83,329 research outputs found
High-Dimensional Density Ratio Estimation with Extensions to Approximate Likelihood Computation
The ratio between two probability density functions is an important component
of various tasks, including selection bias correction, novelty detection and
classification. Recently, several estimators of this ratio have been proposed.
Most of these methods fail if the sample space is high-dimensional, and hence
require a dimension reduction step, the result of which can be a significant
loss of information. Here we propose a simple-to-implement, fully nonparametric
density ratio estimator that expands the ratio in terms of the eigenfunctions
of a kernel-based operator; these functions reflect the underlying geometry of
the data (e.g., submanifold structure), often leading to better estimates
without an explicit dimension reduction step. We show how our general framework
can be extended to address another important problem, the estimation of a
likelihood function in situations where that function cannot be
well-approximated by an analytical form. One is often faced with this situation
when performing statistical inference with data from the sciences, due the
complexity of the data and of the processes that generated those data. We
emphasize applications where using existing likelihood-free methods of
inference would be challenging due to the high dimensionality of the sample
space, but where our spectral series method yields a reasonable estimate of the
likelihood function. We provide theoretical guarantees and illustrate the
effectiveness of our proposed method with numerical experiments.Comment: With supplementary materia
A Wavelet-Based Algorithm for the Spatial Analysis of Poisson Data
Wavelets are scaleable, oscillatory functions that deviate from zero only
within a limited spatial regime and have average value zero. In addition to
their use as source characterizers, wavelet functions are rapidly gaining
currency within the source detection field. Wavelet-based source detection
involves the correlation of scaled wavelet functions with binned,
two-dimensional image data. If the chosen wavelet function exhibits the
property of vanishing moments, significantly non-zero correlation coefficients
will be observed only where there are high-order variations in the data; e.g.,
they will be observed in the vicinity of sources.
In this paper, we describe the mission-independent, wavelet-based source
detection algorithm WAVDETECT, part of the CIAO software package. Aspects of
our algorithm include: (1) the computation of local, exposure-corrected
normalized (i.e. flat-fielded) background maps; (2) the correction for exposure
variations within the field-of-view; (3) its applicability within the
low-counts regime, as it does not require a minimum number of background counts
per pixel for the accurate computation of source detection thresholds; (4) the
generation of a source list in a manner that does not depend upon a detailed
knowledge of the point spread function (PSF) shape; and (5) error analysis.
These features make our algorithm considerably more general than previous
methods developed for the analysis of X-ray image data, especially in the low
count regime. We demonstrate the algorithm's robustness by applying it to
various images.Comment: Accepted for publication in Ap. J. Supp. (v. 138 Jan. 2002). 61
pages, 23 figures, expands to 3.8 Mb. Abstract abridged for astro-ph
submissio
A Modified Cross Correlation Algorithm for Reference-free Image Alignment of Non-Circular Projections in Single-Particle Electron Microscopy
In this paper we propose a modified cross correlation method to align images
from the same class in single-particle electron microscopy of highly
non-spherical structures. In this new method, First we coarsely align
projection images, and then re-align the resulting images using the cross
correlation (CC) method. The coarse alignment is obtained by matching the
centers of mass and the principal axes of the images. The distribution of
misalignment in this coarse alignment can be quantified based on the
statistical properties of the additive background noise. As a consequence, the
search space for re-alignment in the cross correlation method can be reduced to
achieve better alignment. In order to overcome problems associated with false
peaks in the cross correlations function, we use artificially blurred images
for the early stage of the iterative cross correlation method and segment the
intermediate class average from every iteration step. These two additional
manipulations combined with the reduced search space size in the cross
correlation method yield better alignments for low signal-to-noise ratio images
than both classical cross correlation and maximum likelihood(ML) methods.Comment: 29page
Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape
Lobe dynamics and escape from a potential well are general frameworks
introduced to study phase space transport in chaotic dynamical systems. While
the former approach studies how regions of phase space are transported by
reducing the flow to a two-dimensional map, the latter approach studies the
phase space structures that lead to critical events by crossing periodic orbit
around saddles. Both of these frameworks require computation with curves
represented by millions of points-computing intersection points between these
curves and area bounded by the segments of these curves-for quantifying the
transport and escape rate. We present a theory for computing these intersection
points and the area bounded between the segments of these curves based on a
classification of the intersection points using equivalence class. We also
present an alternate theory for curves with nontransverse intersections and a
method to increase the density of points on the curves for locating the
intersection points accurately.The numerical implementation of the theory
presented herein is available as an open source software called Lober. We used
this package to demonstrate the application of the theory to lobe dynamics that
arises in fluid mechanics, and rate of escape from a potential well that arises
in ship dynamics.Comment: 33 pages, 17 figure
ADAM: a general method for using various data types in asteroid reconstruction
We introduce ADAM, the All-Data Asteroid Modelling algorithm. ADAM is simple
and universal since it handles all disk-resolved data types (adaptive optics or
other images, interferometry, and range-Doppler radar data) in a uniform manner
via the 2D Fourier transform, enabling fast convergence in model optimization.
