Related papers: A Variational Approach to Parameter Estimation in …
Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…
Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…
Differences-in-differences (DiD) is a causal inference method for observational longitudinal data that assumes parallel expected potential outcome trajectories between treatment groups under the counterfactual scenario where all units…
We propose a novel regression adjustment method designed for estimating distributional treatment effect parameters in randomized experiments. Randomized experiments have been extensively used to estimate treatment effects in various…
We present an optimization process to estimate parameters in systems of ordinary differential equations from chaotic time series. The optimization technique is based on a variational approach, and numerical studies on noisy time series…
Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…
Differential equations are important tools to portray dynamic problems, and are widely used in finance, engineering and biology. Here, multiple dynamic differential models were built innovatively, and discretized with the Runge-Kutta…
Estimating a causal query from observational data is an essential task in the analysis of biomolecular networks. Estimation takes as input a network topology, a query estimation method, and observational measurements on the network…
This paper re-examines the problem of parameter estimation in Bayesian networks with missing values and hidden variables from the perspective of recent work in on-line learning [Kivinen & Warmuth, 1994]. We provide a unified framework for…
Discrete choice models are commonly used by applied statisticians in numerous fields, such as marketing, economics, finance, and operations research. When agents in discrete choice models are assumed to have differing preferences, exact…
This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…
We consider chemical reaction networks modeled by a discrete state and continuous in time Markov process for the vector copy number of the species and provide a novel particle filter method for state and parameter estimation based on exact…
The development of chemical reaction models aids understanding and prediction in areas ranging from biology to electrochemistry and combustion. A systematic approach to building reaction network models uses observational data not only to…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…