Making Prediction Intervals Using
Neural Networks
ECE539 fall 2005
Claus Benjaminsen
Neural Networks are very popular as a tool for solving regression problems.
Training
a neural network creates a model for making point estimates of yet unseen outputs, b
ut the quality
of the prediction of the output
is
normally
not given
,
and can
not
be evaluated
until the actual output
is available. In many real world applications it is very useful to know, how precise a predicted value
is, or how certain it is.
This can
be accomplished by prediction intervals,
which give a lot more
information about the predictio
n than just the point estimate
. In for instance predicting the price of a
specific stock, it might be much more useful to know with a 95 % certainty, that the pr
ice will be
lower tomorrow than it was today
, instead of an estimated value of the
exact
price of the stock
tomorrow.
In this project I will implement a neural network that can do prediction by intervals
instead of only point estimates.
The straight forwar
d way to do this is to train several independent
neural networks for the same task, and through the distribution of the outputs estimate prediction
intervals. This approach is rather simple, but results in
a fairly
big model as
many neural networks
might b
e
needed.
There are several
other
ways
to achieve prediction intervals
, and I will look at
different possibilities and discuss the advantages and potential disadvantages by the different
approaches.
To train the
neural
network I will use different environ
mental datasets, which comes
from the Predictive Uncertainty in Environmental
Modeling
Competition.
This competition focuses
on evolving the best neural network for doing i
nterval prediction, so the data
sets are well suited for
this project. Further enviro
nmental data is often contaminated by non

Gaussian noise, which is
interesting because it might make alternative methods to interval predictions more feasible than the
standard methods.
References:
Predictive Uncertainty in Environmental Modeling Competi
tion
http://theoval.cmp.uea.ac.uk/~gcc/competition/
Papadopoulos, G.; Edwards, P.J.; Murray, A.F.;
“
Confidence Estimation Methods for Neural Networks:
A Practical Comparison
”
IEEE Transaction
s on
Neural Networks, Volume 12,
Issue 6,
Nov. 2001 Page(s):1278

1287
Carney, J.G.; Cunningham, P.; Bhagwan, U.;
“
Confidence and prediction intervals for neural network ensembles
”
IJCNN '99. International Joint Conference on
Neural Networks, 1999.
V
olume 2,
10

16 July 1999 Page(s):1215

1218 vol.2
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