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

Michael E. Tipping, University of Bath
Neil D. Lawrence, University of Sheffield

Neurocomputing 69, pp 123-141

#### 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.

  @Article{tipping-variational05, title = {Variational inference for Student-$t$ models: Robust Bayesian interpolation and generalised component analysis}, journal = {Neurocomputing}, author = {Michael E. Tipping and Neil D. Lawrence}, pages = {123}, year = {2005}, volume = {69}, month = {00}, edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2005-01-01-tipping-variational05.md}, 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.}, key = {Tipping-variational05}, OPTgroup = {} }
 %T Variational inference for Student-$t$ models: Robust Bayesian interpolation and generalised component analysis %A Michael E. Tipping and Neil D. Lawrence %B %C Neurocomputing %D %F tipping-variational05 %J Neurocomputing %P 123--141 %R %U http://inverseprobability.com/publications/tipping-variational05.html %V 69 %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. 
 TY - CPAPER TI - Variational inference for Student-$t$ models: Robust Bayesian interpolation and generalised component analysis AU - Michael E. Tipping AU - Neil D. Lawrence PY - 2005/01/01 DA - 2005/01/01 ID - tipping-variational05 SP - 123 EP - 141 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 - 
 Tipping, M.E. & Lawrence, N.D.. (2005). Variational inference for Student-$t$ models: Robust Bayesian interpolation and generalised component analysis. Neurocomputing 69:123-141