeX

```
@InProceedings{/tipping-variational05,
title = {Variational inference for Student-$t$ models: Robust Bayesian interpolation and generalised component analysis},
author = {Michael E. Tipping and Neil D. Lawrence},
pages = {123--141},
year = {},
editor = {},
volume = {69},
url = {http://inverseprobability.com/publications/tipping-variational05.html},
abstract = {We demonstrate how a variational approximation scheme enables effective inference of key parameters in probabilisitic signal models which employ the Student-t distribution. Using the two scenarios of previous termrobustnext term interpolation and independent component analysis (ICA) as examples, we illustrate the key feature of the approach: that the form of the noise distribution in the interpolation case, and the source distributions in the ICA case, can be inferred from the data concurrent with all other model parameters.}
}
```

Endnote

```
%0 Conference Paper
%T Variational inference for Student-$t$ models: Robust Bayesian interpolation and generalised component analysis
%A Michael E. Tipping
%A Neil D. Lawrence
%B
%C Proceedings of Machine Learning Research
%D
%E
%F /tipping-variational05
%I PMLR
%J Proceedings of Machine Learning Research
%P 123--141
%U http://inverseprobability.com
%V
%W PMLR
%X We demonstrate how a variational approximation scheme enables effective inference of key parameters in probabilisitic signal models which employ the Student-t distribution. Using the two scenarios of previous termrobustnext term interpolation and independent component analysis (ICA) as examples, we illustrate the key feature of the approach: that the form of the noise distribution in the interpolation case, and the source distributions in the ICA case, can be inferred from the data concurrent with all other model parameters.
```

RIS

```
TY - CPAPER
TI - Variational inference for Student-$t$ models: Robust Bayesian interpolation and generalised component analysis
AU - Michael E. Tipping
AU - Neil D. Lawrence
BT -
PY -
DA -
ED -
ID - /tipping-variational05
PB - PMLR
SP - 123
DP - PMLR
EP - 141
L1 -
UR - http://inverseprobability.com/publications/tipping-variational05.html
AB - We demonstrate how a variational approximation scheme enables effective inference of key parameters in probabilisitic signal models which employ the Student-t distribution. Using the two scenarios of previous termrobustnext term interpolation and independent component analysis (ICA) as examples, we illustrate the key feature of the approach: that the form of the noise distribution in the interpolation case, and the source distributions in the ICA case, can be inferred from the data concurrent with all other model parameters.
ER -
```

APA

`Tipping, M.E. & Lawrence, N.D.. (). Variational inference for Student-$t$ models: Robust Bayesian interpolation and generalised component analysis. `*, in PMLR* :123-141