Abstract:
A new method of entropy-robust nonparametric estimation of probability density functions (PDF) is proposed in the paper. Characteristics of dynamic randomized models with structured nonlinearities are estimated under small amount of data. We have shown that optimal PDF are of exponential class, where parameters are Lagrange multipliers. To determine the parameters a system of equations with integral components has been built. We developed an algorithm for solving this problem, based on parallel Monte Carlo techniques. Estimates of solutions’s accuracy for the class of given integral components and probability of its achivement have been obtained. The method was applied to the problem with nonlinear dynamic system with given structured nonlinearity.
Keywords:
entropy, robustness, randomized model, structure of exponential nonlinearity, functional entropy-linear programming, Monte Carlo trials, numerical integration, entropy estimation, small amounts of data, graphic processor.
Citation:
Y. S. Popkov, A. Y. Popkov, B. S. Darkhovskiy, “Parallel Monte Carlo for entropy-robust estimation”, Mat. Model., 27:6 (2015), 14–32; Math. Models Comput. Simul., 8:1 (2016), 27–39
Yu. S. Popkov, “Mathematical methods of randomized machine teaching”, J. Math. Sci. (N. Y.), 254:5 (2021), 652–676
Yuri S. Popkov, Yuri A. Dubnov, Alexey Y. Popkov, Studies in Computational Intelligence, 756, Learning Systems: From Theory to Practice, 2018, 199
Yu. S. Popkov, Yu. A. Dubnov, “Entropy-robust randomized forecasting under small sets of retrospective data”, Autom. Remote Control, 77:5 (2016), 839–854
Popkov Yu.S., Dubnov Yu.A., Popkov A.Yu., “Randomized Machine Learning: Statement, Solution, Applications”, 2016 IEEE 8Th International Conference on Intelligent Systems (Is), eds. Yager R., Sgurev V., Hadjiski M., Jotsov V., IEEE, 2016, 27–39