= Roman Vershynin
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<Roman Vershynin> studies high-dimensional <probability theory> and its applications to data. His <High-Dimensional Probability by Roman Vershynin> develops tools including <concentration inequalities>, random-matrix estimates and <generic chaining>, which turn geometry and independence into bounds that hold simultaneously over many directions.<High-Dimensional Probability by Roman Vershynin>[First edition, random matrices and Chapter 8, chaining]{ref}
A representative question is how many random observations are needed to preserve information about a high-dimensional object. Controlling one fixed direction is easier than controlling every direction at once, so the geometry of a whole family of directions becomes part of the probability calculation. His research page describes this connection between probability and mathematical data science; his author-hosted expository work also treats geometric methods for constrained estimation.https://webapps.math.uci.edu/~rvershyn/index.html[Research description]{ref}https://arxiv.org/abs/1405.5103[Author's Estimation in high dimensions: a geometric perspective, abstract]{ref}
\Image[https://webapps.math.uci.edu/~rvershyn/support-files/portrait.jpg]
{title=Roman Vershynin, portrait identified by the linked author, institutional or Commons source}
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