Testing Preferential Domains Using Sampling

02/24/2019
by   Palash Dey, et al.
0

A preferential domain is a collection of sets of preferences which are linear orders over a set of alternatives. These domains have been studied extensively in social choice theory due to both its practical importance and theoretical elegance. Examples of some extensively studied preferential domains include single peaked, single crossing, Euclidean, etc. In this paper, we study the sample complexity of testing whether a given preference profile is close to some specific domain. We consider two notions of closeness: (a) closeness via preferences, and (b) closeness via alternatives. We further explore the effect of assuming that the outlier preferences/alternatives to be random (instead of arbitrary) on the sample complexity of the testing problem. In most cases, we show that the above testing problem can be solved with high probability for all commonly used domains by observing only a small number of samples (independent of the number of preferences, n, and often the number of alternatives, m). In the remaining few cases, we prove either impossibility results or Ω(n) lower bound on the sample complexity. We complement our theoretical findings with extensive simulations to figure out the actual constant factors of our asymptotic sample complexity bounds.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/30/2017

Testing Conditional Independence of Discrete Distributions

We study the problem of testing conditional independence for discrete di...
research
09/23/2022

The complexity of unsupervised learning of lexicographic preferences

This paper considers the task of learning users' preferences on a combin...
research
10/15/2018

Small One-Dimensional Euclidean Preference Profiles

We characterize one-dimensional Euclidean preference profiles with a sma...
research
04/10/2018

Testing Identity of Multidimensional Histograms

We investigate the problem of identity testing for multidimensional hist...
research
05/01/2021

Generalized Kings and Single-Elimination Winners in Random Tournaments

Tournaments can be used to model a variety of practical scenarios includ...
research
02/23/2022

Sign representation of single-peaked preferences and Bruhat orders

Single-peaked preferences and domains are extensively researched in soci...
research
04/18/2016

Learning Sparse Additive Models with Interactions in High Dimensions

A function f: R^d →R is referred to as a Sparse Additive Model (SPAM), i...

Please sign up or login with your details

Forgot password? Click here to reset