Related papers: Stability of Linear Structural Equation Models of …
Structural-equations models (SEMs) are perhaps the most commonly used framework for modeling causality. However, as we show, naively extending this framework to infinitely many variables, which is necessary, for example, to model dynamical…
Causality and stability are fundamental requirements for the differential equations describing predictable relativistic many-body systems. In this work, we investigate the stability and causality criteria in linear mode analysis. We discuss…
Frame design for phaseless reconstruction is now part of the broader problem of nonlinear reconstruction and is an emerging topic in harmonic analysis. The problem of phaseless reconstruction can be simply stated as follows. Given the…
The structural stability of a lightsail under the laser flux necessary for interstellar flight is studied analytically and numerically. A sinusoidal perturbation is introduced into a two-dimensional thin-film sail to determine if the sail…
A criterion on the asymptotic stability of fractional-order systems with incomensurate orders is proposed in this paper. Existing methods always assume order parameters be rational numbers or the ratios of any two orders be rational…
In this article, we provide stability estimates for the finite element discretization of a class of inverse parameter problems of the form $-\nabla\cdot(\mu S) = \g f$ in a domain $\Omega$ of $\R^d$. Here $\mu$ is the unknown parameter to…
Obtaining initial conditions and parameterizations leading to a model consistent with available measurements or safety specifications is important for many applications. Examples include model (in-)validation, prediction, fault diagnosis,…
Identifying latent variables and the causal structure involving them is essential across various scientific fields. While many existing works fall under the category of constraint-based methods (with e.g. conditional independence or rank…
We present a basis for studying questions of cause and effect in statistics which subsumes and reconciles the models proposed by Pearl, Robins, Rubin and others, and which, as far as mathematical notions and notation are concerned, is…
Causal representation learning aims to unveil latent high-level causal representations from observed low-level data. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as…
Maintaining numerical stability in machine learning models is crucial for their reliability and performance. One approach to maintain stability of a network layer is to integrate the condition number of the weight matrix as a regularizing…
Linear structural causal models (SCMs) -- in which each observed variable is generated by a subset of the other observed variables as well as a subset of the exogenous sources -- are pervasive in causal inference and casual discovery.…
For high-dimensional sparse parameter estimation problems, Log-Sum Penalty (LSP) regularization effectively reduces the sampling sizes in practice. However, it still lacks theoretical analysis to support the experience from previous…
Generalized structural equations models (GSEMs) [Peters and Halpern 2021], are, as the name suggests, a generalization of structural equations models (SEMs). They can deal with (among other things) infinitely many variables with infinite…
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…
When dealing with time series data, causal inference methods often employ structural vector autoregressive (SVAR) processes to model time-evolving random systems. In this work, we rephrase recursive SVAR processes with possible latent…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
In this study, the combined use of structural equation modeling (SEM) and Bayesian network modeling (BNM) in causal inference analysis is revisited. The perspective highlights the debate between proponents of using BNM as either an…
We study a sample complexity vs. conditioning tradeoff in modern signal recovery problems (including sparse recovery, low-rank matrix sensing, covariance estimation, and abstract phase retrieval), where convex optimization problems are…
We find a complete characterization for sets of isotropic conductivities with stable recovery in the $L^2$ norm when the data of the Calder\'on Inverse Conductivity Problem is obtained in the boundary of a disk and the conductivities are…