140,016 research outputs found
Asymptotic normality of the Parzen-Rosenblatt density estimator for strongly mixing random fields
We prove the asymptotic normality of the kernel density estimator (introduced
by Rosenblatt (1956) and Parzen (1962)) in the context of stationary strongly
mixing random fields. Our approach is based on the Lindeberg's method rather
than on Bernstein's small-block-large-block technique and coupling arguments
widely used in previous works on nonparametric estimation for spatial
processes. Our method allows us to consider only minimal conditions on the
bandwidth parameter and provides a simple criterion on the (non-uniform) strong
mixing coefficients which do not depend on the bandwith.Comment: 16 page
Consistent estimation of the basic neighborhood of Markov random fields
For Markov random fields on with finite state space, we
address the statistical estimation of the basic neighborhood, the smallest
region that determines the conditional distribution at a site on the condition
that the values at all other sites are given. A modification of the Bayesian
Information Criterion, replacing likelihood by pseudo-likelihood, is proved to
provide strongly consistent estimation from observing a realization of the
field on increasing finite regions: the estimated basic neighborhood equals the
true one eventually almost surely, not assuming any prior bound on the size of
the latter. Stationarity of the Markov field is not required, and phase
transition does not affect the results.Comment: Published at http://dx.doi.org/10.1214/009053605000000912 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Hidden Gibbs random fields model selection using Block Likelihood Information Criterion
Performing model selection between Gibbs random fields is a very challenging
task. Indeed, due to the Markovian dependence structure, the normalizing
constant of the fields cannot be computed using standard analytical or
numerical methods. Furthermore, such unobserved fields cannot be integrated out
and the likelihood evaluztion is a doubly intractable problem. This forms a
central issue to pick the model that best fits an observed data. We introduce a
new approximate version of the Bayesian Information Criterion. We partition the
lattice into continuous rectangular blocks and we approximate the probability
measure of the hidden Gibbs field by the product of some Gibbs distributions
over the blocks. On that basis, we estimate the likelihood and derive the Block
Likelihood Information Criterion (BLIC) that answers model choice questions
such as the selection of the dependency structure or the number of latent
states. We study the performances of BLIC for those questions. In addition, we
present a comparison with ABC algorithms to point out that the novel criterion
offers a better trade-off between time efficiency and reliable results
Modeling heterogeneity in random graphs through latent space models: a selective review
We present a selective review on probabilistic modeling of heterogeneity in
random graphs. We focus on latent space models and more particularly on
stochastic block models and their extensions that have undergone major
developments in the last five years
Exploring Context with Deep Structured models for Semantic Segmentation
State-of-the-art semantic image segmentation methods are mostly based on
training deep convolutional neural networks (CNNs). In this work, we proffer to
improve semantic segmentation with the use of contextual information. In
particular, we explore `patch-patch' context and `patch-background' context in
deep CNNs. We formulate deep structured models by combining CNNs and
Conditional Random Fields (CRFs) for learning the patch-patch context between
image regions. Specifically, we formulate CNN-based pairwise potential
functions to capture semantic correlations between neighboring patches.
Efficient piecewise training of the proposed deep structured model is then
applied in order to avoid repeated expensive CRF inference during the course of
back propagation. For capturing the patch-background context, we show that a
network design with traditional multi-scale image inputs and sliding pyramid
pooling is very effective for improving performance. We perform comprehensive
evaluation of the proposed method. We achieve new state-of-the-art performance
on a number of challenging semantic segmentation datasets including ,
-, , -, -,
-, and datasets. Particularly, we report an
intersection-over-union score of on the - dataset.Comment: 16 pages. Accepted to IEEE T. Pattern Analysis & Machine
Intelligence, 2017. Extended version of arXiv:1504.0101
Multi-Context Attention for Human Pose Estimation
In this paper, we propose to incorporate convolutional neural networks with a
multi-context attention mechanism into an end-to-end framework for human pose
estimation. We adopt stacked hourglass networks to generate attention maps from
features at multiple resolutions with various semantics. The Conditional Random
Field (CRF) is utilized to model the correlations among neighboring regions in
the attention map. We further combine the holistic attention model, which
focuses on the global consistency of the full human body, and the body part
attention model, which focuses on the detailed description for different body
parts. Hence our model has the ability to focus on different granularity from
local salient regions to global semantic-consistent spaces. Additionally, we
design novel Hourglass Residual Units (HRUs) to increase the receptive field of
the network. These units are extensions of residual units with a side branch
incorporating filters with larger receptive fields, hence features with various
scales are learned and combined within the HRUs. The effectiveness of the
proposed multi-context attention mechanism and the hourglass residual units is
evaluated on two widely used human pose estimation benchmarks. Our approach
outperforms all existing methods on both benchmarks over all the body parts.Comment: The first two authors contribute equally to this wor
Discriminative Training of Deep Fully-connected Continuous CRF with Task-specific Loss
Recent works on deep conditional random fields (CRF) have set new records on
many vision tasks involving structured predictions. Here we propose a
fully-connected deep continuous CRF model for both discrete and continuous
labelling problems. We exemplify the usefulness of the proposed model on
multi-class semantic labelling (discrete) and the robust depth estimation
(continuous) problems.
In our framework, we model both the unary and the pairwise potential
functions as deep convolutional neural networks (CNN), which are jointly
learned in an end-to-end fashion. The proposed method possesses the main
advantage of continuously-valued CRF, which is a closed-form solution for the
Maximum a posteriori (MAP) inference.
To better adapt to different tasks, instead of using the commonly employed
maximum likelihood CRF parameter learning protocol, we propose task-specific
loss functions for learning the CRF parameters.
It enables direct optimization of the quality of the MAP estimates during the
course of learning.
Specifically, we optimize the multi-class classification loss for the
semantic labelling task and the Turkey's biweight loss for the robust depth
estimation problem.
Experimental results on the semantic labelling and robust depth estimation
tasks demonstrate that the proposed method compare favorably against both
baseline and state-of-the-art methods.
In particular, we show that although the proposed deep CRF model is
continuously valued, with the equipment of task-specific loss, it achieves
impressive results even on discrete labelling tasks
Structural Equation Modeling and simultaneous clustering through the Partial Least Squares algorithm
The identification of different homogeneous groups of observations and their
appropriate analysis in PLS-SEM has become a critical issue in many appli-
cation fields. Usually, both SEM and PLS-SEM assume the homogeneity of all
units on which the model is estimated, and approaches of segmentation present
in literature, consist in estimating separate models for each segments of
statistical units, which have been obtained either by assigning the units to
segments a priori defined. However, these approaches are not fully accept- able
because no causal structure among the variables is postulated. In other words,
a modeling approach should be used, where the obtained clusters are homogeneous
with respect to the structural causal relationships. In this paper, a new
methodology for simultaneous non-hierarchical clus- tering and PLS-SEM is
proposed. This methodology is motivated by the fact that the sequential
approach of applying first SEM or PLS-SEM and second the clustering algorithm
such as K-means on the latent scores of the SEM/PLS-SEM may fail to find the
correct clustering structure existing in the data. A simulation study and an
application on real data are included to evaluate the performance of the
proposed methodology
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