Abstract
Randomized machine learning focuses on problems with considerable uncertainty in data and models. Machine learning algorithms are formulated in terms of a functional entropy-linear programming problem. We adapt these algorithms to forecasting problems on an example of the evolution of thermokarst lakes area in permafrost zones. Thermokarst lakes generate methane, a greenhouse gas affecting climate change. We propose randomized machine learning procedures using dynamic regression models with random parameters and retrospective data (climatic parameters and remote sensing of the Earth’s surface). The randomized machine learning algorithm developed below estimates the probability density functions of model parameters and measurement noises. Randomized forecasting is implemented as algorithms transforming the optimal distributions into the corresponding random sequences (sampling algorithms). The randomized forecasting procedures and technologies are trained, tested, and then applied to forecast the evolution of thermokarst lakes area in Western Siberia.






REFERENCES
Vapnik, V.N., Statistical Learning Theory, John Willey & Sons, 1998.
Bishop, C., Pattern Recognition and Machine Learning, New York: Springer, 2007.
Friedman, J., Hastie T., and Tibshirani, R., The Elements of Statistical Learning, Springer Series in Statistics, vol. 1, Berlin: Springer, 2009.
Popkov, Yu.S., Dubnov, Yu.A., and Popkov, A.Yu., Randomized machine learning: statement, solution, applications, Proc. IEEE Int. Conf. on Intelligent Systems, 2016, pp. 27–39.
Zuidhoff, F.S. and Kolstrup, E., Changes in palsa distribution in relation to climate change in Laivadalen, Northern Sweden, especially 1960–1997, Permafrost and Periglacial Processes, 2000, vol. 11, pp. 55–69.
Kirpotin, S., Polishchuk, Y., and Bruksina, N., Abrupt changes of thermokarst lakes in Western Siberia: Impacts of climatic warming on permafrost melting, Int. J. Environmental Studies, 2009, vol. 66, no. 4, pp. 423–431.
Karlson, J.M., Lyon, S.W., and Destouni, G., Temporal behavior of lake size-distribution in a thawing permafrost landscape in Northwestern Siberia, Remote Sensing, 2014, no. 6, pp. 621–636.
Bryksina, N.A. and Polishchuk, Yu.M., Analysis of changes in the number of thermokarst lakes in permafrost of Western Siberia on the basis of satellite images, Cryosphere of Earth, 2015, vol. 19, no. 2, pp. 114–120.
Liu, Q., Rowe, M.D., Anderson, E.J., Stow, C.A., and Stumpf, R.P., Probabilistic forecast of microcystin toxin using satellite remote sensing, in situ observation and numerical modeling, Environment Modelling and Software, 2020, vol. 128, p. 104705.
Vidyasagar, M., Statistical learning theory and randomized algorithms for control, IEEE Control System Magazine, 1998, vol. 1, no. 17, pp. 69–88.
Granichin, O.N. and Polyak, B.T., Randomizirovannye algoritmy otsenivaniya i optimizatsii pri pochti proizvol’nykh pomekhakh (Randomized Estimation and Optimization Algorithms under Almost Arbitrary Noises), Moscow: Nauka, 2002.
Biondo, A.E., Pluchino, A., Rapisarda, A., and Helbing, D., Are random traiding strategies more successful than technical ones?, PLoS ONE, 2013, vol. 6, no. 7, p. e68344.
Lutz, W., Sandersen, S., and Scherbov, S., The end of world population growth, Nature, 2001, vol. 412, no. 6846, pp. 543–545.
Tsirlin, A.M., Metody usrednennoi optimizatsii i ikh primenenie (Average Optimization Methods and Their Application), Moscow: Fizmatlit, 1997.
Shannon, C., Communication theory of secrecy systems, Bell System Technical Journal, 1949, vol. 28, no. 4, pp. 656–715.
Jaynes, E.T., Information theory and statistical mechanics, Physics Review, 1957, vol. 106, pp. 620–630.
Jaynes, E.T., Papers on Probability, Statistics and Statistical Physics, Dordrecht: Kluwer Academic Publisher, 1989.
Jaynes, E.T., Probability Theory. The Logic and Science, Cambridge University Press, 2003.
Popkov, Yu.S., Popkov, A.Yu., and Dubnov, Yu.A., Entropy Randomization in Machine Learning, Chapman & Hall/CRC, 2022.
Popkov, Y. and Popkov, A., New method of entropy-robust estimation for randomized models under limited data, Entropy, 2014, vol. 16, pp. 675–698.
Ioffe, A.D. and Tihomirov, V.M., Theory of Extremal Problems, Amsterdam: NorthHolland, 1979.
Darkhovsky, B.S., Popkov, Y.S., Popkov, A.Y., and Aliev, A.S., A method of generating random vectors with a given probability density function, Autom. Remote Control, 2018, vol. 79, no. 9, pp. 1569–1581. https://doi.org/10.1134/S0005117918090035
Aivazyan, S.A., Enyukov, I.S., and Meshalkin, L.D., Prikladnaya statistika: Issledovanie zavisimostei (Applied Statistics: Study of Dependencies), Moscow: Finansy i Statistika, 1985.
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This work was supported by the Russian Science Foundation, project no. 22-11-20023.
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This paper was recommended for publication by A.N. Sobolevski, a member of the Editorial Board
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Dubnov, Y.A., Popkov, A.Y., Polishchuk, V.Y. et al. Randomized Machine Learning Algorithms to Forecast the Evolution of Thermokarst Lakes Area in Permafrost Zones. Autom Remote Control 84, 56–70 (2023). https://doi.org/10.1134/S0005117923010034
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DOI: https://doi.org/10.1134/S0005117923010034