Session title: Recent development of Statistical Neuroimaging Analysis
Organizer: Lexin Li (UC Berkeley)
Chair: Jason Lee (USC)
Time: June 4th, 1:45pm – 3:15pm
Location: VEC 1402/1403
Speech 1: Analyzing Non-Stationary High-Dimensional Time Series: Structural Break Detection and Parameter Estimation
Speaker: Ali Shojaie (U of Washington)
Abstract: Assuming stationarity is unrealistic in many time series applications, including neuroscience. A more realistic alternative is to assume piecewise stationarity, where the model is allowed to change at potentially many time points. We propose a three-stage procedure for consistent estimation of both structural change points and parameters of high-dimensional piecewise vector autoregressive (VAR) models. In the first step, we reformulate the change point detection problem as a high-dimensional variable selection one, and solve it using a penalized least square estimator with a total variation penalty. We show that the proposed penalized estimation method over-estimates the number of change points. We then propose a backward selection criterion to identify the change points. In the last step of our procedure, we estimate the VAR parameters in each of the segments. We show that the proposed procedure consistently detects the number of change points and their locations. We also show that the procedure consistently estimates the VAR parameters. The performance of the method is illustrated through several simulation studies, as well as an analysis of EEG data.
Speech 2: Tensor-on-tensor regression
Speaker: Eric Lock (U of Minnesota)
Abstract: In neuroimaging analysis and other fields, both predictors and outcomes can take the form of a multi-way array (i.e., a tensor). We propose a framework for the linear prediction of a multi-way array from another multi-way array of arbitrary dimension, using the contracted tensor product. This framework generalizes several existing approaches, including methods to predict a scalar outcome from a tensor, a matrix from a matrix, or a tensor from a scalar. We describe an approach that exploits the multiway structure of both the predictors and the outcomes by restricting the coefficients to have reduced CP-rank. We propose a general and efficient algorithm for penalized least-squares estimation, which allows for a ridge ($L_2$) penalty on the coefficients. The objective is shown to give the mode of a Bayesian posterior, which motivates a Gibbs sampling algorithm for inference. We illustrate the approach with an application to facial image data.
Speech 3: A Joint Modeling Approach for Baseline Matrix-valued Imaging Data and Treatment Outcome
Speaker: Bei Jiang (University of Alberta)
Abstract: In this talk we propose a unified Bayesian joint modeling framework for studying association between a binary treatment outcome and a baseline matrix-valued predictor, such as imaging data. Under this framework, a theoretically implied relationship can be established between the treatment outcome and the matrix-valued imaging data, although the imaging data is not directly considered in the model. The proposed joint modeling approach provides a promising framework for both association estimation and prediction. Properties of this method are examined using simulated datasets. Finally, a detailed illustration of the proposed modeling approach is provided using a motivating depression study that aims to explore the association between the baseline EEG data and the probability of a favorable response to an antidepressant treatment.