Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning a Compressed Sensing Measurement Matrix via Gradient Unrolling   Linear encoding of sparse vectors is widely popular, but is commonly
data-independent -- missing any possible extra (but a priori unknown) structure
beyond sparsity. In this paper we present a new method to learn linear encoders
that adapt to data, while still performing well with the widely used $\ell_1$
decoder. The convex $\ell_1$ decoder prevents gradient propagation as needed in
standard gradient-based training. Our method is based on the insight that
unrolling the convex decoder into $T$ projected subgradient steps can address
this issue. Our method can be seen as a data-driven way to learn a compressed
sensing measurement matrix. We compare the empirical performance of 10
algorithms over 6 sparse datasets (3 synthetic and 3 real). Our experiments
show that there is indeed additional structure beyond sparsity in the real
datasets; our method is able to discover it and exploit it to create excellent
reconstructions with fewer measurements (by a factor of 1.1-3x) compared to the
previous state-of-the-art methods. We illustrate an application of our method
in learning label embeddings for extreme multi-label classification, and
empirically show that our method is able to match or outperform the precision
scores of SLEEC, which is one of the state-of-the-art embedding-based
approaches.

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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol