Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Fast Algorithm for Separated Sparsity via Perturbed Lagrangians   Sparsity-based methods are widely used in machine learning, statistics, and
signal processing. There is now a rich class of structured sparsity approaches
that expand the modeling power of the sparsity paradigm and incorporate
constraints such as group sparsity, graph sparsity, or hierarchical sparsity.
While these sparsity models offer improved sample complexity and better
interpretability, the improvements come at a computational cost: it is often
challenging to optimize over the (non-convex) constraint sets that capture
various sparsity structures. In this paper, we make progress in this direction
in the context of separated sparsity -- a fundamental sparsity notion that
captures exclusion constraints in linearly ordered data such as time series.
While prior algorithms for computing a projection onto this constraint set
required quadratic time, we provide a perturbed Lagrangian relaxation approach
that computes provably exact projection in only nearly-linear time. Although
the sparsity constraint is non-convex, our perturbed Lagrangian approach is
still guaranteed to find a globally optimal solution. In experiments, our new
algorithms offer a 10$\times$ speed-up already on moderately-size inputs.

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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th