Efficient Gaussian Process-Based Modelling and Prediction of Image Time Series.

Area of Science:

• Neuroimaging
• Statistical Modeling
• Machine Learning

Background:

• Longitudinal studies in Alzheimer's disease (AD) require sophisticated models to capture complex structural changes over time.
• Existing parametric models may not adequately represent the nuanced, non-linear progression of AD.
• Accurate spatio-temporal modeling is crucial for understanding disease dynamics and individual variability.

Purpose of the Study:

• To introduce a novel, non-parametric Gaussian process-based spatio-temporal model for analyzing time series of images.
• To demonstrate the model's efficiency and robustness in computing marginal likelihood and posterior predictions.
• To apply the framework to longitudinal Alzheimer's disease data for improved within-subject modeling and prediction.

Main Methods:

• Development of a separable Gaussian process model for spatial and temporal image data.
• Utilizing Kronecker products for efficient parameterization of covariance structures.
• Implementation of the Hoffman-Ribak method for efficient inference on posterior processes and uncertainty quantification.
• Application to longitudinal neuroimaging data in Alzheimer's disease.

Main Results:

• The proposed non-parametric model significantly outperforms conventional parametric methods in modeling within-subject structural changes in Alzheimer's disease.
• The framework demonstrates efficient and robust computation of marginal likelihood and posterior predictions.
• Bayesian model comparison using marginal likelihood enables effective comparison of different hypotheses regarding individual image change processes.

Conclusions:

• The novel Gaussian process framework provides a powerful and flexible tool for non-parametric spatio-temporal modeling of image time series.
• This approach offers significant advantages over traditional methods for analyzing longitudinal neuroimaging data, particularly in the context of Alzheimer's disease.
• The model facilitates a deeper understanding of individual disease progression and allows for robust hypothesis testing on change processes.