Семинар HDI Lab: Sharp deviation bounds for quadratic forms and their use in machine learning
1 июня 2023 г. в 16:20 состоится очередной семинар Международной лаборатории стохастических алгоритмов и анализа многомерных данных. С докладом "Sharp deviation bounds for quadratic forms and their use in machine learning" выступит профессор-исследователь НИУ ВШЭ Владимир Спокойный (НИУ ВШЭ, ИППИ РАН, Humboldt University, WIAS Berlin).
Under a mild assumption of linearity on the log-likelihood function, the tools of empirical processes are not necessary, the analysis of a general MLE can be reduced to a deviation bound for a quadratic form. This paper explains how the recent advances in Laplace approximation from [Spokoiny, 2022, 2023] can be used for obtaining sharp Gaussian-like finite sample bounds and for stating the prominent concentration phenomenon for the squared norm of a sub-gaussian vector. Some extensions and open problems will be discussed as well.