Bayesian Non-linear Modeling for the Energy Prediction Competition

David J C MacKay

Bayesian probability theory provides a unifying framework for data modeling. A model space may include numerous control parameters which influence the complexity of the model (for example regularisation constants). Bayesian methods can automatically set such parameters so that the model becomes probabilistically well-matched to the data. The 1993 energy prediction competition involved the prediction of a series of building energy loads from a series of environmental input variables. Non-linear regression using `neural networks' is a popular technique for such modeling tasks. Since it is not obvious how large a time-window of inputs is appropriate, or what preprocessing of inputs is best, this can be viewed as a regression problem in which there are many possible input variables, some of which may actually be irrelevant to the prediction of the output variable. Because a finite data set will show random correlations between the irrelevant inputs and the output, any conventional neural network (even with `weight decay') will not set the coefficients for these junk inputs to zero. Thus the irrelevant variables will hurt the model's performance. The Automatic Relevance Determination (ARD) model puts a prior over the regression parameters which embodies the concept of relevance. This is done in a simple and `soft' way by introducing multiple `weight decay' constants, one `alpha' associated with each input. Using Bayesian methods, the decay rates for junk inputs are automatically inferred to be large, preventing those inputs from causing significant overfitting. An entry using the ARD model won the prediction competition by a significant margin.



 KEY            ="MacKay",
 AUTHOR         ="D. J. C.  MacKay",
 TITLE          ="Bayesian non-linear modelling for the  prediction 
 BOOKTITLE      ="ASHRAE Transactions, V.100, Pt.2",
 EDITOR 	="",
 ADDRESS	="Atlanta Georgia",
 YEAR           ="1994",
 PAGES ="1053-1062",
 ANNOTE ="Date submitted: ; Date accepted: ; Collaborating institutes: none"}

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