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The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…
Models based on deep convolutional networks have dominated recent image interpretation tasks; we investigate whether models which are also recurrent, or "temporally deep", are effective for tasks involving sequences, visual and otherwise.…
This study addresses the challenge of predicting network dynamics, such as forecasting disease spread in social networks or estimating species populations in predator-prey networks. Accurate predictions in large networks are difficult due…
In applications such as biomedical studies, epidemiology, and social sciences, recurrent events often co-occur with longitudinal measurements and a terminal event, such as death. Therefore, jointly modeling longitudinal measurements,…
Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…
Analyzing signals arising from dynamical systems typically requires many modeling assumptions and parameter estimation. In high dimensions, this modeling is particularly difficult due to the "curse of dimensionality". In this paper, we…
We jointly model longitudinal values of a psychometric test and diagnosis of dementia. The model is based on a continuous-time latent process representing cognitive ability. The link between the latent process and the observations is…
The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…
Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with representative datasets. Recently, an augmented framework has been…
Model-based design of experiments (MBDOE) is essential for efficient parameter estimation in nonlinear dynamical systems. However, conventional adaptive MBDOE requires costly posterior inference and design optimization between each…
Deep learning methods achieve remarkable predictive performance in modeling complex, large-scale data. However, assessing the quality of derived models has become increasingly challenging, as more classical statistical assumptions may no…
Differential Privacy (DP) provides a rigorous framework for releasing statistics while protecting individual information present in a dataset. Although substantial progress has been made on differentially private linear regression, existing…
Forest transitions, characterized by dynamic shifts between forest, agricultural, and abandoned lands, are complex phenomena. This study developed a stochastic differential equation model to capture the intricate dynamics of these…
Given a sequence of sets, where each set contains an arbitrary number of elements, the problem of temporal sets prediction aims to predict the elements in the subsequent set. In practice, temporal sets prediction is much more complex than…
Data-driven modeling and machine learning are widely used to model the behavior of dynamic systems. One application is the residual evaluation of technical systems where model predictions are compared with measurement data to create…
Predicting high-fidelity future human poses, from a historically observed sequence, is decisive for intelligent robots to interact with humans. Deep end-to-end learning approaches, which typically train a generic pre-trained model on…
When developing clinical prediction models, it can be challenging to balance between global models that are valid for all patients and personalized models tailored to individuals or potentially unknown subgroups. To aid such decisions, we…
We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. We show how to estimate parameters from max-stable processes, where inference is…
Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary…
In an increasingly connected world, the resilience of networked dynamical systems is important in the fields of ecology, economics, critical infrastructures, and organizational behaviour. Whilst we understand small-scale resilience well,…