4,584 research outputs found
Penalized Likelihood and Bayesian Function Selection in Regression Models
Challenging research in various fields has driven a wide range of
methodological advances in variable selection for regression models with
high-dimensional predictors. In comparison, selection of nonlinear functions in
models with additive predictors has been considered only more recently. Several
competing suggestions have been developed at about the same time and often do
not refer to each other. This article provides a state-of-the-art review on
function selection, focusing on penalized likelihood and Bayesian concepts,
relating various approaches to each other in a unified framework. In an
empirical comparison, also including boosting, we evaluate several methods
through applications to simulated and real data, thereby providing some
guidance on their performance in practice
Regularization and Bayesian Learning in Dynamical Systems: Past, Present and Future
Regularization and Bayesian methods for system identification have been
repopularized in the recent years, and proved to be competitive w.r.t.
classical parametric approaches. In this paper we shall make an attempt to
illustrate how the use of regularization in system identification has evolved
over the years, starting from the early contributions both in the Automatic
Control as well as Econometrics and Statistics literature. In particular we
shall discuss some fundamental issues such as compound estimation problems and
exchangeability which play and important role in regularization and Bayesian
approaches, as also illustrated in early publications in Statistics. The
historical and foundational issues will be given more emphasis (and space), at
the expense of the more recent developments which are only briefly discussed.
The main reason for such a choice is that, while the recent literature is
readily available, and surveys have already been published on the subject, in
the author's opinion a clear link with past work had not been completely
clarified.Comment: Plenary Presentation at the IFAC SYSID 2015. Submitted to Annual
Reviews in Contro
Semiparametric Bayesian models for human brain mapping
Functional magnetic resonance imaging (fMRI) has led to enormous progress in human brain mapping. Adequate analysis of the massive spatiotemporal data sets generated by this imaging technique, combining parametric and non-parametric components, imposes challenging problems in statistical modelling. Complex hierarchical Bayesian models in combination with computer-intensive Markov chain Monte Carlo inference are promising tools.The purpose of this paper is twofold. First, it provides a review of general semiparametric Bayesian models for the analysis of fMRI data. Most approaches focus on important but separate temporal or spatial aspects of the overall problem, or they proceed by stepwise procedures. Therefore, as a second aim, we suggest a complete spatiotemporal model for analysing fMRI data within a unified semiparametric Bayesian framework. An application to data from a visual stimulation experiment illustrates our approach and demonstrates its computational feasibility
A Joint 3D-2D based Method for Free Space Detection on Roads
In this paper, we address the problem of road segmentation and free space
detection in the context of autonomous driving. Traditional methods either use
3-dimensional (3D) cues such as point clouds obtained from LIDAR, RADAR or
stereo cameras or 2-dimensional (2D) cues such as lane markings, road
boundaries and object detection. Typical 3D point clouds do not have enough
resolution to detect fine differences in heights such as between road and
pavement. Image based 2D cues fail when encountering uneven road textures such
as due to shadows, potholes, lane markings or road restoration. We propose a
novel free road space detection technique combining both 2D and 3D cues. In
particular, we use CNN based road segmentation from 2D images and plane/box
fitting on sparse depth data obtained from SLAM as priors to formulate an
energy minimization using conditional random field (CRF), for road pixels
classification. While the CNN learns the road texture and is unaffected by
depth boundaries, the 3D information helps in overcoming texture based
classification failures. Finally, we use the obtained road segmentation with
the 3D depth data from monocular SLAM to detect the free space for the
navigation purposes. Our experiments on KITTI odometry dataset, Camvid dataset,
as well as videos captured by us, validate the superiority of the proposed
approach over the state of the art.Comment: Accepted for publication at IEEE WACV 201
Maximum Entropy Vector Kernels for MIMO system identification
Recent contributions have framed linear system identification as a
nonparametric regularized inverse problem. Relying on -type
regularization which accounts for the stability and smoothness of the impulse
response to be estimated, these approaches have been shown to be competitive
w.r.t classical parametric methods. In this paper, adopting Maximum Entropy
arguments, we derive a new penalty deriving from a vector-valued
kernel; to do so we exploit the structure of the Hankel matrix, thus
controlling at the same time complexity, measured by the McMillan degree,
stability and smoothness of the identified models. As a special case we recover
the nuclear norm penalty on the squared block Hankel matrix. In contrast with
previous literature on reweighted nuclear norm penalties, our kernel is
described by a small number of hyper-parameters, which are iteratively updated
through marginal likelihood maximization; constraining the structure of the
kernel acts as a (hyper)regularizer which helps controlling the effective
degrees of freedom of our estimator. To optimize the marginal likelihood we
adapt a Scaled Gradient Projection (SGP) algorithm which is proved to be
significantly computationally cheaper than other first and second order
off-the-shelf optimization methods. The paper also contains an extensive
comparison with many state-of-the-art methods on several Monte-Carlo studies,
which confirms the effectiveness of our procedure
Image Reconstruction in Optical Interferometry
This tutorial paper describes the problem of image reconstruction from
interferometric data with a particular focus on the specific problems
encountered at optical (visible/IR) wavelengths. The challenging issues in
image reconstruction from interferometric data are introduced in the general
framework of inverse problem approach. This framework is then used to describe
existing image reconstruction algorithms in radio interferometry and the new
methods specifically developed for optical interferometry.Comment: accepted for publication in IEEE Signal Processing Magazin
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