We study independent component analysis with noisy observations. We present, for the first time in the literature, consistent, polynomial-time algorithms to recover non-Gaussian source signals and the mixing matrix with a reconstruction error that vanishes at a 1/ √ T rate using T observations and scales only polynomially with the natural parameters of the problem. Our algorithms and analysis a...

pervasive problem in neuroscience is A determining which regions of the brain are active, given voltage measurements at the scalp. If accurate solutions to such problems could be obtained, neurologists would gain noninvasive access to patient-specific cortical activity. Access to such data would ultimately increase the number of patients who could be effectively treated for neural pathologies s...

Delayed mixing is a problem of theoretical interest and practical importance, e.g., in speech processing, bio-medical signal analysis and nancial data modelling. Most previous analyses have been based on models with integer shifts, i.e., shifts by a number of samples, and have often been carried out using time-domain representation. Here, we explore the fact that a shift in the time domain corr...

Independent Component Analysis (ICA) (Comon, 1994) was originally proposed to solve the blind source separation problem of recovering independent source signals (e.g., different voice, music, or noise sources) after they are linearly mixed by an unknown matrix, A (cf. Figure 1). Nothing is known about the sources or the mixing process except that there are N different recorded mixtures. The tas...

We present a class of algorithms for independent component analysis (ICA) which use contrast functions based on canonical correlations in a reproducing kernel Hilbert space. On the one hand, we show that our contrast functions are related to mutual information and have desirable mathematical properties as measures of statistical dependence. On the other hand, building on recent developments in ...

Independent component analysis (ICA) of a mixed signal into a linear combination of its independent components, is one of the main problems in statistics, with wide range of applications. The un-mixing is usually performed by finding a rotation that optimizes a functional closely related to the differential entropy. In this paper we solve the linear ICA problem by analyzing the spectrum and eig...

This paper addresses an independent component analysis (ICA) learning algorithm with exible nonlinearity, so named as exible ICA, that is able to separate instantaneous mixtures of suband super-Gaussian source signals. In the framework of natural Riemannian gradient, we employ the parameterized generalized Gaussian density model for hypothesized source distributions. The nonlinear function in t...

The paper presents a novel technique of constrained independent component analysis (CICA) to introduce constraints into the classical ICA and solve the constrained optimization problem by using Lagrange multiplier methods. This paper shows that CICA can be used to order the resulted independent components in a specific manner and normalize the demixing matrix in the signal separation procedure....

This discussion paper proposes to generalize the notion of Independent Component Analysis (ICA) to the notion of Multidimensional Independent Component Analysis (MICA). We start from the ICA or blind source separation (BSS) model and show that it can be uniquely identified provided it is properly parameterized in terms of one-dimensional subspaces. From this standpoint, the BSS/ICA model is gen...

Background and Objectives: Evaluating the performance of clinical units is critical for effective management of health settings. Certain assessment of clinical variables for performance analysis is not always possible, calling for use of uncertainty theory. This study aimed to develop and evaluate an integrated independent component analysis-fuzzy-data envelopment analysis approach to accurate ...