Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning to Partition using Score Based Compatibilities   We study the problem of learning to partition users into groups, where one
must learn the compatibilities between the users to achieve optimal groupings.
We define four natural objectives that optimize for average and worst case
compatibilities and propose new algorithms for adaptively learning optimal
groupings. When we do not impose any structure on the compatibilities, we show
that the group formation objectives considered are $NP$ hard to solve and we
either give approximation guarantees or prove inapproximability results. We
then introduce an elegant structure, namely that of \textit{intrinsic scores},
that makes many of these problems polynomial time solvable. We explicitly
characterize the optimal groupings under this structure and show that the
optimal solutions are related to \emph{homophilous} and \emph{heterophilous}
partitions, well-studied in the psychology literature. For one of the four
objectives, we show $NP$ hardness under the score structure and give a
$\frac{1}{2}$ approximation algorithm for which no constant approximation was
known thus far. Finally, under the score structure, we propose an online low
sample complexity PAC algorithm for learning the optimal partition. We
demonstrate the efficacy of the proposed algorithm on synthetic and real world
datasets.

29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn