Session title: Nonparameteric and Robust Statistical Methods for Imaging
Organizer: Hernando Ombao (KAUST)
Chair: Wei Pan(UMN)
Time: June 5th, 8:30am – 10:00am
Location: VEC 405
Speech 1: Nonparametric Collective Spectral Density Estimation and Clustering with Application to Brian Activities
Speaker: Mehdi Maadooliat (Marquette University)
Abstract: In this paper, we develop a method for the simultaneous estimation of spectral density functions (SDFs) for a collection of stationary time series that share some common features. Due to the similarities among the SDFs, the log-SDF can be represented using a common set of basis functions. The basis shared by the collection of the log-SDFs is estimated as a low-dimensional manifold of a large space spanned by a pre-specified rich basis. A collective estimation approach pools information and borrows strength across the SDFs to achieve better estimation efficiency. Also, each estimated spectral density has a concise representation using the coefficients of the basis expansion, and these coefficients can be used for visualization, clustering, and classification purposes. The Whittle pseudo-maximum likelihood approach is used to fit the model and an alternating blockwise Newton-type algorithm is developed for the computation. A web-based shiny Appfound at https://ncsde.shinyapps.io/NCSDE is developed for visualization, training and learning the SDFs collectively using the proposed technique. Finally, we apply our method to cluster similar brain signals recorded by the electroencephalogram for identifying synchronized brain regions according to their spectral densities.
Speech 2: A Flexible Non-parametric Framework for Imaging Genetics
Speaker: Zhaoxia Yu (UC Irvine)
Abstract: Data collected in many scientific areas are inherently high-dimensional and multi-way. While such data provides an excellent opportunity for us to conduct an integrative analysis of multiple data modalities, it is challenging to model associations between sets of massive, complexly structured, and high-dimensional data. Here we propose a flexible, easy-to-implement, and non-parametric framework to assessing the overall association between high-dimensional modalities. We illustrate how the methods are connected to classical regression-based methods. To take some important structure of brain imaging data into consideration, we also extend our method to non-Euclidean space. The principles that we propose are applicable to various types of high dimensional data, such as genetic variants and brain connectivity.
Speech 3: Hybrid Principal Components Analysis For Region-Referenced Longitudinal Functional EEG Data
Speaker: Damla Senturk (UCLA)
Abstract: Electroencephalography (EEG) data possess a complex structure that includes regional, functional, and longitudinal dimensions. Our motivating example is a word segmentation paradigm in which typically developing (TD) children and children with Autism Spectrum Disorder (ASD) were exposed to a continuous speech stream. For each subject, continuous EEG signals recorded at each electrode were divided into one-second segments and projected into the frequency domain via Fast Fourier Transform. Following a spectral principal components analysis, the resulting data consist of region-referenced principal power indexed regionally by scalp location, functionally across frequencies and longitudinally by one-second segments. Standard EEG power analyses often collapse information across the longitudinal and functional dimensions by averaging power across segments and concentrating on specific frequency bands. We propose a hybrid principal components analysis (HPCA) for region-referenced longitudinal functional EEG data which utilizes both vector and functional principal components analyses and does not collapse information along any of the three dimensions of the data. The proposed decomposition only assumes weak separability of the higher-dimensional covariance process and utilizes a product of one dimensional eigenvectors and eigenfunctions, obtained from the regional, functional, and longitudinal marginal covariances, to represent the observed data, providing a computationally feasible non-parametric approach. A mixed effects framework is proposed to estimate the model components coupled with a bootstrap test for group level inference, both geared towards sparse data applications. Analysis of the data from the word segmentation paradigm leads to valuable insights about group-region differences among the TD and verbal and minimally verbal children with ASD. Finite sample properties of the proposed estimation framework and bootstrap inference procedure are further studied via extensive simulations.