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348
Inferring Parameters and Structure of Latent Variable Models by Variational Bayes
, 1999
"... Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance, carrying out the Bayesian program of computing the full posterior ..."
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Cited by 136 (1 self)
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Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance, carrying out the Bayesian program of computing the full posterior distributions over the parameters remains a difficult problem. Moreover, learning the structure of models with latent variables, for which the Bayesian approach is crucial, is yet a harder problem. In this paper I present the Variational Bayes framework, which provides a solution to these problems. This approach approximates full posterior distributions over model parameters and structures, as well as latent variables, in an analytical manner without resorting to sampling methods. Unlike in the Laplace approximation, these posteriors are generally nonGaussian and no Hessian needs to be computed. The resulting algorithm generalizes the standard Expectation Maximization a...
Convolutive Blind Separation of NonStationary
"... Acoustic signals recorded simultaneously in a reverberant environment can be described as sums of differently convolved sources. The task of source separation is to identify the multiple channels and possibly to invert those in order to obtain estimates of the underlying sources. We tackle the probl ..."
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Cited by 129 (3 self)
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Acoustic signals recorded simultaneously in a reverberant environment can be described as sums of differently convolved sources. The task of source separation is to identify the multiple channels and possibly to invert those in order to obtain estimates of the underlying sources. We tackle the problem by explicitly exploiting the nonstationarity of the acoustic sources. Changing crosscorrelations at multiple times give a sufficient set of constraints for the unknown channels. A least squares optimization allows us to estimate a forward model, identifying thus the multipath channel. In the same manner we can find an FIR backward model, which generates well separated model sources. Furthermore, for more than three channels we have sufficient conditions to estimate underlying additive sensor noise powers. We show good performance in real room environments and demonstrate the algorithm's utility for automatic speech recognition.
Learning Spatially Localized, PartsBased Representation
, 2001
"... In this paper, we propose a novel method, called local nonnegative matrix factorization (LNMF), for learning spatially localized, partsbased subspace representation of visual patterns. An objective function is defined to impose localization constraint, in addition to the nonnegativity constraint i ..."
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Cited by 114 (3 self)
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In this paper, we propose a novel method, called local nonnegative matrix factorization (LNMF), for learning spatially localized, partsbased subspace representation of visual patterns. An objective function is defined to impose localization constraint, in addition to the nonnegativity constraint in the standard NMF [1]. This gives a set of bases which not only allows a nonsubtractive (partbased) representation of images but also manifests localized features. An algorithm is presented for the learning of such basis components. Experimental results are presented to compare LNMF with the NMF and PCA methods for face representation and recognition, which demonstrates advantages of LNMF.
Blind Separation of Mixture of Independent Sources Through a Maximum Likelihood Approach
 In Proc. EUSIPCO
, 1997
"... In this paper we propose two methods for separating mixtures of independent sources without any precise knowledge of their probability distribution. They are obtained by considering a maximum likelihood solution corresponding to some given distributions of the sources and relaxing this assumption af ..."
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Cited by 101 (8 self)
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In this paper we propose two methods for separating mixtures of independent sources without any precise knowledge of their probability distribution. They are obtained by considering a maximum likelihood solution corresponding to some given distributions of the sources and relaxing this assumption afterward. The first method is specially adapted to temporally independent non Gaussian sources and is based on the use of nonlinear separating functions. The second method is specially adapted to correlated sources with distinct spectra and is based on the use of linear separating filters. A theoretical analysis of the performance of the methods has been made. A simple procedure for choosing optimally the separating functions from a given linear space of functions is proposed. Further, in the second method, a simple implementation based on the simultaneous diagonalization of two symmetric matrices is provided. Finally, some numerical and simulation results are given illustrating the performan...
Blind Separation Of Convolved Sources Based On Information Maximization
 IN IEEE WORKSHOP ON NEURAL NETWORKS FOR SIGNAL PROCESSING
, 1996
"... Blind separation of independent sources from their convolutive mixtures is a problem in many real world multisensor applications. In this paper we present a solution to this problem based on the information maximization principle, which was recently proposed by Bell and Sejnowski for the case of bl ..."
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Cited by 93 (1 self)
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Blind separation of independent sources from their convolutive mixtures is a problem in many real world multisensor applications. In this paper we present a solution to this problem based on the information maximization principle, which was recently proposed by Bell and Sejnowski for the case of blind separation of instantaneous mixtures. We present a feedback network architecture capable of coping with convolutive mixtures, and we derive the adaptation equations for the adaptive filters in the network by maximizing the information transferred through the network. Examples using speech signals are presented to illustrate the algorithm.
Sparse Code Shrinkage: Denoising of Nongaussian Data by Maximum Likelihood Estimation
, 1999
"... Sparse coding is a method for finding a representation of data in which each of the components of the representation is only rarely significantly active. Such a representation is closely related to redundancy reduction and independent component analysis, and has some neurophysiological plausibility. ..."
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Cited by 93 (15 self)
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Sparse coding is a method for finding a representation of data in which each of the components of the representation is only rarely significantly active. Such a representation is closely related to redundancy reduction and independent component analysis, and has some neurophysiological plausibility. In this paper, we show how sparse coding can be used for denoising. Using maximum likelihood estimation of nongaussian variables corrupted by gaussian noise, we show how to apply a softthresholding (shrinkage) operator on the components of sparse coding so as to reduce noise. Our method is closely related to the method of wavelet shrinkage, but it has the important benefit over wavelet methods that the representation is determined solely by the statistical properties of the data. The wavelet representation, on the other hand, relies heavily on certain mathematical properties (like selfsimilarity) that may be only weakly related to the properties of natural data.
A Fast FixedPoint Algorithm for Independent Component Analysis of Complex Valued Signals
, 2000
"... Separation of complex valued signals is a frequently arising problem in signal processing. For example, separation of convolutively mixed source signals involves computations on complex valued signals. In this article it is assumed that the original, complex valued source signals are mutually statis ..."
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Cited by 84 (1 self)
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Separation of complex valued signals is a frequently arising problem in signal processing. For example, separation of convolutively mixed source signals involves computations on complex valued signals. In this article it is assumed that the original, complex valued source signals are mutually statistically independent, and the problem is solved by the independent component analysis (ICA) model. ICA is a statistical method for transforming an observed multidimensional random vector into components that are mutually as independent as possible. In this article, a fast xedpoint type algorithm that is capable of separating complex valued, linearly mixed source signals is presented and its computational efficiency is shown by simulations. Also, the local consistency of the estimator given by the algorithm is proved.
A Unifying Informationtheoretic Framework for Independent Component Analysis
, 1999
"... We show that different theories recently proposed for Independent Component Analysis (ICA) lead to the same iterative learning algorithm for blind separation of mixed independent sources. We review those theories and suggest that information theory can be used to unify several lines of research. Pea ..."
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Cited by 82 (8 self)
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We show that different theories recently proposed for Independent Component Analysis (ICA) lead to the same iterative learning algorithm for blind separation of mixed independent sources. We review those theories and suggest that information theory can be used to unify several lines of research. Pearlmutter and Parra (1996) and Cardoso (1997) showed that the infomax approach of Bell and Sejnowski (1995) and the maximum likelihood estimation approach are equivalent. We show that negentropy maximization also has equivalent properties and therefore all three approaches yield the same learning rule for a fixed nonlinearity. Girolami and Fyfe (1997a) have shown that the nonlinear Principal Component Analysis (PCA) algorithm of Karhunen and Joutsensalo (1994) and Oja (1997) can also be viewed from informationtheoretic principles since it minimizes the sum of squares of the fourthorder marginal cumulants and therefore approximately minimizes the mutual information (Comon, 1994). Lambert (19...
Probabilistic Independent Component Analysis
, 2003
"... Independent Component Analysis is becoming a popular exploratory method for analysing complex data such as that from FMRI experiments. The application of such 'modelfree' methods, however, has been somewhat restricted both by the view that results can be uninterpretable and by the lack of ability t ..."
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Cited by 74 (12 self)
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Independent Component Analysis is becoming a popular exploratory method for analysing complex data such as that from FMRI experiments. The application of such 'modelfree' methods, however, has been somewhat restricted both by the view that results can be uninterpretable and by the lack of ability to quantify statistical significance. We present an integrated approach to Probabilistic ICA for FMRI data that allows for nonsquare mixing in the presence of Gaussian noise. We employ an objective estimation of the amount of Gaussian noise through Bayesian analysis of the true dimensionality of the data, i.e. the number of activation and nonGaussian noise sources. Reduction of the data to this 'true' subspace before the ICA decomposition automatically results in an estimate of the noise, leading to the ability to assign significance to voxels in ICA spatial maps. Estimation of the number of intrinsic sources not only enables us to carry out probabilistic modelling, but also achieves an asymptotically unique decomposition of the data. This reduces problems of interpretation, as each final independent component is now much more likely to be due to only one physical or physiological process. We also describe other improvements to standard ICA, such as temporal prewhitening and variance normafisation of timeseries, the latter being particularly useful in the context of dimensionality reduction when weak activation is present. We discuss the use of prior information about the spatiotemporal nature of the source processes, and an alternativehypothesis testing approach for inference, using Gaussian mixture models. The performance of our approach is illustrated and evaluated on real and complex artificial FMRI data, and compared to the spatiotemporal accuracy of restfits obtaine...
A TwoLayer Sparse Coding Model Learns Simple and Complex Cell Receptive Fields and Topography From Natural Images
 VISION RESEARCH
, 2001
"... The classical receptive fields of simple cells in the visual cortex have been shown to emerge from the statistical properties of natural images by forcing the cell responses to be maximally sparse, i.e. significantly activated only rarely. Here, we show that this single principle of sparseness can ..."
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Cited by 68 (18 self)
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The classical receptive fields of simple cells in the visual cortex have been shown to emerge from the statistical properties of natural images by forcing the cell responses to be maximally sparse, i.e. significantly activated only rarely. Here, we show that this single principle of sparseness can also lead to emergence of topography (columnar organization) and complex cell properties as well. These are obtained by maximizing the sparsenesses of locally pooled energies, which correspond to complex cell outputs. Thus we obtain a highly parsimonious model of how these properties of the visual cortex are adapted to the characteristics of the natural input.