An e–E-insensitive support vector regression machine

According to the Statistical Learning Theory, the support vectors represent the most informative data points and compress the information contained in training set. However, a basic problem in the standard support vector machine is that when the data is noisy, there exists no guaranteed scheme in support vector machines’ formulation to dissuade the machine from learning noise. Therefore, the noise which is typically presents in financial time series data may be taken into account as support vectors. In turn, noisy support vectors are modeled into the estimated function. As such, the inclusion of noise in support vectors may lead to an over-fitting and in turn to a poor generalization. The standard support vector regression (SVR) is reformulated in this article in such a way that the large errors which correspond to noise are restricted by a new parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$E$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>E</mi> </math> </EquationSource> </InlineEquation>. The simulation and real world experiments indicate that the novel SVR machine meaningfully performs better than the standard SVR in terms of accuracy and precision especially where the data is noisy, but in expense of a longer computation time. Copyright Springer-Verlag Berlin Heidelberg 2014