Papers available on Missing and Noisy Data in Nonlinear Time-Series Prediction

[Volker Tresp]

The  file  tresp.miss_time.ps.Z  can now be copied from Neuroprose.

The paper is 11 pages long.
Hardcopies copies are not available.


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          Missing and Noisy Data in Nonlinear Time-Series Prediction

                   by Volker Tresp and Reimar Hofmann




We discuss the issue   of missing and noisy data in nonlinear
time-series prediction. We derive fundamental equations  both for
prediction and for training.  Our discussion  shows that if
measurements are noisy or missing,  treating the time series as a
static input/output mapping problem (the usual time-delay neural
network  approach) is suboptimal. We describe approximations of the
solutions which are based on stochastic simulations.
 A special case is $K$-step prediction in which a one-step predictor is
 iterated $K$ times.  Our solutions provide error bars for prediction
with missing or noisy data and for $K$-step prediction.  Using the
$K$-step iterated logistic map as an example, we show that the proposed
solutions are  a considerable  improvement over simple heuristic
solutions.  Using our  formalism we derive  algorithms for training
recurrent networks, for   control of stochastic systems and for
reinforcement learning problems.