2,082 research outputs found
Kullback-Leibler aggregation and misspecified generalized linear models
In a regression setup with deterministic design, we study the pure
aggregation problem and introduce a natural extension from the Gaussian
distribution to distributions in the exponential family. While this extension
bears strong connections with generalized linear models, it does not require
identifiability of the parameter or even that the model on the systematic
component is true. It is shown that this problem can be solved by constrained
and/or penalized likelihood maximization and we derive sharp oracle
inequalities that hold both in expectation and with high probability. Finally
all the bounds are proved to be optimal in a minimax sense.Comment: Published in at http://dx.doi.org/10.1214/11-AOS961 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Bregman Voronoi Diagrams: Properties, Algorithms and Applications
The Voronoi diagram of a finite set of objects is a fundamental geometric
structure that subdivides the embedding space into regions, each region
consisting of the points that are closer to a given object than to the others.
We may define many variants of Voronoi diagrams depending on the class of
objects, the distance functions and the embedding space. In this paper, we
investigate a framework for defining and building Voronoi diagrams for a broad
class of distance functions called Bregman divergences. Bregman divergences
include not only the traditional (squared) Euclidean distance but also various
divergence measures based on entropic functions. Accordingly, Bregman Voronoi
diagrams allow to define information-theoretic Voronoi diagrams in statistical
parametric spaces based on the relative entropy of distributions. We define
several types of Bregman diagrams, establish correspondences between those
diagrams (using the Legendre transformation), and show how to compute them
efficiently. We also introduce extensions of these diagrams, e.g. k-order and
k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set
of points and their connexion with Bregman Voronoi diagrams. We show that these
triangulations capture many of the properties of the celebrated Delaunay
triangulation. Finally, we give some applications of Bregman Voronoi diagrams
which are of interest in the context of computational geometry and machine
learning.Comment: Extend the proceedings abstract of SODA 2007 (46 pages, 15 figures
Quantifying tensions in cosmological parameters: Interpreting the DES evidence ratio
We provide a new interpretation for the Bayes factor combination used in the
Dark Energy Survey (DES) first year analysis to quantify the tension between
the DES and Planck datasets. The ratio quantifies a Bayesian confidence in our
ability to combine the datasets. This interpretation is prior-dependent, with
wider prior widths boosting the confidence. We therefore propose that if there
are any reasonable priors which reduce the confidence to below unity, then we
cannot assert that the datasets are compatible. Computing the evidence ratios
for the DES first year analysis and Planck, given that narrower priors drop the
confidence to below unity, we conclude that DES and Planck are, in a Bayesian
sense, incompatible under LCDM. Additionally we compute ratios which confirm
the consensus that measurements of the acoustic scale by the Baryon Oscillation
Spectroscopic Survey (SDSS) are compatible with Planck, whilst direct
measurements of the acceleration rate of the Universe by the SHOES
collaboration are not. We propose a modification to the Bayes ratio which
removes the prior dependency using Kullback-Leibler divergences, and using this
statistical test find Planck in strong tension with SHOES, in moderate tension
with DES, and in no tension with SDSS. We propose this statistic as the optimal
way to compare datasets, ahead of the next DES data releases, as well as future
surveys. Finally, as an element of these calculations, we introduce in a
cosmological setting the Bayesian model dimensionality, which is a
parameterisation-independent measure of the number of parameters that a given
dataset constrains.Comment: 16 pages, 9 figures. v2 & v3: updates post peer-review. v4:
typographical correction to the reported errors in the log S column of Table
II. v5: typographical correction to equation 2
Exploring Human Vision Driven Features for Pedestrian Detection
Motivated by the center-surround mechanism in the human visual attention
system, we propose to use average contrast maps for the challenge of pedestrian
detection in street scenes due to the observation that pedestrians indeed
exhibit discriminative contrast texture. Our main contributions are first to
design a local, statistical multi-channel descriptorin order to incorporate
both color and gradient information. Second, we introduce a multi-direction and
multi-scale contrast scheme based on grid-cells in order to integrate
expressive local variations. Contributing to the issue of selecting most
discriminative features for assessing and classification, we perform extensive
comparisons w.r.t. statistical descriptors, contrast measurements, and scale
structures. This way, we obtain reasonable results under various
configurations. Empirical findings from applying our optimized detector on the
INRIA and Caltech pedestrian datasets show that our features yield
state-of-the-art performance in pedestrian detection.Comment: Accepted for publication in IEEE Transactions on Circuits and Systems
for Video Technology (TCSVT
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