On Independent Component Analysis and Supervised Dimension Reduction for Time Series

The main goal of this thesis work has been to develop tools to recover hidden structures, latent variables, or latent subspaces for multivariate and dependent time series data. The secondary goal has been to write computationally efficient algorithms for the methods to an R-package. In Blind Source Separation (BSS) the goal is to find uncorrelated latent sources by transforming the observed data in an appropriate way. In Independent Component Analysis (ICA) the latent sources are assumed to be independent. The well-known ICA methods FOBI and JADE are generalized to work with multivariate time series, where the latent components exhibit stochastic volatility. In such time series the volatility cannot be regarded as a constant in time, as often there are periods of high and periods of low volatility. The new methods are called gFOBI and gJADE. Also SOBI, a classic method which works well once the volatility is assumed to be constant, is given a variant called vSOBI, that also works with time series with stochastic volatility. In dimension reduction the idea is to transform the data into a new coordinate system, where the components are uncorrelated or even independent, and then keep only some of the transformed variables in such way that we do not lose too much of the important information of the data. The aforementioned BSS methods can be used in unsupervised dimension reduction; all the variables or time series have the same role. In supervised dimension reduction the relationship between a response and predictor variables needs to be considered as well. Wellknown supervised dimension reduction methods for independent and identically distributed data, SIR and SAVE, are generalized to work for time series data. The methods TSIR and TSAVE are introduced and shown to work well for time series, as they also use the information on the past values of the predictor time series. Also TSSH, a hybrid version of TSIR and TSAVE, is introduced. All the methods that have been developed in this thesis have also been implemented in R package tsBSS

Stationary subspace analysis based on second-order statistics

In stationary subspace analysis (SSA) one assumes that the observable p-variate time series is a linear mixture of a k-variate nonstationary time series and a (p-k)-variate stationary time series. The aim is then to estimate the unmixing matrix which transforms the observed multivariate time series onto stationary and nonstationary components. In the classical approach multivariate data are projected onto stationary and nonstationary subspaces by minimizing a Kullback-Leibler divergence between Gaussian distributions, and the method only detects nonstationarities in the first two moments. In this paper we consider SSA in a more general multivariate time series setting and propose SSA methods which are able to detect nonstationarities in mean, variance and autocorrelation, or in all of them. Simulation studies illustrate the performances of proposed methods, and it is shown that especially the method that detects all three types of nonstationarities performs well in various time series settings. The paper is concluded with an illustrative example

Dimension Reduction for Time Series in a Blind Source Separation Context Using R

Multivariate time series observations are increasingly common in multiple fields of science but the complex dependencies of such data often translate into intractable models with large number of parameters. An alternative is given by first reducing the dimension of the series and then modelling the resulting uncorrelated signals univariately, avoiding the need for any covariance parameters. A popular and effective framework for this is blind source separation. In this paper we review the dimension reduction tools for time series available in the R package tsBSS. These include methods for estimating the signal dimension of second-order stationary time series, dimension reduction techniques for stochastic volatility models and supervised dimension reduction tools for time series regression. Several examples are provided to illustrate the functionality of the package

Association between microglial activation and serum kynurenine pathway metabolites in multiple sclerosis patients

Microglial activation associates with MS progression but it is unclear what drives their persistent pro-inflammatory state. Metabolites of the kynurenine pathway (KP), the main metabolism route of tryptophan, can influence the function of brain innate immune cells.To investigate whether tryptophan metabolites in blood associate with TSPO-PET measurable microglial activation in MS brain.Microglial activation was detected using PET imaging and the TSPO-binding radioligand [11C]PK11195. Distribution volume ratios (DVR) for specific [11C]PK11195-binding in the normal appearing white matter (NAWM), lesions, and thalamus were calculated. Ultrahigh performance liquid chromatography-tandem mass spectrometry was used to measure serum levels of tryptophan and kynurenine pathway metabolites.The study cohort consisted of 48 MS patients. Increased DVR in the NAWM and thalamus correlated with decreased serum 3-hydroxykynurenine level (R = -0.31, p = 0.031 and R = -0.32, p = 0.028). Increased EDSS correlated with decreased 3-hydroxykynurenine and xanthurenic acid (R = -0.36, p = 0.012 and R = -0.31, p = 0.034) and increased DVR in the NAWM and thalamus (R = 0.33, p = 0.023 and R = 0.34, p = 0.020, respectively).This clinical study demonstrates an association between low serum 3-hydroxykynurenine and high microglial activation in MS. Further investigations are warranted for elucidation of the biological mechanisms behind this association

