V. Koltchinskii

activity

20042024

most cited2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization

379 citations · 1.2k across the 30 of their papers we have counts for

collaborators

Showing 2015Show all

4 papers · 1 filter

stat.ML2015★ 29 cited

Optimal Estimation of Low Rank Density Matrices

Vladimir Koltchinskii, Dong Xia

The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bo…

math.PR2015★ 2 cited

Perturbation of linear forms of singular vectors under Gaussian noise

Vladimir Koltchinskii, Dong Xia

Let $A \in R^{m \times n}$ be a matrix of rank $r$ with singular value decomposition (SVD) $A = \sum_{k = 1}^{r} σ_{k} (u_{k} \otimes v_{k}),$ where ${σ_{k}, k = 1, \dots, r}$ are singular va…

math.ST2015★ 67 cited

Normal approximation and concentration of spectral projectors of sample covariance

Vladimir Koltchinskii, Karim Lounici

Let $X, X_{1}, \dots, X_{n}$ be i.i.d. Gaussian random variables in a separable Hilbert space $H$ with zero mean and covariance operator $Σ = E (X \otimes X),$ and let $\…

math.ST2015

Estimation of Low-Rank Covariance Function

Vladimir Koltchinskii, Karim Lounici, Alexander B. Tsybakov

We consider the problem of estimating a low rank covariance function $K (t, u)$ of a Gaussian process $S (t), t \in [0, 1]$ based on $n$ i.i.d. copies of $S$ observed in a white noise.…