Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The regularized tau estimator: A robust and efficient solution to
  ill-posed linear inverse problems   Linear inverse problems are ubiquitous. Often the measurements do not follow
a Gaussian distribution. Additionally, a model matrix with a large condition
number can complicate the problem further by making it ill-posed. In this case,
the performance of popular estimators may deteriorate significantly. We have
developed a new estimator that is both nearly optimal in the presence of
Gaussian errors while being also robust against outliers. Furthermore, it
obtains meaningful estimates when the problem is ill-posed through the
inclusion of $\ell_1$ and $\ell_2$ regularizations. The computation of our
estimate involves minimizing a non-convex objective function. Hence, we are not
guaranteed to find the global minimum in a reasonable amount of time. Thus, we
propose two algorithms that converge to a good local minimum in a reasonable
(and adjustable) amount of time, as an approximation of the global minimum. We
also analyze how the introduction of the regularization term affects the
statistical properties of our estimator. We confirm high robustness against
outliers and asymptotic efficiency for Gaussian distributions by deriving
measures of robustness such as the influence function, sensitivity curve, bias,
asymptotic variance, and mean square error. We verify the theoretical results
using numerical experiments and show that the proposed estimator outperforms
recently proposed methods, especially for increasing amounts of outlier
contamination. Python code for all of the algorithms are available online in
the spirit of reproducible research.

7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