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# Семинар HDI Lab: Dmitrii Ostrovskii (University of Southern California), Near-Optimal Model Discrimination with Non-Disclosure

Мероприятие завершено

22 июня 2021 г. в 17:00 состоится очередной семинар международной лаборатории стохастических алгоритмов и анализа многомерных данных. С докладом "Near-Optimal Model Discrimination with Non-Disclosure" выступит Dmitrii Ostrovskii (University of Southern California).

Аннотация: In the standard setup of parametric M-estimation with convex loss, we consider two population risk minimizers associated with two possible distributions of a random observation, and then ask the following question:
Given the value of one of the two minimizers and access to i.i.d. sampling from both distributions, what sample sizes allow to identify the “right” distribution, i.e., the one corresponding to the given value?
Making the first steps towards answering this question in full generality, we first consider the case of a well-specified linear model with squared loss. Here we provide nearly matching upper and lower bounds on the sample complexity, showing it to be min{1/Δ^2,\sqrt{r}/Δ} up to a constant factor, where Δ is a measure of separation between the two distributions and r is the maximum (resp., minimum) of the ranks of the design covariance matrices in the case of the upper (resp., lower) bound. This bound is dimension-independent and rank-independent for large enough separation. We then extend this result in two directions: (i) for the general parametric setup in asymptotic regime; (ii) for generalized linear models in the small-sample regime n≤r and under weak moment assumptions. In both cases, we derive sample complexity bounds of a similar form, even under misspecification. Our testing procedures only access the known'' value through a certain functional of empirical risk. In addition, the number of observations that allows to reach statistical confidence for testing does not allow to "resolve" the two models -- that is, recover both minimizers up to O(Δ) prediction accuracy. These two properties open the prospect of applying our testing framework in practical tasks, where one would like to identify a prediction model, which can be proprietary, while guaranteeing that the model cannot be actually inferred by the identifying agent.
The talk will be following the recent paper arxiv:2012.02901.

Ссылка на семинар:  https://us02web.zoom.us/j/9252879297

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