36,462 research outputs found
A survey on rotation optimization in structure from motion
We consider the problem of robust rotation optimization
in Structure from Motion applications. A number of different
approaches have been recently proposed, with solutions that
are at times incompatible, and at times complementary. The
goal of this paper is to survey and compare these ideas in a
unified manner, and to benchmark their robustness against
the presence of outliers. In all, we have tested more than
forty variants of a these methods (including novel ones), and
we find the best performing combination.NSFDGE-0966142 (IGERT), NSF-IIS-1317788, NSF-IIP-1439681 (I/UCRC), NSF-IIS-1426840, ARL MAST-CTA W911NF-08-2-0004, ARL RCTA W911NF-10-2-0016, ONR N000141310778
Bayesian Restricted Likelihood Methods: Conditioning on Insufficient Statistics in Bayesian Regression
Bayesian methods have proven themselves to be successful across a wide range
of scientific problems and have many well-documented advantages over competing
methods. However, these methods run into difficulties for two major and
prevalent classes of problems: handling data sets with outliers and dealing
with model misspecification. We outline the drawbacks of previous solutions to
both of these problems and propose a new method as an alternative. When working
with the new method, the data is summarized through a set of insufficient
statistics, targeting inferential quantities of interest, and the prior
distribution is updated with the summary statistics rather than the complete
data. By careful choice of conditioning statistics, we retain the main benefits
of Bayesian methods while reducing the sensitivity of the analysis to features
of the data not captured by the conditioning statistics. For reducing
sensitivity to outliers, classical robust estimators (e.g., M-estimators) are
natural choices for conditioning statistics. A major contribution of this work
is the development of a data augmented Markov chain Monte Carlo (MCMC)
algorithm for the linear model and a large class of summary statistics. We
demonstrate the method on simulated and real data sets containing outliers and
subject to model misspecification. Success is manifested in better predictive
performance for data points of interest as compared to competing methods
Robustness to outliers in location-scale parameter model using log-regularly varying distributions
Estimating the location and scale parameters is common in statistics, using,
for instance, the well-known sample mean and standard deviation. However,
inference can be contaminated by the presence of outliers if modeling is done
with light-tailed distributions such as the normal distribution. In this paper,
we study robustness to outliers in location-scale parameter models using both
the Bayesian and frequentist approaches. We find sufficient conditions (e.g.,
on tail behavior of the model) to obtain whole robustness to outliers, in the
sense that the impact of the outliers gradually decreases to nothing as the
conflict grows infinitely. To this end, we introduce the family of
log-Pareto-tailed symmetric distributions that belongs to the larger family of
log-regularly varying distributions.Comment: Published at http://dx.doi.org/10.1214/15-AOS1316 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Taming outliers in pulsar-timing datasets with hierarchical likelihoods and Hamiltonian sampling
Pulsar-timing datasets have been analyzed with great success using
probabilistic treatments based on Gaussian distributions, with applications
ranging from studies of neutron-star structure to tests of general relativity
and searches for nanosecond gravitational waves. As for other applications of
Gaussian distributions, outliers in timing measurements pose a significant
challenge to statistical inference, since they can bias the estimation of
timing and noise parameters, and affect reported parameter uncertainties. We
describe and demonstrate a practical end-to-end approach to perform Bayesian
inference of timing and noise parameters robustly in the presence of outliers,
and to identify these probabilistically. The method is fully consistent (i.e.,
outlier-ness probabilities vary in tune with the posterior distributions of the
timing and noise parameters), and it relies on the efficient sampling of the
hierarchical form of the pulsar-timing likelihood. Such sampling has recently
become possible with a "no-U-turn" Hamiltonian sampler coupled to a highly
customized reparametrization of the likelihood; this code is described
elsewhere, but it is already available online. We recommend our method as a
standard step in the preparation of pulsar-timing-array datasets: even if
statistical inference is not affected, follow-up studies of outlier candidates
can reveal unseen problems in radio observations and timing measurements;
furthermore, confidence in the results of gravitational-wave searches will only
benefit from stringent statistical evidence that datasets are clean and
outlier-free.Comment: 6 pages, 2 figures, RevTeX 4.
Modeling Perceptual Aliasing in SLAM via Discrete-Continuous Graphical Models
Perceptual aliasing is one of the main causes of failure for Simultaneous
Localization and Mapping (SLAM) systems operating in the wild. Perceptual
aliasing is the phenomenon where different places generate a similar visual
(or, in general, perceptual) footprint. This causes spurious measurements to be
fed to the SLAM estimator, which typically results in incorrect localization
and mapping results. The problem is exacerbated by the fact that those outliers
are highly correlated, in the sense that perceptual aliasing creates a large
number of mutually-consistent outliers. Another issue stems from the fact that
most state-of-the-art techniques rely on a given trajectory guess (e.g., from
odometry) to discern between inliers and outliers and this makes the resulting
pipeline brittle, since the accumulation of error may result in incorrect
choices and recovery from failures is far from trivial. This work provides a
unified framework to model perceptual aliasing in SLAM and provides practical
algorithms that can cope with outliers without relying on any initial guess. We
present two main contributions. The first is a Discrete-Continuous Graphical
Model (DC-GM) for SLAM: the continuous portion of the DC-GM captures the
standard SLAM problem, while the discrete portion describes the selection of
the outliers and models their correlation. The second contribution is a
semidefinite relaxation to perform inference in the DC-GM that returns
estimates with provable sub-optimality guarantees. Experimental results on
standard benchmarking datasets show that the proposed technique compares
favorably with state-of-the-art methods while not relying on an initial guess
for optimization.Comment: 13 pages, 14 figures, 1 tabl
Bayesian outlier detection in Capital Asset Pricing Model
We propose a novel Bayesian optimisation procedure for outlier detection in
the Capital Asset Pricing Model. We use a parametric product partition model to
robustly estimate the systematic risk of an asset. We assume that the returns
follow independent normal distributions and we impose a partition structure on
the parameters of interest. The partition structure imposed on the parameters
induces a corresponding clustering of the returns. We identify via an
optimisation procedure the partition that best separates standard observations
from the atypical ones. The methodology is illustrated with reference to a real
data set, for which we also provide a microeconomic interpretation of the
detected outliers
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