The University of Arizona: A Combinatorial Geometry View of Inference and Learning Problems

In statistical inference we wish to learn the properties or parameters of a distribution through sufficiently many samples.

A famous example is logistic regression, a popular non-linear model in multivariate statistics and supervised learning. Users often rely on optimizing of maximum likelihood estimation, but how much training data do we need, as a function of the dimension of the covariates of the data, before we expect an MLE to exist with high probability? 

 Similarly, for unsupervised learning and non-parametric statistics, one wishes to uncover the shape and patterns from samples of a measure or measures. We use only the intrinsic geometry and topology of the sample. A famous example of this type of method is the k-means clustering algorithm. A fascinating challenge is to explain the variability of behavior of k-means algorithms with distinct random initializations and the shapes of the clusters.

In this talk we explain new stochastic combinatorial theorems, that give bounds on the probability of existence of maximum likelihood estimators in multinomial logistic regression and also relate to the variability of clustering initializations. Along the way we will see fascinating connections to the coupon collector problem, topological data analysis, and to the computation of Tukey centerpoints of data clouds (a high-dimensional generalization of median). This is joint work with T. Hogan, R.  D. Oliveros, E. Jaramillo-Rodriguez, and A. Torres-Hernandez.

Series: TRIPODS Seminar

12:00 PM

Online

Presenter: Jesus DeLoera, US Davis, Department of Mathematics

 

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ID: 84582669520

  • Audience: Adult
  • Genre: Mathematics
  • Type: Online, Presentation

The event is finished.

Date

Nov 22 2021
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Time

12:00 pm - 1:00 pm

Cost

Free

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Location

Online

Organizer

The University of Arizona College of Mathematics
Phone
(520) 621-6866
Website
https://crr.math.arizona.edu/
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