A review of second-order blind identification methods

Second-order source separation (SOS) is a data analysis tool which can be used for revealing hidden structures in multivariate time series data or as a tool for dimension reduction. Such methods are nowadays increasingly important as more and more high-dimensional multivariate time series data are measured in numerous fields of applied science. Dimension reduction is crucial, as modeling such high-dimensional data with multivariate time series models is often impractical as the number of parameters describing dependencies between the component time series is usually too high. SOS methods have their roots in the signal processing literature, where they were first used to separate source signals from an observed signal mixture. The SOS model assumes that the observed time series (signals) is a linear mixture of latent time series (sources) with uncorrelated components. The methods make use of the second-order statistics-hence the name "second-order source separation." In this review, we discuss the classical SOS methods and their extensions to more complex settings. An example illustrates how SOS can be performed.This article is categorized under:Statistical Models > Time Series ModelsStatistical and Graphical Methods of Data Analysis > Dimension ReductionData: Types and Structure > Time Series, Stochastic Processes, and Functional Dat

Supervised dimension reduction for multivariate time series

A regression model where the response as well as the explaining variables are time series is considered. A general model which allows supervised dimension reduction in this context is suggested without considering the form of dependence. The method for this purpose combines ideas from sliced inverse regression (SIR) and blind source separation methods to obtain linear combinations of the explaining time series which are ordered according to their relevance with respect to the response. The method gives also an indication of which lags of the linear combinations are of importance. The method is demonstrated using simulations and a real data example.</p

Dimension Reduction for Time Series in a Blind Source Separation Context Using R

Multivariate time series observations are increasingly common in multiple fields of science but the complex dependencies of such data often translate into intractable models with large number of parameters. An alternative is given by first reducing the dimension of the series and then modelling the resulting uncorrelated signals univariately, avoiding the need for any covariance parameters. A popular and effective framework for this is blind source separation. In this paper we review the dimension reduction tools for time series available in the R package tsBSS. These include methods for estimating the signal dimension of second-order stationary time series, dimension reduction techniques for stochastic volatility models and supervised dimension reduction tools for time series regression. Several examples are provided to illustrate the functionality of the package.</p

Sex-driven variability in TSPO-expressing microglia in MS patients and healthy individuals

Background: Males with multiple sclerosis (MS) have a higher risk for disability progression than females, but the reasons for this are unclear.Objective: We hypothesized that potential differences in TSPO-expressing microglia between female and male MS patients could contribute to sex differences in clinical disease progression.Methods: The study cohort consisted of 102 MS patients (mean (SD) age 45.3 (9.7) years, median (IQR) disease duration 12.1 (7.0–17.2) years, 72% females, 74% relapsing–remitting MS) and 76 age- and sex-matched healthy controls. TSPO-expressing microglia were measured using the TSPO-binding radioligand [11C](R)-PK11195 and brain positron emission tomography (PET). TSPO-binding was quantified as distribution volume ratio (DVR) in normal-appearing white matter (NAWM), thalamus, whole brain and cortical gray matter (cGM).Results: Male MS patients had higher DVRs compared to female patients in the whole brain [1.22 (0.04) vs. 1.20 (0.02), p = 0.002], NAWM [1.24 (0.06) vs. 1.21 (0.05), p = 0.006], thalamus [1.37 (0.08) vs. 1.32 (0.02), p = 0.008] and cGM [1.25 (0.04) vs. 1.23 (0.04), p = 0.028]. Similarly, healthy men had higher DVRs compared to healthy women except for cGM. Of the studied subgroups, secondary progressive male MS patients had the highest DVRs in all regions, while female controls had the lowest DVRs.Conclusion: We observed higher TSPO-binding in males compared to females among people with MS and in healthy individuals. This sex-driven inherent variability in TSPO-expressing microglia may predispose male MS patients to greater likelihood of disease progression.<br/