相关论文: From Ordinary Differential Equations to Structural…

In contemporary scientific research, understanding the distinction between correlation and causation is crucial. While correlation is a widely used analytical standard, it does not inherently imply causation. This paper addresses the…

Spurred by tremendous success in pattern matching and prediction tasks, researchers increasingly resort to machine learning to aid original scientific discovery. Given large amounts of observational data about a system, can we uncover the…

Many econometrics textbooks imply that under mean independence of the regressors and the error term, the OLS parameters have a causal interpretation. We show that even when this assumption is satisfied, OLS might identify a pseudo-parameter…

It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schr\"odinger equation are derived from the causal action principle. The…

Causal modelling provides a powerful set of tools for identifying causal structure from observed correlations. It is well known that such techniques fail for quantum systems, unless one introduces `spooky' hidden mechanisms. Whether one can…

Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…

Causal discovery, i.e., inferring underlying causal relationships from observational data, is highly challenging for AI systems. In a time series modeling context, traditional causal discovery methods mainly consider constrained scenarios…

In the field of causal modeling, potential outcomes (PO) and structural causal models (SCMs) stand as the predominant frameworks. However, these frameworks face notable challenges in practically modeling counterfactuals, formalized as…

This paper provides a comprehensive review of deep structural causal models (DSCMs), particularly focusing on their ability to answer counterfactual queries using observational data within known causal structures. It delves into the…

The ultimate goal of most scientific studies is to understand the underlying causal mechanism between the involved variables. Structural causal models (SCMs) are widely used to represent such causal mechanisms. Given an SCM, causal queries…

A new method for estimating structural equation models (SEM) is proposed and evaluated. In contrast to most other methods, it is based directly on the data, not on the covariance matrix of the data. The new approach is flexible enough to…

We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…

We describe basic ideas underlying research to build and understand artificially intelligent systems: from symbolic approaches via statistical learning to interventional models relying on concepts of causality. Some of the hard open…

Let $k$ be a differential field of characteristic zero with an algebraically closed field of constants. In this article, we provide a classification of first order differential equations over $k$ and study the algebraic dependence of…

Realizations of stochastic process are often observed temporal data or functional data. There are growing interests in classification of dynamic or functional data. The basic feature of functional data is that the functional data have…

Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…

Reasoning semantically in first-order logic is notoriously a challenge. This paper surveys a selection of semantically-guided or model-based methods that aim at meeting aspects of this challenge. For first-order logic we touch upon…

Real-world complex systems are often modelled by sets of equations with endogenous and exogenous variables. What can we say about the causal and probabilistic aspects of variables that appear in these equations without explicitly solving…

We study a class of linear ordinary differential equations (ODE)s with distributional coefficients. These equations are defined using an {\it intrinsic} multiplicative product of Schwartz distributions which is an extension of the…

We present an adaptation of the so-called structural method \cite{CMM23} for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled differential systems. Structural schemes decompose the problem…