68,901 research outputs found
Distributed estimation from relative measurements of heterogeneous and uncertain quality
This paper studies the problem of estimation from relative measurements in a
graph, in which a vector indexed over the nodes has to be reconstructed from
pairwise measurements of differences between its components associated to nodes
connected by an edge. In order to model heterogeneity and uncertainty of the
measurements, we assume them to be affected by additive noise distributed
according to a Gaussian mixture. In this original setup, we formulate the
problem of computing the Maximum-Likelihood (ML) estimates and we design two
novel algorithms, based on Least Squares regression and
Expectation-Maximization (EM). The first algorithm (LS- EM) is centralized and
performs the estimation from relative measurements, the soft classification of
the measurements, and the estimation of the noise parameters. The second
algorithm (Distributed LS-EM) is distributed and performs estimation and soft
classification of the measurements, but requires the knowledge of the noise
parameters. We provide rigorous proofs of convergence of both algorithms and we
present numerical experiments to evaluate and compare their performance with
classical solutions. The experiments show the robustness of the proposed
methods against different kinds of noise and, for the Distributed LS-EM,
against errors in the knowledge of noise parameters.Comment: Submitted to IEEE transaction
A new method for the estimation of variance matrix with prescribed zeros in nonlinear mixed effects models
We propose a new method for the Maximum Likelihood Estimator (MLE) of
nonlinear mixed effects models when the variance matrix of Gaussian random
effects has a prescribed pattern of zeros (PPZ). The method consists in
coupling the recently developed Iterative Conditional Fitting (ICF) algorithm
with the Expectation Maximization (EM) algorithm. It provides positive definite
estimates for any sample size, and does not rely on any structural assumption
on the PPZ. It can be easily adapted to many versions of EM.Comment: Accepted for publication in Statistics and Computin
EM Algorithms for Weighted-Data Clustering with Application to Audio-Visual Scene Analysis
Data clustering has received a lot of attention and numerous methods,
algorithms and software packages are available. Among these techniques,
parametric finite-mixture models play a central role due to their interesting
mathematical properties and to the existence of maximum-likelihood estimators
based on expectation-maximization (EM). In this paper we propose a new mixture
model that associates a weight with each observed point. We introduce the
weighted-data Gaussian mixture and we derive two EM algorithms. The first one
considers a fixed weight for each observation. The second one treats each
weight as a random variable following a gamma distribution. We propose a model
selection method based on a minimum message length criterion, provide a weight
initialization strategy, and validate the proposed algorithms by comparing them
with several state of the art parametric and non-parametric clustering
techniques. We also demonstrate the effectiveness and robustness of the
proposed clustering technique in the presence of heterogeneous data, namely
audio-visual scene analysis.Comment: 14 pages, 4 figures, 4 table
A dynamic network model with persistent links and node-specific latent variables, with an application to the interbank market
We propose a dynamic network model where two mechanisms control the
probability of a link between two nodes: (i) the existence or absence of this
link in the past, and (ii) node-specific latent variables (dynamic fitnesses)
describing the propensity of each node to create links. Assuming a Markov
dynamics for both mechanisms, we propose an Expectation-Maximization algorithm
for model estimation and inference of the latent variables. The estimated
parameters and fitnesses can be used to forecast the presence of a link in the
future. We apply our methodology to the e-MID interbank network for which the
two linkage mechanisms are associated with two different trading behaviors in
the process of network formation, namely preferential trading and trading
driven by node-specific characteristics. The empirical results allow to
recognise preferential lending in the interbank market and indicate how a
method that does not account for time-varying network topologies tends to
overestimate preferential linkage.Comment: 19 pages, 6 figure
Construction of Bayesian Deformable Models via Stochastic Approximation Algorithm: A Convergence Study
The problem of the definition and the estimation of generative models based
on deformable templates from raw data is of particular importance for modelling
non aligned data affected by various types of geometrical variability. This is
especially true in shape modelling in the computer vision community or in
probabilistic atlas building for Computational Anatomy (CA). A first coherent
statistical framework modelling the geometrical variability as hidden variables
has been given by Allassonni\`ere, Amit and Trouv\'e (JRSS 2006). Setting the
problem in a Bayesian context they proved the consistency of the MAP estimator
and provided a simple iterative deterministic algorithm with an EM flavour
leading to some reasonable approximations of the MAP estimator under low noise
conditions. In this paper we present a stochastic algorithm for approximating
the MAP estimator in the spirit of the SAEM algorithm. We prove its convergence
to a critical point of the observed likelihood with an illustration on images
of handwritten digits
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