Related papers: Dynamic survival analysis: modelling the hazard fu…

This paper presents a learning from demonstration approach to programming safe, autonomous behaviors for uncommon driving scenarios. Simulation is used to re-create a targeted driving situation, one containing a road-side hazard creating a…

This paper explores and develops alternative statistical representations and estimation approaches for dynamic mortality models. The framework we adopt is to reinterpret popular mortality models such as the Lee-Carter class of models in a…

Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on…

We propose a reduced-order model for the instantaneous hydrodynamic force on a cylinder. The model consists of a system of two ordinary differential equations (ODEs), which can be integrated in time to yield very accurate histories of the…

This work establishes a rigorous connection between stability properties of discrete-time algorithms (DTAs) and corresponding continuous-time dynamical systems derived through $ O(s^r) $-resolution ordinary differential equations (ODEs). We…

This paper focuses on learning a model of system dynamics online while satisfying safety constraints.Our motivation is to avoid offline system identification or hand-specified dynamics models and allowa system to safely and autonomously…

Machine learning applications for longitudinal electronic health records often forecast the risk of events at fixed time points, whereas survival analysis achieves dynamic risk prediction by estimating time-to-event distributions. Here, we…

Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior…

We propose a dynamical model for the estimation of Operational Risk in banking institutions. Operational Risk is the risk that a financial loss occurs as the result of failed processes. Examples of operational losses are the ones generated…

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal…

In this short communication, we describe the recent debate on whether the hazard function should be used for causal inference in time-to-event studies and consider three different potential outcomes frameworks (by Rubin, Robins, and Pearl,…

This article shows how to specify and construct a discrete, stochastic, continuous-time model specifically for ecological systems. The model is more broad than typical chemical kinetics models in two ways. First, using time-dependent hazard…

Accurate estimation of long-term risk is essential for the design and analysis of stochastic dynamical systems. Existing risk quantification methods typically rely on extensive datasets involving risk events observed over extended time…

Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…

To derive the hidden dynamics from observed data is one of the fundamental but also challenging problems in many different fields. In this study, we propose a new type of interpretable network called the ordinary differential equation…

We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives…

We develop a numerical method to reconstruct systems of ordinary differential equations (ODEs) from time series data without {\it a priori} knowledge of the underlying ODEs using sparse basis learning and sparse function reconstruction. We…

In many biomedical applications, outcome is measured as a ``time-to-event'' (eg. disease progression or death). To assess the connection between features of a patient and this outcome, it is common to assume a proportional hazards model,…

Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…