Non-convex cost functionals in boosting
Title: Non-convex cost functionals in boosting
Researchers: M. Visentin
Abstract: This research proposes a new improvement for boosting techniques used in modeling and forecasting additive time series. The idea is to introduce a correlation term to better deal with forecasting additive time series. The problem is discussed in a theoretical way to prove the existence of a minimizing sequence, and in a numerical way to propose an ArgMin algorithm. The model has been used to perform touristic presence forecast for the winter season 1999/2000 in Trentino (Italian Alps).
Introduction: The research focuses on the possibility of using non-convex cost functionals to adapt boosting techniques for additive time series. By an additive time series, they mean the additive aggregation of a family of time series. The problem is to model the point-wise sum of time series. Like in previous works [2, 3], they want an additive model of the form:
P(x) = ∑ (f_i(x))
where f_i(x) are the functions of the time series. They require that the model chooses the best function itself. They also want to improve the predictive power of the model by introducing a smoothing parameter.
The algorithm computes only the parameters f_i(x) and the smoothing parameter for every fixed choice of the metaparameters. After fitting the training set, one has to establish the metaparameters. The main metaparameters they have to discuss in a predictive way are:
- Choice of functions subset D
- Best partition of the time series
- Number of functions to estimate the global presence function
- Additional smoothing coefficients for the global presence
The interesting part of the problem is the choice of metaparameters in a predictive way. They give an application of this study to solve the problem of touristic presence. They consider a global time series representing the global presence of time series units, up to a fixed day.
Minimization of a functional in I7J: They consider a bounded interval I7J of real numbers and the Hilbert space KML. If x is a convex function in K_L
Link to Article: https://arxiv.org/abs/0102015v1 Authors: arXiv ID: 0102015v1