Simultaneous Estimation of Nongaussian Components and Their Correlation Structure.

Abstract:

:The statistical dependencies that independent component analysis (ICA) cannot remove often provide rich information beyond the linear independent components. It would thus be very useful to estimate the dependency structure from data. While such models have been proposed, they have usually concentrated on higher-order correlations such as energy (square) correlations. Yet linear correlations are a fundamental and informative form of dependency in many real data sets. Linear correlations are usually completely removed by ICA and related methods so they can only be analyzed by developing new methods that explicitly allow for linearly correlated components. In this article, we propose a probabilistic model of linear nongaussian components that are allowed to have both linear and energy correlations. The precision matrix of the linear components is assumed to be randomly generated by a higher-order process and explicitly parameterized by a parameter matrix. The estimation of the parameter matrix is shown to be particularly simple because using score-matching (Hyvärinen, 2005 ), the objective function is a quadratic form. Using simulations with artificial data, we demonstrate that the proposed method improves the identifiability of nongaussian components by simultaneously learning their correlation structure. Applications on simulated complex cells with natural image input, as well as spectrograms of natural audio data, show that the method finds new kinds of dependencies between the components.

journal_name

Neural Comput

journal_title

Neural computation

authors

Sasaki H,Gutmann MU,Shouno H,Hyvärinen A

doi

10.1162/neco_a_01006

subject

Has Abstract

pub_date

2017-11-01 00:00:00

pages

2887-2924

issue

11

eissn

0899-7667

issn

1530-888X

journal_volume

29

pub_type

杂志文章
  • Regularized neural networks: some convergence rate results.

    abstract::In a recent paper, Poggio and Girosi (1990) proposed a class of neural networks obtained from the theory of regularization. Regularized networks are capable of approximating arbitrarily well any continuous function on a compactum. In this paper we consider in detail the learning problem for the one-dimensional case. W...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.1995.7.6.1225

    authors: Corradi V,White H

    更新日期:1995-11-01 00:00:00

  • A Mathematical Analysis of Memory Lifetime in a Simple Network Model of Memory.

    abstract::We study the learning of an external signal by a neural network and the time to forget it when this network is submitted to noise. The presentation of an external stimulus to the recurrent network of binary neurons may change the state of the synapses. Multiple presentations of a unique signal lead to its learning. Th...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco_a_01286

    authors: Helson P

    更新日期:2020-07-01 00:00:00

  • Hidden Quantum Processes, Quantum Ion Channels, and 1/ fθ-Type Noise.

    abstract::In this letter, we perform a complete and in-depth analysis of Lorentzian noises, such as those arising from [Formula: see text] and [Formula: see text] channel kinetics, in order to identify the source of [Formula: see text]-type noise in neurological membranes. We prove that the autocovariance of Lorentzian noise de...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_01067

    authors: Paris A,Vosoughi A,Berman SA,Atia G

    更新日期:2018-07-01 00:00:00

  • Sufficient dimension reduction via squared-loss mutual information estimation.

    abstract::The goal of sufficient dimension reduction in supervised learning is to find the low-dimensional subspace of input features that contains all of the information about the output values that the input features possess. In this letter, we propose a novel sufficient dimension-reduction method using a squared-loss variant...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00407

    authors: Suzuki T,Sugiyama M

    更新日期:2013-03-01 00:00:00

  • Convergence of the IRWLS Procedure to the Support Vector Machine Solution.

    abstract::An iterative reweighted least squares (IRWLS) procedure recently proposed is shown to converge to the support vector machine solution. The convergence to a stationary point is ensured by modifying the original IRWLS procedure. ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/0899766052530875

    authors: Pérez-Cruz F,Bousoño-Calzón C,Artés-Rodríguez A

    更新日期:2005-01-01 00:00:00

  • ISO learning approximates a solution to the inverse-controller problem in an unsupervised behavioral paradigm.

    abstract::In "Isotropic Sequence Order Learning" (pp. 831-864 in this issue), we introduced a novel algorithm for temporal sequence learning (ISO learning). Here, we embed this algorithm into a formal nonevaluating (teacher free) environment, which establishes a sensor-motor feedback. The system is initially guided by a fixed r...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/08997660360581930

    authors: Porr B,von Ferber C,Wörgötter F

    更新日期:2003-04-01 00:00:00

  • Dependence of neuronal correlations on filter characteristics and marginal spike train statistics.

    abstract::Correlated neural activity has been observed at various signal levels (e.g., spike count, membrane potential, local field potential, EEG, fMRI BOLD). Most of these signals can be considered as superpositions of spike trains filtered by components of the neural system (synapses, membranes) and the measurement process. ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2008.05-07-525

    authors: Tetzlaff T,Rotter S,Stark E,Abeles M,Aertsen A,Diesmann M

    更新日期:2008-09-01 00:00:00

  • Clustering based on gaussian processes.

    abstract::In this letter, we develop a gaussian process model for clustering. The variances of predictive values in gaussian processes learned from a training data are shown to comprise an estimate of the support of a probability density function. The constructed variance function is then applied to construct a set of contours ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2007.19.11.3088

    authors: Kim HC,Lee J

    更新日期:2007-11-01 00:00:00

  • Weight Perturbation: An Optimal Architecture and Learning Technique for Analog VLSI Feedforward and Recurrent Multilayer Networks.

    abstract::Previous work on analog VLSI implementation of multilayer perceptrons with on-chip learning has mainly targeted the implementation of algorithms like backpropagation. Although backpropagation is efficient, its implementation in analog VLSI requires excessive computational hardware. In this paper we show that, for anal...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.1991.3.4.546

    authors: Jabri M,Flower B

    更新日期:1991-01-01 00:00:00

  • Mirror symmetric topographic maps can arise from activity-dependent synaptic changes.

    abstract::Multiple adjacent, roughly mirror-image topographic maps are commonly observed in the sensory neocortex of many species. The cortical regions occupied by these maps are generally believed to be determined initially by genetically controlled chemical markers during development, with thalamocortical afferent activity su...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/0899766053491904

    authors: Schulz R,Reggia JA

    更新日期:2005-05-01 00:00:00

  • Connection topology selection in central pattern generators by maximizing the gain of information.

    abstract::A study of a general central pattern generator (CPG) is carried out by means of a measure of the gain of information between the number of available topology configurations and the output rhythmic activity. The neurons of the CPG are chaotic Hindmarsh-Rose models that cooperate dynamically to generate either chaotic o...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2007.19.4.974

    authors: Stiesberg GR,Reyes MB,Varona P,Pinto RD,Huerta R

    更新日期:2007-04-01 00:00:00

  • Are loss functions all the same?

    abstract::In this letter, we investigate the impact of choosing different loss functions from the viewpoint of statistical learning theory. We introduce a convexity assumption, which is met by all loss functions commonly used in the literature, and study how the bound on the estimation error changes with the loss. We also deriv...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976604773135104

    authors: Rosasco L,De Vito E,Caponnetto A,Piana M,Verri A

    更新日期:2004-05-01 00:00:00

  • Feature selection in simple neurons: how coding depends on spiking dynamics.

    abstract::The relationship between a neuron's complex inputs and its spiking output defines the neuron's coding strategy. This is frequently and effectively modeled phenomenologically by one or more linear filters that extract the components of the stimulus that are relevant for triggering spikes and a nonlinear function that r...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2009.02-09-956

    authors: Famulare M,Fairhall A

    更新日期:2010-03-01 00:00:00

  • A general probability estimation approach for neural comp.

    abstract::We describe an analytical framework for the adaptations of neural systems that adapt its internal structure on the basis of subjective probabilities constructed by computation of randomly received input signals. A principled approach is provided with the key property that it defines a probability density model that al...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976600300015862

    authors: Khaikine M,Holthausen K

    更新日期:2000-02-01 00:00:00

  • The relationship between synchronization among neuronal populations and their mean activity levels.

    abstract::In the past decade the importance of synchronized dynamics in the brain has emerged from both empirical and theoretical perspectives. Fast dynamic synchronous interactions of an oscillatory or nonoscillatory nature may constitute a form of temporal coding that underlies feature binding and perceptual synthesis. The re...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976699300016287

    authors: Chawla D,Lumer ED,Friston KJ

    更新日期:1999-08-15 00:00:00

  • On the classification capability of sign-constrained perceptrons.

    abstract::The perceptron (also referred to as McCulloch-Pitts neuron, or linear threshold gate) is commonly used as a simplified model for the discrimination and learning capability of a biological neuron. Criteria that tell us when a perceptron can implement (or learn to implement) all possible dichotomies over a given set of ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2008.20.1.288

    authors: Legenstein R,Maass W

    更新日期:2008-01-01 00:00:00

  • Constraint on the number of synaptic inputs to a visual cortical neuron controls receptive field formation.

    abstract::To date, Hebbian learning combined with some form of constraint on synaptic inputs has been demonstrated to describe well the development of neural networks. The previous models revealed mathematically the importance of synaptic constraints to reproduce orientation selectivity in the visual cortical neurons, but biolo...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2009.04-08-752

    authors: Tanaka S,Miyashita M

    更新日期:2009-09-01 00:00:00

  • Attractive periodic sets in discrete-time recurrent networks (with emphasis on fixed-point stability and bifurcations in two-neuron networks).

    abstract::We perform a detailed fixed-point analysis of two-unit recurrent neural networks with sigmoid-shaped transfer functions. Using geometrical arguments in the space of transfer function derivatives, we partition the network state-space into distinct regions corresponding to stability types of the fixed points. Unlike in ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/08997660152002898

    authors: Tino P,Horne BG,Giles CL

    更新日期:2001-06-01 00:00:00

  • An oscillatory Hebbian network model of short-term memory.

    abstract::Recurrent neural architectures having oscillatory dynamics use rhythmic network activity to represent patterns stored in short-term memory. Multiple stored patterns can be retained in memory over the same neural substrate because the network's state persistently switches between them. Here we present a simple oscillat...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2008.02-08-715

    authors: Winder RK,Reggia JA,Weems SA,Bunting MF

    更新日期:2009-03-01 00:00:00

  • The computational structure of spike trains.

    abstract::Neurons perform computations, and convey the results of those computations through the statistical structure of their output spike trains. Here we present a practical method, grounded in the information-theoretic analysis of prediction, for inferring a minimal representation of that structure and for characterizing it...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2009.12-07-678

    authors: Haslinger R,Klinkner KL,Shalizi CR

    更新日期:2010-01-01 00:00:00

  • Fast recursive filters for simulating nonlinear dynamic systems.

    abstract::A fast and accurate computational scheme for simulating nonlinear dynamic systems is presented. The scheme assumes that the system can be represented by a combination of components of only two different types: first-order low-pass filters and static nonlinearities. The parameters of these filters and nonlinearities ma...

    journal_title:Neural computation

    pub_type: 信件

    doi:10.1162/neco.2008.04-07-506

    authors: van Hateren JH

    更新日期:2008-07-01 00:00:00

  • A modified algorithm for generalized discriminant analysis.

    abstract::Generalized discriminant analysis (GDA) is an extension of the classical linear discriminant analysis (LDA) from linear domain to a nonlinear domain via the kernel trick. However, in the previous algorithm of GDA, the solutions may suffer from the degenerate eigenvalue problem (i.e., several eigenvectors with the same...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976604773717612

    authors: Zheng W,Zhao L,Zou C

    更新日期:2004-06-01 00:00:00

  • Toward a biophysically plausible bidirectional Hebbian rule.

    abstract::Although the commonly used quadratic Hebbian-anti-Hebbian rules lead to successful models of plasticity and learning, they are inconsistent with neurophysiology. Other rules, more physiologically plausible, fail to specify the biological mechanism of bidirectionality and the biological mechanism that prevents synapses...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976698300017629

    authors: Grzywacz NM,Burgi PY

    更新日期:1998-04-01 00:00:00

  • Determining Burst Firing Time Distributions from Multiple Spike Trains.

    abstract::Recent experimental findings have shown the presence of robust and cell-type-specific intraburst firing patterns in bursting neurons. We address the problem of characterizing these patterns under the assumption that the bursts exhibit well-defined firing time distributions. We propose a method for estimating these dis...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2008.07-07-571

    authors: Lago-Fernández LF,Szücs A,Varona P

    更新日期:2009-04-01 00:00:00

  • Sparse coding on the spot: spontaneous retinal waves suffice for orientation selectivity.

    abstract::Ohshiro, Hussain, and Weliky (2011) recently showed that ferrets reared with exposure to flickering spot stimuli, in the absence of oriented visual experience, develop oriented receptive fields. They interpreted this as refutation of efficient coding models, which require oriented input in order to develop oriented re...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00333

    authors: Hunt JJ,Ibbotson M,Goodhill GJ

    更新日期:2012-09-01 00:00:00

  • Generalization and selection of examples in feedforward neural networks.

    abstract::In this work, we study how the selection of examples affects the learning procedure in a boolean neural network and its relationship with the complexity of the function under study and its architecture. We analyze the generalization capacity for different target functions with particular architectures through an analy...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976600300014999

    authors: Franco L,Cannas SA

    更新日期:2000-10-01 00:00:00

  • Replicating receptive fields of simple and complex cells in primary visual cortex in a neuronal network model with temporal and population sparseness and reliability.

    abstract::We propose a new principle for replicating receptive field properties of neurons in the primary visual cortex. We derive a learning rule for a feedforward network, which maintains a low firing rate for the output neurons (resulting in temporal sparseness) and allows only a small subset of the neurons in the network to...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00341

    authors: Tanaka T,Aoyagi T,Kaneko T

    更新日期:2012-10-01 00:00:00

  • Computing sparse representations of multidimensional signals using Kronecker bases.

    abstract::Recently there has been great interest in sparse representations of signals under the assumption that signals (data sets) can be well approximated by a linear combination of few elements of a known basis (dictionary). Many algorithms have been developed to find such representations for one-dimensional signals (vectors...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00385

    authors: Caiafa CF,Cichocki A

    更新日期:2013-01-01 00:00:00

  • Similarity, connectionism, and the problem of representation in vision.

    abstract::A representational scheme under which the ranking between represented similarities is isomorphic to the ranking between the corresponding shape similarities can support perfectly correct shape classification because it preserves the clustering of shapes according to the natural kinds prevailing in the external world. ...

    journal_title:Neural computation

    pub_type: 杂志文章,评审

    doi:10.1162/neco.1997.9.4.701

    authors: Edelman S,Duvdevani-Bar S

    更新日期:1997-05-15 00:00:00

  • Generalization and multirate models of motor adaptation.

    abstract::When subjects adapt their reaching movements in the setting of a systematic force or visual perturbation, generalization of adaptation can be assessed psychophysically in two ways: by testing untrained locations in the work space at the end of adaptation (slow postadaptation generalization) or by determining the influ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00262

    authors: Tanaka H,Krakauer JW,Sejnowski TJ

    更新日期:2012-04-01 00:00:00