Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robust Mahalanobis Metric Learning via Geometric Approximation
  Algorithms   Learning Mahalanobis metric spaces is an important problem that has found
numerous applications. Several algorithms have been designed for this problem,
including Information Theoretic Metric Learning (ITML) [Davis et al. 2007] and
Large Margin Nearest Neighbor (LMNN) classification [Weinberger and Saul 2009].
We study the problem of learning a Mahalanobis metric space in the presence of
adversarial label noise. To that end, we consider a formulation of Mahalanobis
metric learning as an optimization problem, where the objective is to minimize
the number of violated similarity/dissimilarity constraints. We show that for
any fixed ambient dimension, there exists a fully polynomial-time approximation
scheme (FPTAS) with nearly-linear running time. This result is obtained using
tools from the theory of linear programming in low dimensions. As a
consequence, we obtain a fully-parallelizable algorithm that recovers a
nearly-optimal metric space, even when a small fraction of the labels is
corrupted adversarially. We also discuss improvements of the algorithm in
practice, and present experimental results on real-world, synthetic, and
poisoned data sets.

35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con