The resolved data can be combined with disk-integrated data (photometry). In
the reconstruction process, the difference between each data type is only a few
code lines defining the particular generalized projection from 3D onto a 2D
image plane. Occultation timings can be included as sparse silhouettes, and
thermal infrared data are efficiently handled with an approximate algorithm
that is sufficient in practice due to the dominance of the high-contrast
(boundary) pixels over the low-contrast (interior) ones. This is of particular
importance to the raw ALMA data that can be directly handled by ADAM without
having to construct the standard image. We study the reliability of the
inversion by using the independent shape supports of function series and
control-point surfaces. When other data are lacking, one can carry out fast
nonconvex lightcurve-only inversion, but any shape models resulting from it
should only be taken as illustrative global-scale ones.Comment: 11 pages, submitted to A&
Query by String word spotting based on character bi-gram indexing
In this paper we propose a segmentation-free query by string word spotting
method. Both the documents and query strings are encoded using a recently
proposed word representa- tion that projects images and strings into a common
atribute space based on a pyramidal histogram of characters(PHOC). These
attribute models are learned using linear SVMs over the Fisher Vector
representation of the images along with the PHOC labels of the corresponding
strings. In order to search through the whole page, document regions are
indexed per character bi- gram using a similar attribute representation. On top
of that, we propose an integral image representation of the document using a
simplified version of the attribute model for efficient computation. Finally we
introduce a re-ranking step in order to boost retrieval performance. We show
state-of-the-art results for segmentation-free query by string word spotting in
single-writer and multi-writer standard datasetsComment: To be published in ICDAR201
The cause of spatial structure in solar He I 1083 nm multiplet images
Context. The He i 1083 nm is a powerful diagnostic for inferring properties
of the upper solar chromosphere, in particular for the magnetic field. The
basic formation of the line in one-dimensional models is well understood, but
the influence of the complex 3D structure of the chromosphere and corona has
however never been investigated. This structure must play an essential role
because images taken in He i 1083 nm show structures with widths down to 100
km. Aims. To understand the effect of the three-dimensional temperature and
density structure in the solar atmosphere on the formation of the He i 1083 nm
line. Methods. We solve the non-LTE radiative transfer problem assuming
statistical equilibrium for a simple 9-level helium atom that nevertheless
captures all essential physics. As a model atmosphere we use a snapshot from a
3D radiation-MHD simulation computed with the Bifrost code. Ionising radiation
from the corona is self-consistently taken into account. Results. The emergent
intensity in the He i 1083 nm is set by the source function and the opacity in
the upper chromosphere. The former is dominated by scattering of photospheric
radiation and does not vary much with spatial location. The latter is
determined by the photonionisation rate in the He i ground state continuum, as
well as the electron density in the chromosphere. The spatial variation of the
flux of ionising radiation is caused by the spatially-structured emissivity of
the ionising photons from material at T = 100 kK in the transition region. The
hotter coronal material produces more ionising photons, but the resulting
radiation field is smooth and does not lead to small-scale variation of the UV
flux. The corrugation of the transition region further increases the spatial
variation of the amount of UV radiation in the chromosphere.Comment: Accepted for publication by A&
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