Related papers: Partial Causal Detectability of Linear Descriptor …
Many important quantities of interest are only partially identified from observable data: the data can limit them to a set of plausible values, but not uniquely determine them. This paper develops a unified framework for covariate-assisted…
We consider basic conceptual questions concerning the relationship between statistical estimation and causal inference. Firstly, we show how to translate causal inference problems into an abstract statistical formalism without requiring any…
State estimation has a pivotal role in several applications, including but not limited to advanced control design. Especially when dealing with nonlinear systems state estimation is a nontrivial task, often entailing approximations and…
Exponential dichotomies play a central role in stability theory for dynamical systems. They allow to split the state space into two subspaces, where all trajectories in one subspace decay whereas all trajectories in the other subspace grow,…
There has been considerable recent interest in estimating heterogeneous causal effects. In this paper, we study conditional average partial causal effects (CAPCE) to reveal the heterogeneity of causal effects with continuous treatment. We…
Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…
Here we introduce Partially Observed Structural Causal Models (POSCMs) that formalize causal systems where latent contexts co-determine both the interaction structure and downstream mechanisms on observed variables. POSCMs provide an…
The presence of unobserved common causes and measurement error poses two major obstacles to causal structure learning, since ignoring either source of complexity can induce spurious causal relations among variables of interest. We study…
In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series…
Dynamical systems, prevalent in various scientific and engineering domains, are susceptible to anomalies that can significantly impact their performance and reliability. This paper addresses the critical challenges of anomaly detection,…
This paper proposes a novel approach for designing functional observers for nonlinear systems, with linear error dynamics and assignable poles. Sufficient conditions for functional observability are first derived, leading to functional…
We introduce a simple diagnostic test for assessing the overall or partial goodness of fit of a linear causal model with errors being independent of the covariates. In particular, we consider situations where hidden confounding is…
Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability.…
This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…
Observed associations in a database may be due in whole or part to variations in unrecorded (latent) variables. Identifying such variables and their causal relationships with one another is a principal goal in many scientific and practical…
This paper addresses the problem of distributed state estimation for discrete-time linear time-invariant systems. Building on the framework proposed in Gao & Yang (2025), we exploit the Jordan canonical form of the system matrix to develop…
The $H_2$ norm is a commonly used performance metric in the design of estimators. However, $H_2$-optimal estimation of most PDEs is complicated by the lack of transfer function and state-space representations. To address this problem, we…
The paper presents linear predictors and causal filters for discrete time signals featuring some different kinds of spectrum degeneracy. These predictors and filters are based on approximation of ideal non-causal transfer functions by…
The idea of neural Ordinary Differential Equations (ODE) is to approximate the derivative of a function (data model) instead of the function itself. In residual networks, instead of having a discrete sequence of hidden layers, the…
This paper considers the H\infty-optimal estimation problem for linear systems with multiple delays in states, output, and disturbances. First, we formulate the H\infty-optimal estimation problem in the Delay-Differential Equation (DDE)…