# Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

### Efficiency of the floating body as a robust measure of dispersion

**Mathematical Physics & Probability**

Speaker: | Luis Rademacher, UC-Davis |

Location: | 2112 MSB |

Start time: | Wed, Mar 13 2019, 4:10PM |

This talk is about multidimensional quantiles, which provide robust

notions of shape, depth and dispersion of a distribution or dataset. It

will focus on Tukey depth and depth curves, which are essentially the same as the convex floating body in convex geometry. These concepts can

be difficult to use because they are computationally intractable in

general. We develop a theory of algorithmic efficiency for these notions

for several broad and relevant families of distributions: symmetric

log-concave distributions and certain multivariate stable distributions

and power-law distributions. As an example of the power of these

results, we show how to solve the Independent Component Analysis problem

for power-law distributions, even when the first moment is infinite.