126 research outputs found
Light Propagation in Arbitrary Spacetimes and the Gravitational Lens Approximation
We reformulate the transport equation which determines the size, shape and
orientation of infinitesimal light beams in arbitrary spacetimes. The behaviour
of such light beams near vertices and conjugate points is investigated, with
special attention to the singular behaviour of the optical scalars. We then
specialize the general transport equation to the case of an approximate metric
of an inhomogeneous universe, which is a Friedmann metric `on average' with
superposed isolated weak matter inhomogeneities. In a series of well-defined
approximations, the equations of gravitational lens theory are derived.
Finally, we derive a relative optical focusing equation which describes the
focusing of light beams relative to the case that the beam is unaffected by
matter inhomogeneities in the universe, from which it follows immediately that
no beam can be focused less than one which is unaffected by matter clumps,
before it propagates through its first conjugate point.Comment: 31 pages, uuencoded compressed postscript; preprint MPA 78
Optimizing weak lensing mass estimates for cluster profile uncertainty
Weak lensing measurements of cluster masses are necessary for calibrating
mass-observable relations (MORs) to investigate the growth of structure and the
properties of dark energy. However, the measured cluster shear signal varies at
fixed mass M_200m due to inherent ellipticity of background galaxies,
intervening structures along the line of sight, and variations in the cluster
structure due to scatter in concentrations, asphericity and substructure. We
use N-body simulated halos to derive and evaluate a weak lensing circular
aperture mass measurement M_ap that minimizes the mass estimate variance <(M_ap
- M_200m)^2> in the presence of all these forms of variability. Depending on
halo mass and observational conditions, the resulting mass estimator improves
on M_ap filters optimized for circular NFW-profile clusters in the presence of
uncorrelated large scale structure (LSS) about as much as the latter improve on
an estimator that only minimizes the influence of shape noise. Optimizing for
uncorrelated LSS while ignoring the variation of internal cluster structure
puts too much weight on the profile near the cores of halos, and under some
circumstances can even be worse than not accounting for LSS at all. We briefly
discuss the impact of variability in cluster structure and correlated
structures on the design and performance of weak lensing surveys intended to
calibrate cluster MORs.Comment: 11 pages, 5 figures; accepted by MNRA
Feature importance for machine learning redshifts applied to SDSS galaxies
We present an analysis of importance feature selection applied to photometric
redshift estimation using the machine learning architecture Decision Trees with
the ensemble learning routine Adaboost (hereafter RDF). We select a list of 85
easily measured (or derived) photometric quantities (or `features') and
spectroscopic redshifts for almost two million galaxies from the Sloan Digital
Sky Survey Data Release 10. After identifying which features have the most
predictive power, we use standard artificial Neural Networks (aNN) to show that
the addition of these features, in combination with the standard magnitudes and
colours, improves the machine learning redshift estimate by 18% and decreases
the catastrophic outlier rate by 32%. We further compare the redshift estimate
using RDF with those from two different aNNs, and with photometric redshifts
available from the SDSS. We find that the RDF requires orders of magnitude less
computation time than the aNNs to obtain a machine learning redshift while
reducing both the catastrophic outlier rate by up to 43%, and the redshift
error by up to 25%. When compared to the SDSS photometric redshifts, the RDF
machine learning redshifts both decreases the standard deviation of residuals
scaled by 1/(1+z) by 36% from 0.066 to 0.041, and decreases the fraction of
catastrophic outliers by 57% from 2.32% to 0.99%.Comment: 10 pages, 4 figures, updated to match version accepted in MNRA
Tuning target selection algorithms to improve galaxy redshift estimates
We showcase machine learning (ML) inspired target selection algorithms to
determine which of all potential targets should be selected first for
spectroscopic follow up. Efficient target selection can improve the ML redshift
uncertainties as calculated on an independent sample, while requiring less
targets to be observed. We compare the ML targeting algorithms with the Sloan
Digital Sky Survey (SDSS) target order, and with a random targeting algorithm.
The ML inspired algorithms are constructed iteratively by estimating which of
the remaining target galaxies will be most difficult for the machine learning
methods to accurately estimate redshifts using the previously observed data.
This is performed by predicting the expected redshift error and redshift offset
(or bias) of all of the remaining target galaxies. We find that the predicted
values of bias and error are accurate to better than 10-30% of the true values,
even with only limited training sample sizes. We construct a hypothetical
follow-up survey and find that some of the ML targeting algorithms are able to
obtain the same redshift predictive power with 2-3 times less observing time,
as compared to that of the SDSS, or random, target selection algorithms. The
reduction in the required follow up resources could allow for a change to the
follow-up strategy, for example by obtaining deeper spectroscopy, which could
improve ML redshift estimates for deeper test data.Comment: 16 pages, 9 figures, updated to match MNRAS accepted version. Minor
text changes, results unchange
Anomaly detection for machine learning redshifts applied to SDSS galaxies
We present an analysis of anomaly detection for machine learning redshift
estimation. Anomaly detection allows the removal of poor training examples,
which can adversely influence redshift estimates. Anomalous training examples
may be photometric galaxies with incorrect spectroscopic redshifts, or galaxies
with one or more poorly measured photometric quantity. We select 2.5 million
'clean' SDSS DR12 galaxies with reliable spectroscopic redshifts, and 6730
'anomalous' galaxies with spectroscopic redshift measurements which are flagged
as unreliable. We contaminate the clean base galaxy sample with galaxies with
unreliable redshifts and attempt to recover the contaminating galaxies using
the Elliptical Envelope technique. We then train four machine learning
architectures for redshift analysis on both the contaminated sample and on the
preprocessed 'anomaly-removed' sample and measure redshift statistics on a
clean validation sample generated without any preprocessing. We find an
improvement on all measured statistics of up to 80% when training on the
anomaly removed sample as compared with training on the contaminated sample for
each of the machine learning routines explored. We further describe a method to
estimate the contamination fraction of a base data sample.Comment: 13 pages, 8 figures, 1 table, minor text updates to macth MNRAS
accepted versio
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