Please email any errors or updates to our website support/editor.
PDF files require Adobe Acrobat Reader.
Visit our COVID-19 information website to learn how Warriors protect Warriors.
Please note: The University of Waterloo is closed for all events until further notice.
Title: High-dimensional probability: Random vectors in high dimensions
Speaker: | Courtney Paquette |
Affiliation: | University of Waterloo |
Room: | MC 5417 |
Abstract:
In this talk, I will finish our discussion of concentration inequalities, particularly, I will discuss the sub-exponential distribution and state Bernstein’s inequality; thereby completing our study of large deviations. Following this, I will introduce random vectors which live in high-dimensions. Life in high dimensions presents new challenges which stems from the fact that there is exponentially more room in high dimensions than in lower dimensions. The abundance of room in higher dimensions makes algorithmic tasks exponentially more difficult. Probability in high dimensions will give us some tools to circumvent these difficulties. I will start by examining the Euclidean norm of a random vector X with independent coordinates, and show that the norm concentrates tightly about its mean. Then I will state and prove some basic results (e.g. isotropic distributions) and give examples of high-dimensional distributions (e.g. multivariant normal, spherical, etc). Finally, I will examine principle component analysis (PCA), a tool which is of utmost importance in probability, statistics, data science, and optimization.
Please email any errors or updates to our website support/editor.
PDF files require Adobe Acrobat Reader.
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.