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We introduce a framework for analyzing ordinary differential equation (ODE) models of biological networks using statistical model checking (SMC). A key aspect of our work is the modeling of single-cell variability by assigning a probability…
Detecting anomalies in irregularly sampled multi-variate time-series is challenging, especially in data-scarce settings. Here we introduce an anomaly detection framework for irregularly sampled time-series that leverages neural jump…
This paper introduces diagnostic tests for the nature of lack of fit in ordinary differential equation models (ODEs) proposed for data. We present a hierarchy of three possible sources of lack of fit: unaccounted-for stochastic variation,…
Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying…
Identification of parameters in ordinary differential equations (ODEs) is an important and challenging task when modeling dynamic systems in biomedical research and other scientific areas, especially with the presence of time-varying…
Inferring the parameters of ordinary differential equations (ODEs) from noisy observations is an important problem in many scientific fields. Currently, most parameter estimation methods that bypass numerical integration tend to rely on…
We present a parameter estimation method for nonlinear mixed effect models based on ordinary differential equations (NLME-ODEs). The method presented here aims at regularizing the estimation problem in presence of model misspecifications,…
Real-world time series data that commonly reflect sequential human behavior are often uniquely irregularly sampled and sparse, with highly nonuniform sampling over time and entities. Yet, commonly-used pretraining and augmentation methods…
Ordinary differential equations (ODEs) are widely used to describe the time evolution of natural phenomena across various scientific fields. Estimating the parameters of these systems from data is a challenging task, particularly when…
Handling missing data in time series is a complex problem due to the presence of temporal dependence. General-purpose imputation methods, while widely used, often distort key statistical properties of the data, such as variance and…
A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a…
Estimating the parameters of ordinary differential equations (ODEs) is of fundamental importance in many scientific applications. While ODEs are typically approximated with deterministic algorithms, new research on probabilistic solvers…
Time-delayed differential equations (TDDEs) are widely used to model complex dynamic systems where future states depend on past states with a delay. However, inferring the underlying TDDEs from observed data remains a challenging problem…
Irregular time series, where data points are recorded at uneven intervals, are prevalent in healthcare settings, such as emergency wards where vital signs and laboratory results are captured at varying times. This variability, which…
This paper proposes a new class of heterogeneous causal quantities, named \textit{outcome conditioned} average structural derivatives (OASD) in a general nonseparable model. OASD is the average partial effect of a marginal change in a…
Ordinary differential equations (ODE) are widely used for modeling in Systems Biology. As most commonly only some of the kinetic parameters are measurable or precisely known, parameter estimation techniques are applied to parametrize the…
Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying…
Inverse problem for the identification of the parameters for large-scale systems of nonlinear ordinary differential equations (ODEs) arising in systems biology is analyzed. In a recent paper in \textit{Mathematical Biosciences, 305(2018),…
Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…
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…