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Friday, November 22, 2024 3:30 pm - 4:30 pm EST (GMT -05:00)

Tutte colloquium-Kate Larson

Title: Soft Condorcet Optimization

Speaker: Kate Larson
Affiliation: University of Waterloo
Location: MC 5501

Abstract:

A common way to drive the progress of AI models and agents is to compare their performance on standardized benchmarks. This often involves aggregating individual performances across a potentially wide variety of tasks and benchmarks and many of the leaderboards that draw greatest attention are Elo-based. 

 

In this paper, we describe a novel ranking scheme inspired by social choice frameworks, called Soft Condorcet Optimization (SCO), to compute the optimal ranking of agents: the one that makes the fewest mistakes in predicting the agent comparisons in the evaluation data. This optimal ranking is the maximum likelihood estimate when evaluation data (which we view as votes) are interpreted as noisy samples from a ground truth ranking, a solution to Condorcet's original voting system criteria and inherits desirable social-choice inspired properties since SCO ratings are maximal for Condorcet winners when they exist, which we show is not necessarily true for the classical rating system Elo.

 

We propose three optimization algorithms to compute SCO ratings and evaluate their empirical performance across a variety of synthetic and real-world datasets, to illustrate different properties.

 

With Marc Lanctot, Ian Gemp, Quentin Berthet, Yoram Bachrach, Manfred Diaz, Roberto-Rafael Maura-Rivero,  Anna Koop, and Doina Precup

 

 

Thursday, November 28, 2024 2:00 pm - 3:00 pm EST (GMT -05:00)

Algebraic and enumerative combinatorics seminar-Mike Cummings

Title:Combinatorial rules for the geometry of Hessenberg varieties

progressions

Speaker Mike Cummings
Affiliation University of Waterloo
Location MC 5479

 Abstract:

Hessenberg varieties were introduced by De Mari, Procesi, and Shayman in the early 1990s and lie at the intersection of geometry, representation theory, and combinatorics.  In 2012, Insko and Yong studied a class of Hessenberg varieties using patch ideals, a technique dating back to at least the 1970s from the study of Schubert varieties. In this talk, we will derive patch ideals and use them to study two classes of Hessenberg varieties.  We will see the combinatorics that govern the behaviour of these patch ideals and translate these results to the geometric setting. Based in part on work with Sergio Da Silva, Megumi Harada, and Jenna Rajchgot.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm,