Related papers: Deep learning and differential equations for model…

Joint models for longitudinal and time-to-event data are often employed to calculate dynamic individualized predictions used in numerous applications of precision medicine. Two components of joint models that influence the accuracy of these…

Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral…

State space models (SSMs) have shown remarkable empirical performance on many long sequence modeling tasks, but a theoretical understanding of these models is still lacking. In this work, we study the learning dynamics of linear SSMs to…

We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for forecasting time series of spatial processes, i.e. series of observations sharing temporal and spatial dependencies. The model learns these…

Accurate and transparent prediction of cancer survival times on the level of individual patients can inform and improve patient care and treatment practices. In this paper, we design a model that concurrently learns to accurately predict…

Modeling sequential patterns from data is at the core of various time series forecasting tasks. Deep learning models have greatly outperformed many traditional models, but these black-box models generally lack explainability in prediction…

A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model…

We propose a generative model for single-channel EEG that incorporates the constraints experts actively enforce during visual scoring. The framework takes the form of a dynamic Bayesian network with depth in both the latent variables and…

Continuously-observed event occurrences, often exhibit self- and mutually-exciting effects, which can be well modeled using temporal point processes. Beyond that, these event dynamics may also change over time, with certain periodic trends.…

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…

Many systems in biology, physics and engineering can be described by systems of ordinary differential equation containing many parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and…

Joint modeling of longitudinal and survival data has become increasingly important in medical research, particularly for understanding disease progression in chronic conditions where both repeated biomarker measurements and time-to-event…

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the…

In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…

For discrete panel data, the dynamic relationship between successive observations is often of interest. We consider a dynamic probit model for short panel data. A problem with estimating the dynamic parameter of interest is that the model…

Individual-level human mobility prediction has emerged as a significant topic of research with applications in infectious disease monitoring, child, and elderly care. Existing studies predominantly focus on the microscopic aspects of human…

The longitudinal analysis of patient response time course following doses of therapeutics is currently performed using Pharmacokinetic/Pharmacodynamic (PK/PD) methodologies, which requires significant human experience and expertise in the…

For many complex diseases, there is a wide variety of ways in which an individual can manifest the disease. The challenge of personalized medicine is to develop tools that can accurately predict the trajectory of an individual's disease,…

In this paper, we focus on learning a linear time-invariant (LTI) model with low-dimensional latent variables but high-dimensional observations. We provide an algorithm that recovers the high-dimensional features, i.e. column space of the…

Deep neural networks have shown remarkable performance when trained on independent and identically distributed data from a fixed set of classes. However, in real-world scenarios, it can be desirable to train models on a continuous stream of…