45,918 research outputs found
Piecewise linear regularized solution paths
We consider the generic regularized optimization problem
. Efron, Hastie,
Johnstone and Tibshirani [Ann. Statist. 32 (2004) 407--499] have shown that for
the LASSO--that is, if is squared error loss and is
the norm of --the optimal coefficient path is piecewise linear,
that is, is piecewise
constant. We derive a general characterization of the properties of (loss ,
penalty ) pairs which give piecewise linear coefficient paths. Such pairs
allow for efficient generation of the full regularized coefficient paths. We
investigate the nature of efficient path following algorithms which arise. We
use our results to suggest robust versions of the LASSO for regression and
classification, and to develop new, efficient algorithms for existing problems
in the literature, including Mammen and van de Geer's locally adaptive
regression splines.Comment: Published at http://dx.doi.org/10.1214/009053606000001370 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Learning Adaptive Discriminative Correlation Filters via Temporal Consistency Preserving Spatial Feature Selection for Robust Visual Tracking
With efficient appearance learning models, Discriminative Correlation Filter
(DCF) has been proven to be very successful in recent video object tracking
benchmarks and competitions. However, the existing DCF paradigm suffers from
two major issues, i.e., spatial boundary effect and temporal filter
degradation. To mitigate these challenges, we propose a new DCF-based tracking
method. The key innovations of the proposed method include adaptive spatial
feature selection and temporal consistent constraints, with which the new
tracker enables joint spatial-temporal filter learning in a lower dimensional
discriminative manifold. More specifically, we apply structured spatial
sparsity constraints to multi-channel filers. Consequently, the process of
learning spatial filters can be approximated by the lasso regularisation. To
encourage temporal consistency, the filter model is restricted to lie around
its historical value and updated locally to preserve the global structure in
the manifold. Last, a unified optimisation framework is proposed to jointly
select temporal consistency preserving spatial features and learn
discriminative filters with the augmented Lagrangian method. Qualitative and
quantitative evaluations have been conducted on a number of well-known
benchmarking datasets such as OTB2013, OTB50, OTB100, Temple-Colour, UAV123 and
VOT2018. The experimental results demonstrate the superiority of the proposed
method over the state-of-the-art approaches
AN ADAPTIVE COMPOSITE QUANTILE APPROACH TO DIMENSION REDUCTION
Sufficient dimension reduction [Li 1991] has long been a prominent issue in multivariate nonparametric regression analysis. To uncover the central dimension reduction space, we propose in this paper an adaptive composite quantile approach. Compared to existing methods, (1) it requires minimal assumptions and is capable of revealing all dimension reduction directions; (2) it is robust against outliers and (3) it is structure-adaptive, thus more efficient. Asymptotic results are proved and numerical examples are provided, including a real data analysis
Design Issues for Generalized Linear Models: A Review
Generalized linear models (GLMs) have been used quite effectively in the
modeling of a mean response under nonstandard conditions, where discrete as
well as continuous data distributions can be accommodated. The choice of design
for a GLM is a very important task in the development and building of an
adequate model. However, one major problem that handicaps the construction of a
GLM design is its dependence on the unknown parameters of the fitted model.
Several approaches have been proposed in the past 25 years to solve this
problem. These approaches, however, have provided only partial solutions that
apply in only some special cases, and the problem, in general, remains largely
unresolved. The purpose of this article is to focus attention on the
aforementioned dependence problem. We provide a survey of various existing
techniques dealing with the dependence problem. This survey includes
discussions concerning locally optimal designs, sequential designs, Bayesian
designs and the quantile dispersion graph approach for comparing designs for
GLMs.Comment: Published at http://dx.doi.org/10.1214/088342306000000105 in the
Statistical Science (http://www.imstat.org/sts/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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