Estimation of Skill Distributions

by   Ali Jadbabaie, et al.

In this paper, we study the problem of learning the skill distribution of a population of agents from observations of pairwise games in a tournament. These games are played among randomly drawn agents from the population. The agents in our model can be individuals, sports teams, or Wall Street fund managers. Formally, we postulate that the likelihoods of game outcomes are governed by the Bradley-Terry-Luce (or multinomial logit) model, where the probability of an agent beating another is the ratio between its skill level and the pairwise sum of skill levels, and the skill parameters are drawn from an unknown skill density of interest. The problem is, in essence, to learn a distribution from noisy, quantized observations. We propose a simple and tractable algorithm that learns the skill density with near-optimal minimax mean squared error scaling as n^-1+ε, for any ε>0, when the density is smooth. Our approach brings together prior work on learning skill parameters from pairwise comparisons with kernel density estimation from non-parametric statistics. Furthermore, we prove minimax lower bounds which establish minimax optimality of the skill parameter estimation technique used in our algorithm. These bounds utilize a continuum version of Fano's method along with a covering argument. We apply our algorithm to various soccer leagues and world cups, cricket world cups, and mutual funds. We find that the entropy of a learnt distribution provides a quantitative measure of skill, which provides rigorous explanations for popular beliefs about perceived qualities of sporting events, e.g., soccer league rankings. Finally, we apply our method to assess the skill distributions of mutual funds. Our results shed light on the abundance of low quality funds prior to the Great Recession of 2008, and the domination of the industry by more skilled funds after the financial crisis.



There are no comments yet.


page 1

page 2

page 3

page 4


Structural adaptation in the density model

This paper deals with non-parametric density estimation on ^2 from i.i.d...

Minimax estimation of norms of a probability density: I. Lower bounds

The paper deals with the problem of nonparametric estimating the L_p–nor...

Optimal Estimation of Change in a Population of Parameters

Paired estimation of change in parameters of interest over a population ...

On learning parametric distributions from quantized samples

We consider the problem of learning parametric distributions from their ...

Stretching the Effectiveness of MLE from Accuracy to Bias for Pairwise Comparisons

A number of applications (e.g., AI bot tournaments, sports, peer grading...

Optimal rates of entropy estimation over Lipschitz balls

We consider the problem of minimax estimation of the entropy of a densit...

Who's Better, Who's Best: Skill Determination in Video using Deep Ranking

This paper presents a method for assessing skill of performance from vid...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.