Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear regression with partially mismatched data: local search with
  theoretical guarantees   Linear regression is a fundamental modeling tool in statistics and related
fields. In this paper, we study an important variant of linear regression in
which the predictor-response pairs are partially mismatched. We use an
optimization formulation to simultaneously learn the underlying regression
coefficients and the permutation corresponding to the mismatches. The
combinatorial structure of the problem leads to computational challenges. We
propose and study a simple greedy local search algorithm for this optimization
problem that enjoys strong theoretical guarantees and appealing computational
performance. We prove that under a suitable scaling of the number of mismatched
pairs compared to the number of samples and features, and certain assumptions
on problem data; our local search algorithm converges to a nearly-optimal
solution at a linear rate. In particular, in the noiseless case, our algorithm
converges to the global optimal solution with a linear convergence rate. We
also propose an approximate local search step that allows us to scale our
approach to much larger instances. We conduct numerical experiments to gather
further insights into our theoretical results and show promising performance
gains compared to existing approaches.

32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat