Abstract
In the paper, we develop the mathematically justified stream data mining algorithm for solving regression problems. The algorithm is based on the Hermite expansions of drifting regression functions. The global convergence, in the \(L_2\) space, is proved both in probability and with probability one. The examples of several concept drifts to be handled by our algorithm, and the illustrative simulations are presented.
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The project is financed under the program of the Minister of Science and Higher Education under the name “Regional Initiative of Excellence” in the years 2019–2022, project number 020/RID/2018/19, the amount of financing 12,000,000 PLN.
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Appendix – Proof of Theorems 1 and 2
Appendix – Proof of Theorems 1 and 2
Let us denote:
Obviously,
Since \(X_n\) and \(Z_n\) are independent random variables, using (7) and (8), one gets:
By the Schwarz inequality, one has:
Combining (44) with (45), using (3), (18), and the orthonormality of system (1), one obtains the following bound:
In view of (25) and (46), a proper application of Theorems 9.3 and 9.4 in [18] concludes the proof of Theorems 1 and 2.
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Rutkowska, D., Rutkowski, L. (2019). On the Hermite Series-Based Generalized Regression Neural Networks for Stream Data Mining. In: Gedeon, T., Wong, K., Lee, M. (eds) Neural Information Processing. ICONIP 2019. Lecture Notes in Computer Science(), vol 11955. Springer, Cham. https://doi.org/10.1007/978-3-030-36718-3_37
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