2,116 research outputs found
Blind extraction of an exoplanetary spectrum through Independent Component Analysis
Blind-source separation techniques are used to extract the transmission
spectrum of the hot-Jupiter HD189733b recorded by the Hubble/NICMOS instrument.
Such a 'blind' analysis of the data is based on the concept of independent
component analysis. The de-trending of Hubble/NICMOS data using the sole
assumption that nongaussian systematic noise is statistically independent from
the desired light-curve signals is presented. By not assuming any prior, nor
auxiliary information but the data themselves, it is shown that spectroscopic
errors only about 10 - 30% larger than parametric methods can be obtained for
11 spectral bins with bin sizes of ~0.09 microns. This represents a reasonable
trade-off between a higher degree of objectivity for the non-parametric methods
and smaller standard errors for the parametric de-trending. Results are
discussed in the light of previous analyses published in the literature. The
fact that three very different analysis techniques yield comparable spectra is
a strong indication of the stability of these results.Comment: ApJ accepte
Adaptive Data Depth via Multi-Armed Bandits
Data depth, introduced by Tukey (1975), is an important tool in data science,
robust statistics, and computational geometry. One chief barrier to its broader
practical utility is that many common measures of depth are computationally
intensive, requiring on the order of operations to exactly compute the
depth of a single point within a data set of points in -dimensional
space. Often however, we are not directly interested in the absolute depths of
the points, but rather in their relative ordering. For example, we may want to
find the most central point in a data set (a generalized median), or to
identify and remove all outliers (points on the fringe of the data set with low
depth). With this observation, we develop a novel and instance-adaptive
algorithm for adaptive data depth computation by reducing the problem of
exactly computing depths to an -armed stochastic multi-armed bandit
problem which we can efficiently solve. We focus our exposition on simplicial
depth, developed by Liu (1990), which has emerged as a promising notion of
depth due to its interpretability and asymptotic properties. We provide general
instance-dependent theoretical guarantees for our proposed algorithms, which
readily extend to many other common measures of data depth including majority
depth, Oja depth, and likelihood depth. When specialized to the case where the
gaps in the data follow a power law distribution with parameter , we
show that we can reduce the complexity of identifying the deepest point in the
data set (the simplicial median) from to
, where suppresses logarithmic
factors. We corroborate our theoretical results with numerical experiments on
synthetic data, showing the practical utility of our proposed methods.Comment: Keywords: multi-armed bandits, data depth, adaptivity, large-scale
computation, simplicial dept
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