67,556 research outputs found
Classification of chirp signals using hierarchical bayesian learning and MCMC methods
This paper addresses the problem of classifying chirp signals using hierarchical Bayesian learning together with Markov chain Monte Carlo (MCMC) methods. Bayesian learning consists of estimating the distribution of the observed data conditional on each class from a set of training samples. Unfortunately, this estimation requires to evaluate intractable multidimensional integrals. This paper studies an original implementation of hierarchical Bayesian learning that estimates the class conditional probability densities using MCMC methods. The performance of this implementation is first studied via an academic example for which the class conditional densities are known. The problem of classifying chirp signals is then addressed by using a similar hierarchical Bayesian learning implementation based on a Metropolis-within-Gibbs algorithm
A Hierarchical Bayesian Model for Frame Representation
In many signal processing problems, it may be fruitful to represent the
signal under study in a frame. If a probabilistic approach is adopted, it
becomes then necessary to estimate the hyper-parameters characterizing the
probability distribution of the frame coefficients. This problem is difficult
since in general the frame synthesis operator is not bijective. Consequently,
the frame coefficients are not directly observable. This paper introduces a
hierarchical Bayesian model for frame representation. The posterior
distribution of the frame coefficients and model hyper-parameters is derived.
Hybrid Markov Chain Monte Carlo algorithms are subsequently proposed to sample
from this posterior distribution. The generated samples are then exploited to
estimate the hyper-parameters and the frame coefficients of the target signal.
Validation experiments show that the proposed algorithms provide an accurate
estimation of the frame coefficients and hyper-parameters. Application to
practical problems of image denoising show the impact of the resulting Bayesian
estimation on the recovered signal quality
Deep Gaussian Mixture Models
Deep learning is a hierarchical inference method formed by subsequent
multiple layers of learning able to more efficiently describe complex
relationships. In this work, Deep Gaussian Mixture Models are introduced and
discussed. A Deep Gaussian Mixture model (DGMM) is a network of multiple layers
of latent variables, where, at each layer, the variables follow a mixture of
Gaussian distributions. Thus, the deep mixture model consists of a set of
nested mixtures of linear models, which globally provide a nonlinear model able
to describe the data in a very flexible way. In order to avoid
overparameterized solutions, dimension reduction by factor models can be
applied at each layer of the architecture thus resulting in deep mixtures of
factor analysers.Comment: 19 pages, 4 figure
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