Abstract
Problem of learning a graphical model (graphical model selection problem) consists of recovering a conditional dependence structure (concentration graph) from data given as a sample of observations from a random vector. Various algorithms to solve this problem are known. One class of algorithms is related with convex optimization problem with additional lasso regularization term. Such algorithms are called graphical lasso algorithms. Various properties and practical efficiency of graphical lasso algorithms were investigated in the literature. In the present paper we study sensitivity of uncertainty (level of error) of graphical lasso algorithms to the change of distribution of the random vector. This issue is not well studied yet. First, we show that uncertainty of the classical version of graphical lasso algorithm is very sensitive to the change of distribution. Next, we suggest simple modifications of this algorithm which are much more robust in the large class of distributions. Finally, we discuss a future development of the proposed approach.
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Acknowledgements
Sections 2 and 3 with general problem setting were prepared within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE University), results of the Sects. 4, 5 and 6 about graphical lasso algorithms are obtained with a support from RSF grant 22-11-00073. Numerical experiments were conducted using HSE HPC resources [18].
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Kalyagin, V., Kostylev, I. (2024). Robustness of Graphical Lasso Optimization Algorithm for Learning a Graphical Model. In: Eremeev, A., Khachay, M., Kochetov, Y., Mazalov, V., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2024. Lecture Notes in Computer Science, vol 14766. Springer, Cham. https://doi.org/10.1007/978-3-031-62792-7_23
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DOI: https://doi.org/10.1007/978-3-031-62792-7_23
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