Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trend Filtering -- I. A Modern Statistical Tool for Time-Domain
  Astronomy and Astronomical Spectroscopy   The problem of denoising a one-dimensional signal possessing varying degrees
of smoothness is ubiquitous in time-domain astronomy and astronomical
spectroscopy. For example, in the time domain, an astronomical object may
exhibit a smoothly varying intensity that is occasionally interrupted by abrupt
dips or spikes. Likewise, in the spectroscopic setting, a noiseless spectrum
typically contains intervals of relative smoothness mixed with localized higher
frequency components such as emission peaks and absorption lines. In this work,
we present trend filtering, a modern nonparametric statistical tool that yields
significant improvements in this broad problem space of denoising $spatially$
$heterogeneous$ signals. When the underlying signal is spatially heterogeneous,
trend filtering is superior to any statistical estimator that is a linear
combination of the observed data---including kernel smoothers, LOESS, smoothing
splines, Gaussian process regression, and many other popular methods.
Furthermore, the trend filtering estimate can be computed with practical and
scalable efficiency via a specialized convex optimization algorithm, e.g.
handling sample sizes of $n\gtrsim10^7$ within a few minutes. In a companion
paper, we explicitly demonstrate the broad utility of trend filtering to
observational astronomy by carrying out a diverse set of spectroscopic and
time-domain analyses.

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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph