Orthogonal Extended Infomax Algorithm

The extended infomax algorithm for independent component analysis (ICA) can separate sub- and super-Gaussian signals but converges slowly as it uses stochastic gradient optimization. In this paper, an improved extended infomax algorithm is presented that converges much faster. Accelerated convergence is achieved by replacing the natural gradient learning rule of extended infomax by a fully-multiplicative orthogonal-group based update scheme of the unmixing matrix leading to an orthogonal extended infomax algorithm (OgExtInf). Computational performance of OgExtInf is compared with two fast ICA algorithms: the popular FastICA and Picard, a L-BFGS algorithm belonging to the family of quasi-Newton methods. Our results demonstrate superior performance of the proposed method on small-size EEG data sets as used for example in online EEG processing systems, such as brain-computer interfaces or clinical systems for spike and seizure detection.Comment: 17 pages, 6 figure

The Applications of Mixtures of Normal Distributions in Empirical Finance: A Selected Survey

This paper provides a selected review of the recent developments and applications of mixtures of normal (MN) distribution models in empirical finance. Once attractive property of the MN model is that it is flexible enough to accommodate various shapes of continuous distributions, and able to capture leptokurtic, skewed and multimodal characteristics of financial time series data. In addition, the MN-based analysis fits well with the related regime-switching literature. The survey is conducted under two broad themes: (1) minimum-distance estimation methods, and (2) financial modeling and its applications.Mixtures of Normal, Maximum Likelihood, Moment Generating Function, Characteristic Function, Switching Regression Model, (G) ARCH Model, Stochastic Volatility Model, Autoregressive Conditional Duration Model, Stochastic Duration Model, Value at Risk.

Modulation Classification for MIMO-OFDM Signals via Approximate Bayesian Inference

The problem of modulation classification for a multiple-antenna (MIMO) system employing orthogonal frequency division multiplexing (OFDM) is investigated under the assumption of unknown frequency-selective fading channels and signal-to-noise ratio (SNR). The classification problem is formulated as a Bayesian inference task, and solutions are proposed based on Gibbs sampling and mean field variational inference. The proposed methods rely on a selection of the prior distributions that adopts a latent Dirichlet model for the modulation type and on the Bayesian network formalism. The Gibbs sampling method converges to the optimal Bayesian solution and, using numerical results, its accuracy is seen to improve for small sample sizes when switching to the mean field variational inference technique after a number of iterations. The speed of convergence is shown to improve via annealing and random restarts. While most of the literature on modulation classification assume that the channels are flat fading, that the number of receive antennas is no less than that of transmit antennas, and that a large number of observed data symbols are available, the proposed methods perform well under more general conditions. Finally, the proposed Bayesian methods are demonstrated to improve over existing non-Bayesian approaches based on independent component analysis and on prior Bayesian methods based on the `superconstellation' method.Comment: To be appear in IEEE Trans. Veh. Technolog

Neuropsychological parameters indexing executive processes are associated with independent components of ERPs

AbstractLesion studies have indicated that at least the three executive processes can be differentiated in the frontal lobe: Energization, monitoring and task setting. Event related potentials (ERPs) in Go/NoGo tasks have been widely used in studying executive processes. In this study, ERPs were obtained from EEG recorded during performance of a cued Go/NoGo task. The Contingent Negative Variation (CNV) and P3NoGo waves were decomposed into four independent components (ICs), by applying Independent Component Analysis (ICA) to a collection of ERPs from 193 healthy individuals. The components were named IC CNVearly, IC CNVlate, IC P3NoGoearly and IC P3NoGolate according to the conditions and time interval in which they occurred. A sub-group of 28 individuals was also assessed with neuropsychological tests. The test parameters were selected on the basis of studies demonstrating their sensitivity to executive processes as defined in the ROtman-Baycrest Battery for Investigating Attention (ROBBIA) model. The test scores were categorized into the domain scores of energization, monitoring and task setting and correlated with the amplitudes of the individual ICs from the sub-group of 28 individuals. The energization domain correlated with the IC CNVlate and IC P3NoGoearly. The monitoring domain correlated with the IC P3NoGolate, while the task setting domain correlated with the IC CNVlate. The IC CNVearly was not correlated with any of the neuropsychological domain scores. The correlations between the domains and ICs remained largely unchanged when controlling for full-scale IQ. This is the first study to demonstrate that executive processes, as indexed by neuropsychological test parameters, are associated with particular event-related potentials in a cued Go/NoGo paradigm

Toward a Functional Characterization of Cognitive Control Networks

Cognitive control is an executive process that has been associated with a distributed set of cortical regions. These distributed regions appear to cluster into distinct networks with dissociable functions. In this study, independent component analysis was used as a tool to investigate functional connectivity in event-related fMRI data. Extracted networks of interest were functionally characterized using a hybrid task that independently probed moment-to-moment adjustments in control, and stable task-set maintenance. A cinguloinsular network was implicated in the processing of moment-to-moment adjustments in control based on its activation patterns during this task. Subsequently, functional connectivity between two networks previously implicated in control, two default mode networks, and a visual network were investigated overall, and in specific condition windows. Findings from this study emphasize the utility of independent component analysis in directly functionally characterizing dissociable cognitive control networks

An ICA-GARCH approach to computing portfolio VAR with applications to South African financial markets

Master of Management in Finance & Investment Faculty of Commerce Law and Management Wits Business School University of The Witwatersrand 2016The Value-at-Risk (VaR) measurement – which is a single summary, distribution independent statistical measure of losses arising as a result of market movements – has become the market standard for measuring downside risk. There are some diverse ways to computing VaR and with this diversity comes the problem of determining which methods accurately measure and forecast Value-at-Risk. The problem is two-fold. First, what is the distribution of returns for the underlying asset? When dealing with linear financial instruments – where the relationship between the return on the financial asset and the return on the underlying is linear– we can assume normality of returns. This assumption becomes problematic for non-linear financial instruments such as options. Secondly, there are different methods of measuring the volatility of the underlying asset. These range from the univariate GARCH to the multivariate GARCH models. Recent studies have introduced the Independent Component Analysis (ICA) GARCH methodology which is aimed at computational efficiency for the multivariate GARCH methodologies. In our study, we focus on non-linear financial instruments and contribute to the body of knowledge by determining the optimal combination for the measure for volatility of the underlying (univariate-GARCH, EWMA, ICA-GARCH) and the distributional assumption of returns for the financial instrument (assumption of normality, the Johnson translation system). We use back-testing and out-of-sample tests to validate the performance of each of these combinations which give rise to six different methods for value-at-risk computations.MT201