60 research outputs found
Adaptive Quantizers for Estimation
In this paper, adaptive estimation based on noisy quantized observations is
studied. A low complexity adaptive algorithm using a quantizer with adjustable
input gain and offset is presented. Three possible scalar models for the
parameter to be estimated are considered: constant, Wiener process and Wiener
process with deterministic drift. After showing that the algorithm is
asymptotically unbiased for estimating a constant, it is shown, in the three
cases, that the asymptotic mean squared error depends on the Fisher information
for the quantized measurements. It is also shown that the loss of performance
due to quantization depends approximately on the ratio of the Fisher
information for quantized and continuous measurements. At the end of the paper
the theoretical results are validated through simulation under two different
classes of noise, generalized Gaussian noise and Student's-t noise
Exploring multimodal data fusion through joint decompositions with flexible couplings
A Bayesian framework is proposed to define flexible coupling models for joint
tensor decompositions of multiple data sets. Under this framework, a natural
formulation of the data fusion problem is to cast it in terms of a joint
maximum a posteriori (MAP) estimator. Data driven scenarios of joint posterior
distributions are provided, including general Gaussian priors and non Gaussian
coupling priors. We present and discuss implementation issues of algorithms
used to obtain the joint MAP estimator. We also show how this framework can be
adapted to tackle the problem of joint decompositions of large datasets. In the
case of a conditional Gaussian coupling with a linear transformation, we give
theoretical bounds on the data fusion performance using the Bayesian Cramer-Rao
bound. Simulations are reported for hybrid coupling models ranging from simple
additive Gaussian models, to Gamma-type models with positive variables and to
the coupling of data sets which are inherently of different size due to
different resolution of the measurement devices.Comment: 15 pages, 7 figures, revised versio
Optimal Asymmetric Binary Quantization for Estimation Under Symmetrically Distributed Noise
Estimation of a location parameter based on noisy and binary quantized
measurements is considered in this letter. We study the behavior of the
Cramer-Rao bound as a function of the quantizer threshold for different
symmetric unimodal noise distributions. We show that, in some cases, the
intuitive choice of threshold position given by the symmetry of the problem,
placing the threshold on the true parameter value, can lead to locally worst
estimation performance.Comment: 4 pages, 5 figure
Quantification asymétrique optimale pour l'estimation d'un paramètre de centrage dans un bruit de loi symétrique
Présentation oraleNational audienceNous traitons de l'estimation d'un paramètre de centrage à partir d'observations bruitées quantifiées sur deux niveaux. Le comportement de la BCR (Borne de Cramér-Rao) est étudié en fonction du centrage du quantifieur pour différentes distributions symétriques de bruit. Nous montrons que, contrairement à ce qui est mentionné dans la littérature, l'emplacement optimal du centrage du quantifieur dépend radicalement de la loi de bruit et que son emplacement sur le paramètre de centrage, un choix intuitif vu la symétrie du problème, peut donner la performance d'estimation localement la plus mauvaise
Adjustable Quantizers for Joint Estimation of Location and Scale Parameters
Poster SessionInternational audienceAn adaptive algorithm to estimate jointly unknown location and scale parameters of a sequence of symmetrically distributed independent and identically distributed random variables using quantized measurements from a quantizer with adjustable input gain and input offset is presented. The asymptotic variance of estimation is obtained, simulations under Cauchy and Gaussian distributions are presented to validate the asymptotic results and they are compared to the continuous optimal estimator performance
A Fusion Center Approach for Estimation Using Quantized Measurements
Rapport interne de GIPSA-labA fusion center approach to estimate a constant location parameter using quantized noisy measurements from multiple sensors is presented. The asymptotic estimation performance is obtained and simulations for different numbers of sensors under Gaussian and Cauchy noise are used for validation. A performance comparison under constrained communication bandwidth between a fusion center approach with two low resolution sensors and a high resolution single sensor approach is presented to motivate the use of low resolution sensor networks
Asymptotic Approximation of Optimal Quantizers for Estimation
Poster SessionInternational audienceIn this paper, the asymptotic approximation of the Fisher information for the estimation of a scalar parameter based on quantized measurements is studied. As the number of quantization intervals tends to infinity, it is shown that the loss of Fisher information due to quantization decreases exponentially as a function of the number of quantization bits. The optimal quantization interval density and the corresponding maximum Fisher information are obtained. Comparison between optimal nonuniform and uniform quantization for the location estimation problem indicates that nonuniform quantization is slightly better. At the end of the paper, an adaptive algorithm for jointly estimating and setting the thresholds is used to show that the theoretical results can be approximately obtained in practice
Data Mining by NonNegative Tensor Approximation
International audienceInferring multilinear dependences within multi-way data can be performed by tensor decompositions. Because of the presence of noise or modeling errors, the problem actually requires an approximation of lower rank. We concentrate on the case of real 3-way data arrays with nonnegative values, and propose an unconstrained algorithm resorting to an hyperspherical parameterization implemented in a novel way, and to a global line search. To illustrate the contribution, we report computer experiments allowing to detect and identify toxic molecules in a solvent with the help of fluorescent spectroscopy measurements
Joint Tensor Compression for Coupled Canonical Polyadic Decompositions
International audienceTo deal with large multimodal datasets, coupled canonical polyadic decompositions are used as an approximation model. In this paper, a joint compression scheme is introduced to reduce the dimensions of the dataset. Joint compression allows to solve the approximation problem in a compressed domain using standard coupled decomposition algorithms. Computational complexity required to obtain the coupled decomposition is therefore reduced. Also, we propose to approximate the update of the coupled factor by a simple weighted average of the independent updates of the coupled factors. The proposed approach and its simplified version are tested with synthetic data and we show that both do not incur substantial loss in approximation performance
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