## The Use of Collective Method for Improvement of Regression Modeling Stability

### by Oleg V. Senko.

**Abstract:**
The collective methods of regression analysis are discussed
in the paper as the tools to improve the mean discrepancy of regression
modeling. The mean discrepancy in the paper is calculated not only by
the space of multidimensional observations but also by the space of training
sets of fixed size. It was shown that mean discrepancy may be represented as
the sum of three component. The first one is irremovable "noise", the second
component is the mean squared deviation of mean regression function from
conditional means of dependent variable in points of independent variables
space, the third component is instability term that is the variance of
regression functions on the space of training sets. It was shown that the
using of simplest voting procedure by the initial set of regression methods
allows to receive new regression model with instability component less than
average instability component of the initial set .The large scale experiments
with Monte-Carlo simulated data demonstrated that voting procedures really
allow to improve regression performance and that the cause of such improvement
is the decrease of instability of training.
**Author:**

Oleg V. Senko, senkoov@mail.ru

**Editor:**
Chaganty, N. Rao,rchagant@odu.edu

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