# Difference between revisions of "Colloquia"

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+ | '''Asymptotics of learning on dependent and structured random objects''' | ||

+ | |||

+ | Classical statistical inference relies on numerous tools from probability theory to study | ||

+ | the properties of estimators. However, these same tools are often inadequate to study | ||

+ | modern machine problems that frequently involve structured data (e.g networks) or | ||

+ | complicated dependence structures (e.g dependent random matrices). In this talk, we | ||

+ | extend universal limit theorems beyond the classical setting. | ||

+ | |||

+ | Firstly, we consider distributionally “structured” and dependent random object–i.e | ||

+ | random objects whose distribution are invariant under the action of an amenable group. | ||

+ | We show, under mild moment and mixing conditions, a series of universal second and | ||

+ | third order limit theorems: central-limit theorems, concentration inequalities, Wigner | ||

+ | semi-circular law and Berry-Esseen bounds. The utility of these will be illustrated by | ||

+ | a series of examples in machine learning, network and information theory. Secondly | ||

+ | by building on these results, we establish the asymptotic distribution of the cross- | ||

+ | validated risk with the number of folds allowed to grow at an arbitrary rate. Using | ||

+ | this, we study the statistical speed-up of cross validation compared to a train-test split | ||

+ | procedure, which reveals surprising results even when used on simple estimators. | ||

== January 29, 2021, [https://sites.google.com/site/isaacpurduemath/ Isaac Harris] (Purdue) == | == January 29, 2021, [https://sites.google.com/site/isaacpurduemath/ Isaac Harris] (Purdue) == |

## Revision as of 15:01, 19 January 2021

**UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. **

# Spring 2021

## January 27, 2021 **[Wed 4-5pm]**, Morgane Austern (Microsoft Research)

(Hosted by Roch)

**Asymptotics of learning on dependent and structured random objects**

Classical statistical inference relies on numerous tools from probability theory to study the properties of estimators. However, these same tools are often inadequate to study modern machine problems that frequently involve structured data (e.g networks) or complicated dependence structures (e.g dependent random matrices). In this talk, we extend universal limit theorems beyond the classical setting.

Firstly, we consider distributionally “structured” and dependent random object–i.e random objects whose distribution are invariant under the action of an amenable group. We show, under mild moment and mixing conditions, a series of universal second and third order limit theorems: central-limit theorems, concentration inequalities, Wigner semi-circular law and Berry-Esseen bounds. The utility of these will be illustrated by a series of examples in machine learning, network and information theory. Secondly by building on these results, we establish the asymptotic distribution of the cross- validated risk with the number of folds allowed to grow at an arbitrary rate. Using this, we study the statistical speed-up of cross validation compared to a train-test split procedure, which reveals surprising results even when used on simple estimators.

## January 29, 2021, Isaac Harris (Purdue)

(Hosted by Smith)

## February 1, 2021 **[Mon 4-5pm]**, Nan Wu (Duke)

(Hosted by Roch)

## February 5, 2021, Hanbaek Lyu (UCLA)

(Hosted by Roch)

## February 8, 2021 **[Mon 4-5pm]**, Mohamed Ndaoud (USC)

(Hosted by Roch)

## February 12, 2021, Bobby Wilson (University of Washington)

(Hosted by Smith)

## February 19, 2021, Maurice Fabien (Brown)

(Hosted by Smith)

## February 26, 2021, Avi Wigderson (Princeton IAS)

(Hosted by Gurevitch)

## March 12, 2021, []

(Hosted by )

## March 26, 2021, []

(Hosted by )

## April 9, 2021, []

(Hosted by )

## April 23, 2021, []

(Hosted by )