38 research outputs found
Proportional Representation in Metric Spaces and Low-Distortion Committee Selection
We introduce a novel definition for a small set R of k points being
"representative" of a larger set in a metric space. Given a set V (e.g.,
documents or voters) to represent, and a set C of possible representatives, our
criterion requires that for any subset S comprising a theta fraction of V, the
average distance of S to their best theta*k points in R should not be more than
a factor gamma compared to their average distance to the best theta*k points
among all of C. This definition is a strengthening of proportional fairness and
core fairness, but - different from those notions - requires that large
cohesive clusters be represented proportionally to their size.
Since there are instances for which - unless gamma is polynomially large - no
solutions exist, we study this notion in a resource augmentation framework,
implicitly stating the constraints for a set R of size k as though its size
were only k/alpha, for alpha > 1. Furthermore, motivated by the application to
elections, we mostly focus on the "ordinal" model, where the algorithm does not
learn the actual distances; instead, it learns only for each point v in V and
each candidate pairs c, c' which of c, c' is closer to v. Our main result is
that the Expanding Approvals Rule (EAR) of Aziz and Lee is (alpha, gamma)
representative with gamma <= 1 + 6.71 * (alpha)/(alpha-1).
Our results lead to three notable byproducts. First, we show that the EAR
achieves constant proportional fairness in the ordinal model, giving the first
positive result on metric proportional fairness with ordinal information.
Second, we show that for the core fairness objective, the EAR achieves the same
asymptotic tradeoff between resource augmentation and approximation as the
recent results of Li et al., which used full knowledge of the metric. Finally,
our results imply a very simple single-winner voting rule with metric
distortion at most 44.Comment: 24 pages, Accepted to AAAI 2
Whither Fair Clustering?
Within the relatively busy area of fair machine learning that has been
dominated by classification fairness research, fairness in clustering has
started to see some recent attention. In this position paper, we assess the
existing work in fair clustering and observe that there are several directions
that are yet to be explored, and postulate that the state-of-the-art in fair
clustering has been quite parochial in outlook. We posit that widening the
normative principles to target for, characterizing shortfalls where the target
cannot be achieved fully, and making use of knowledge of downstream processes
can significantly widen the scope of research in fair clustering research. At a
time when clustering and unsupervised learning are being increasingly used to
make and influence decisions that matter significantly to human lives, we
believe that widening the ambit of fair clustering is of immense significance.Comment: Accepted at the AI for Social Good Workshop, Harvard, July 20-21,
202
Proportionally Representative Clustering
In recent years, there has been a surge in effort to formalize notions of
fairness in machine learning. We focus on clustering -- one of the fundamental
tasks in unsupervised machine learning. We propose a new axiom ``proportional
representation fairness'' (PRF) that is designed for clustering problems where
the selection of centroids reflects the distribution of data points and how
tightly they are clustered together. Our fairness concept is not satisfied by
existing fair clustering algorithms. We design efficient algorithms to achieve
PRF both for unconstrained and discrete clustering problems. Our algorithm for
the unconstrained setting is also the first known polynomial-time approximation
algorithm for the well-studied Proportional Fairness (PF) axiom (Chen, Fain,
Lyu, and Munagala, ICML, 2019). Our algorithm for the discrete setting also
matches the best known approximation factor for PF.Comment: Revised version includes a new author (Jeremy Vollen) and new
results: Our algorithm for the unconstrained setting is also the first known
polynomial-time approximation algorithm for the well-studied Proportional
Fairness (PF) axiom (Chen, Fain, Lyu, and Munagala, ICML, 2019). Our
algorithm for the discrete setting also matches the best known approximation
factor for P
Approximation Algorithms for Fair Range Clustering
This paper studies the fair range clustering problem in which the data points
are from different demographic groups and the goal is to pick centers with
the minimum clustering cost such that each group is at least minimally
represented in the centers set and no group dominates the centers set. More
precisely, given a set of points in a metric space where each point
belongs to one of the different demographics (i.e., ) and a set of intervals on desired number of centers from
each group, the goal is to pick a set of centers with minimum
-clustering cost (i.e., ) such that for
each group , . In particular,
the fair range -clustering captures fair range -center, -median
and -means as its special cases. In this work, we provide efficient constant
factor approximation algorithms for fair range -clustering for all
values of .Comment: ICML 202
Proportional Fairness in Clustering: A Social Choice Perspective
We study the proportional clustering problem of Chen et al. [ICML'19] and
relate it to the area of multiwinner voting in computational social choice. We
show that any clustering satisfying a weak proportionality notion of Brill and
Peters [EC'23] simultaneously obtains the best known approximations to the
proportional fairness notion of Chen et al. [ICML'19], but also to individual
fairness [Jung et al., FORC'20] and the "core" [Li et al. ICML'21]. In fact, we
show that any approximation to proportional fairness is also an approximation
to individual fairness and vice versa. Finally, we also study stronger notions
of proportional representation, in which deviations do not only happen to
single, but multiple candidate centers, and show that stronger proportionality
notions of Brill and Peters [EC'23] imply approximations to these stronger
guarantees