Connectomics, Non-Euclidean data, and Statistics: Tutorial and Hands-on

I will begin the talk with a tutorial on functional data analysis. Then I will present two applications of deep neural networks (DNNs) to functional data. Traditional methods require dimension reduction via pre-selected basis expansions, which may not be optimal. We propose an adaptive approach using a DNN with a basis-layer, where hidden units act as basis functions through micro neural networks. This architecture focuses on relevant information, improving dimension reduction and outperforming other DNNs in classification and regression tasks. This approach requires fully or intensively observed functional data, so it is not suitable for longitudinal data, aka sparsely and irregularly observed functional data. Transformers are well suited to handle longitudinal data and we demonstrate this in the second part of the talk. *Based on joint work with Cynthia Juang, Jonas Mueller and Junwen Yao.

Neuroscience has now truly transitioned into the era of big data and is witnessing an explosion of the number and types of biological measures that can -and are- measured in clinical populations. This has given rise to the emerging field of population neuroscience, which holds enormous potential to improve prediction of disease states in many clinical conditions. However, achieving this objective places increasing demands on the statistical and machine learning methodology that are used to analyse these cohorts, in particular, finding methods to understand population variation in  imaging derived markers and understanding their relationship between environmental and behavioural factors remain an enormous challenge. In this talk I will describe conceptual innovations that enable us to make progress in this domain, including normative modelling or ‘brain growth charting’ techniques that allow us to chart variability at the level of each individual,  techniques rooted in the statistics of extremes that allow us to reconceptualise pathology as extreme deviations from an expected pattern and statistical approaches to predict clinical variables on the basis of smartphone based digital phenotyping data. I will illustrate this discussion by showing applications of these methods to cross-diagnostic psychiatric cohorts and I will argue that these innovations provide a principled method to move beyond simple statements about group averages and can instead provide a way to dissect the inherent heterogeneity in mental disorders, ultimately enabling more accurate prediction of the onset, course and outcome of brain disorders and paving the way to earlier and personalised interventions. 

Motivated by a study on adolescent mental health, we conduct a dynamic connectivity analysis using resting-state functional magnetic resonance imaging (fMRI) data. A dynamic connectivity analysis investigates how the interactions between different regions of the brain, represented by the different dimensions of a multivariate time series, change over time. We will discuss the modeling framework from two distinct approaches: Hidden Markov models (HMMs), and changepoint analysis. We will discuss the strengths and limitations of these approaches, and show their utility in the analysis of resting-fMRI data from two studies: the Brain Imaging Development of Girls’ Emotion and Self (BRIDGES) and the Adolescent Brain Cognitive Development Study (ABCD).

Neuroimaging is poised to take a substantial leap forward in understanding the neurophysiological underpinnings of human behavior, due to a combination of improved analytic techniques and the quality of imaging data. These advances are allowing researchers to develop population-level multivariate models of the functional brain representations underlying behavior, performance, clinical status and prognosis, and other outcomes. Population-based models can identify patterns of brain activity, or ‘signatures’, that can predict behavior and decode mental states in new individuals, producing generalizable knowledge and highly reproducible maps. These signatures can capture behavior with large effect sizes and can be used and tested across research groups. However, the potential of such signatures is limited by neuroanatomical constraints, in particular individual variation in functional brain anatomy. To circumvent this problem, current models are either applied only to individual participants, severely limiting generalizability, or force participants’ data into anatomical reference spaces (atlases) that do not respect individual functional topology and boundaries. Here we seek to overcome this shortcoming by developing new topographical models for inter-subject alignment, which register participants’ functional brain maps to one another. This increases effective spatial resolution, and more importantly allows us to explicitly analyze the spatial topology of functional maps and make inferences on differences in activation location and shape across persons and psychological states. In this talk we discuss several approaches towards functional alignment and highlight promises and pitfalls.

Many functional neuroimaging modalities (e.g., fMRI, EEG, dynamic PET) produce, for each subject, a collection of time courses observed across brain regions, sensors, or sources. This talk outlines a body of work that uses a multivariate functional data framework for representing the resulting spatial and temporal dependence, with conditional spatial dependence being of primary interest.  Several formulations and approaches to functional graphical models, in which nodes correspond to entire component processes at each spatial location and edges encode conditional relationships between them, will be described, including both Gaussian and non-Gaussian formulations.  A central challenge is that functional covariance operators are compact and generally lack bounded inverses. We will then examine how notions covariance separability across space and time can provide parsimonious representations, facilitate graphical modeling, and be assessed empirically. Finally, in connection with the Gaussian case, we will discuss recent approaches to sparse functional precision operator estimation.

The unintended memorization of training data in large language models (LLMs) raises important privacy and reliability concerns, particularly in medical applications. In this talk, I will present recent advances from our group in evaluating and controlling LLM memorization, including input-dependent soft prompts for measuring memorization and model-editing methods for inducing or suppressing it. I will then discuss structural memorization in biomedical language models, focusing on PubMed-scale scientific text. Beyond memorizing individual passages, models may retain higher-order structures such as relationships among biomedical concepts, entities, and scientific knowledge. I will discuss how such structural memorization can be characterized and its implications for reliable and trustworthy medical AI.