Related papers: Deep learning and differential equations for model…
Ordinary differential equations (ODEs) can provide mechanistic models of temporally local changes of processes, where parameters are often informed by external knowledge. While ODEs are popular in systems modeling, they are less established…
A core problem in machine learning is to learn expressive latent variables for model prediction on complex data that involves multiple sub-components in a flexible and interpretable fashion. Here, we develop an approach that improves…
There has been much recent, exciting work on combining the complementary strengths of latent variable models and deep learning. Latent variable modeling makes it easy to explicitly specify model constraints through conditional independence…
The individual data collected throughout patient follow-up constitute crucial information for assessing the risk of a clinical event, and eventually for adapting a therapeutic strategy. Joint models and landmark models have been proposed to…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to…
Mathematical models of cognition are often memoryless and ignore potential fluctuations of their parameters. However, human cognition is inherently dynamic. Thus, we propose to augment mechanistic cognitive models with a temporal dimension…
Deep latent variable models learn condensed representations of data that, hopefully, reflect the inner workings of the studied phenomena. Unfortunately, these latent representations are not statistically identifiable, meaning they cannot be…
Longitudinal biomedical data are often characterized by a sparse time grid and individual-specific development patterns. Specifically, in epidemiological cohort studies and clinical registries we are facing the question of what can be…
Often in follow-up studies intermediate events occur in some patients, such as reinterventions or adverse events. These intermediate events directly affect the shapes of their longitudinal profiles. Our work is motivated by two studies in…
The accurate prediction of patient prognosis is a critical challenge in clinical practice. With the availability of various patient information, physicians can optimize medical care by closely monitoring disease progression and therapy…
Climate models play a critical role in understanding and projecting climate change. Due to their complexity, their horizontal resolution of about 40-100 km remains too coarse to resolve processes such as clouds and convection, which need to…
Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms of biological processes. The mathematical mechanisms…
A deep latent variable model is a powerful method for capturing complex distributions. These models assume that underlying structures, but unobserved, are present within the data. In this dissertation, we explore high-dimensional problems…
Deep Metric Learning (DML) approaches learn to represent inputs to a lower-dimensional latent space such that the distance between representations in this space corresponds with a predefined notion of similarity. This paper investigates how…
Machine learning models are essential tools in various domains, but their performance can degrade over time due to changes in data distribution or other factors. On one hand, detecting and addressing such degradations is crucial for…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
A key question in clinical practice is accurate prediction of patient prognosis. To this end, nowadays, physicians have at their disposal a variety of tests and biomarkers to aid them in optimizing medical care. These tests are often…
We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…
Joint models for longitudinal and time-to-event data are commonly used in longitudinal studies to forecast disease trajectories over time. While there are many advantages to joint modeling, the standard forms suffer from limitations that…