Zobrazeno 1 - 10
of 84
pro vyhledávání: '"Minsker, Stanislav"'
Autor:
Minsker, Stanislav, Shen, Yinan
Is there a natural way to order data in dimension greater than one? The approach based on the notion of data depth, often associated with the name of John Tukey, is among the most popular. Tukey's depth has found applications in robust statistics, gr
Externí odkaz:
http://arxiv.org/abs/2410.00219
We prove Fuk-Nagaev and Rosenthal-type inequalities for the sums of independent random matrices, focusing on the situation when the norms of the matrices possess finite moments of only low orders. Our bounds depend on the "intrinsic" dimensional char
Externí odkaz:
http://arxiv.org/abs/2407.12948
Autor:
Minsker, Stanislav, Strawn, Nate
This paper is devoted to the statistical and numerical properties of the geometric median, and its applications to the problem of robust mean estimation via the median of means principle. Our main theoretical results include (a) an upper bound for th
Externí odkaz:
http://arxiv.org/abs/2307.03111
Autor:
Minsker, Stanislav
The goal of this note is to present a modification of the popular median of means estimator that achieves sub-Gaussian deviation bounds with nearly optimal constants under minimal assumptions on the underlying distribution. We build on a recent work
Externí odkaz:
http://arxiv.org/abs/2305.18681
We consider the high-dimensional linear regression model and assume that a fraction of the measurements are altered by an adversary with complete knowledge of the data and the underlying distribution. We are interested in a scenario where dense addit
Externí odkaz:
http://arxiv.org/abs/2210.16808
Autor:
Minsker, Stanislav
This dissertation investigates the learning scenarios where a high-dimensional parameter has to be estimated from a given sample of fixed size, often smaller than the dimension of the problem. The first part answers some open questions for the binary
Externí odkaz:
http://hdl.handle.net/1853/44808
Autor:
Minsker, Stanislav, Yao, Shunan
The topic of robustness is experiencing a resurgence of interest in the statistical and machine learning communities. In particular, robust algorithms making use of the so-called median of means estimator were shown to satisfy strong performance guar
Externí odkaz:
http://arxiv.org/abs/2203.06617
Autor:
Minsker, Stanislav, Wang, Lang
Publikováno v:
Statistica Sinica 34 (2024), 1565-1583
We consider the problem of estimating the covariance structure of a random vector $Y\in \mathbb R^d$ from a sample $Y_1,\ldots,Y_n$. We are interested in the situation when $d$ is large compared to $n$ but the covariance matrix $\Sigma$ of interest h
Externí odkaz:
http://arxiv.org/abs/2203.02880
Autor:
Minsker, Stanislav
This paper addresses the following question: given a sample of i.i.d. random variables with finite variance, can one construct an estimator of the unknown mean that performs nearly as well as if the data were normally distributed? One of the most pop
Externí odkaz:
http://arxiv.org/abs/2202.11842
We study the supervised clustering problem under the two-component anisotropic Gaussian mixture model in high dimensions and in the non-asymptotic setting. We first derive a lower and a matching upper bound for the minimax risk of clustering in this
Externí odkaz:
http://arxiv.org/abs/2111.07041