Abstract
The article concerns of the problem of regression functions estimation when the output is contaminated by additive nonstationary noise. We investigate the model \(y_i = R\left( {{\bf x _i}} \right) + Z _i ,\,i = 1,2, \ldots n\), where x i is assumed to be the set of deterministic inputs (d-dimensional vector), y i is the scalar, probabilistic outputs, and Z i is a measurement noise with zero mean and variance depending on n. \(R\left( . \right)\) is a completely unknown function. The problem of finding function \(R\left( . \right)\) may be solved by applying non-parametric methodology, for instance: algorithms based on the Parzen kernel or algorithms derived from orthogonal series. In this work we present the orthogonal series approach. The analysis has been made for some class of nonstationarity. We present the conditions of convergence of the estimation algorithm for the variance of noise growing up when number of observations is tending to infinity. The results of numerical simulations are presented.
Keywords
- IEEE Transaction
- Generalize Regression Neural Network
- Orthogonal Series
- Deep Belief Network
- Multiple Fourier Series
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Galkowski, T., Pawlak, M. (2015). Orthogonal Series Estimation of Regression Functions in Nonstationary Conditions. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2015. Lecture Notes in Computer Science(), vol 9119. Springer, Cham. https://doi.org/10.1007/978-3-319-19324-3_39
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