 Karim Lounici

Karim Lounici develops the theoretical foundations of statistical models and algorithms for structured data. His own research page identifies this focus.^[ref]

With Vladimir Koltchinskii, he bounded the error of sample covariance operators in the operator norm. For a centered Gaussian vector with covariance $\Sigma$, the expected error has scale comparable to $\Vert \Sigma \Vert \max \{\sqrt{r/n},r/n\}$, where $r=(\mathbb{E}\Vert X\Vert {)}^2/\Vert \Sigma \Vert$. This effective dimension reflects the distribution's geometry rather than merely the number of recorded coordinates.^[ref]