= Vladimir Koltchinskii
{c}
<Vladimir Koltchinskii> studies the mathematics of <statistical learning>. His joint work with <Karim Lounici> gives <concentration inequalities> and expectation bounds for sample <covariance operators> of centered Gaussian observations.<Concentration Inequalities and Moment Bounds for Sample Covariance Operators by Vladimir Koltchinskii and Karim Lounici>[Original byline and abstract]{ref}
Their bounds separate two questions: the typical size of the <operator norm> error, and its fluctuations around that typical size. In finite-dimensional <Euclidean space>, their effective dimension is comparable to $\operatorname{tr}(\Sigma)/\|\Sigma\|$. If most covariance <eigenvalues> are small, this quantity can be much smaller than the ambient dimension, explaining why statistical difficulty need not track the raw number of coordinates.<Concentration Inequalities and Moment Bounds for Sample Covariance Operators by Vladimir Koltchinskii and Karim Lounici>[Trace-rank discussion and Corollary2]{ref}
\Image[https://math.gatech.edu/sites/default/files/styles/profile_page_image/public/vladimir-koltchinskii.jpeg?itok=zI8aFzEm]
{title=Vladimir Koltchinskii}
{description=Portrait identified on the linked official researcher profile; photographer and licence are not asserted.}
{source=https://math.gatech.edu/people/vladimir-koltchinskii}
{width=220}
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