Related papers: Identifiability of latent-variable and structural-…
Linear non-Gaussian causal models postulate that each random variable is a linear function of parent variables and non-Gaussian exogenous error terms. We study identification of the linear coefficients when such models contain latent…
The estimation of linear causal models (also known as structural equation models) from data is a well-known problem which has received much attention in the past. Most previous work has, however, made an explicit or implicit assumption of…
Factor analysis models are widely utilized in social and behavioral sciences, such as psychology, education, and marketing, to measure unobservable latent traits. In this article, we introduce a nonlinear structured latent factor analysis…
We consider the problem of learning causal models from observational data generated by linear non-Gaussian acyclic causal models with latent variables. Without considering the effect of latent variables, one usually infers wrong causal…
Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be…
We consider linear non-Gaussian structural equation models that involve latent confounding. In this setting, the causal structure is identifiable, but, in general, it is not possible to identify the specific causal effects. Instead, a…
A tacit assumption in classical linear regression problems is the full knowledge of the existing link between the covariates and responses. In Unlinked Linear Regression (ULR) this link is either partially or completely missing. While the…
We consider linear structural equation models with explicitly modelled latent variables. In such models, observed and latent variables solve linear equations including stochastic noise terms. The goal of our work is to identify the direct…
Linear structural equation models, which relate random variables via linear interdependencies and Gaussian noise, are a popular tool for modeling multivariate joint distributions. These models correspond to mixed graphs that include both…
Causal discovery with latent variables is a fundamental task. Yet most existing methods rely on strong structural assumptions, such as enforcing specific indicator patterns for latents or restricting how they can interact with others. We…
Nearly all identifiability results in unsupervised representation learning inspired by, e.g., independent component analysis, factor analysis, and causal representation learning, rely on assumptions of additive independent noise or…
We consider structural equation models in which variables can be written as a function of their parents and noise terms, which are assumed to be jointly independent. Corresponding to each structural equation model, there is a directed…
In this work, we consider the identifiability assumption of Gaussian linear structural equation models (SEMs) in which each variable is determined by a linear function of its parents plus normally distributed error. It has been shown that…
The bifactor model and its extensions are multidimensional latent variable models, under which each item measures up to one subdimension on top of the primary dimension(s). Despite their wide applications to educational and psychological…
Structural equation models are multivariate statistical models that are defined by specifying noisy functional relationships among random variables. We consider the classical case of linear relationships and additive Gaussian noise terms.…
We develop a criterion to certify whether causal effects are identifiable in linear structural equation models with latent variables. Linear structural equation models correspond to directed graphs whose nodes represent the random variables…
A parameter of a mathematical model is structurally identifiable if it can be determined from noiseless experimental data. Here, we examine the identifiability properties of two important classes of linear compartmental models:…
The paradigm of linear structural equation modeling readily allows one to incorporate causal feedback loops in the model specification. These appear as directed cycles in the common graphical representation of the models. However, the…
We consider learning the possible causal direction of two observed variables in the presence of latent confounding variables. Several existing methods have been shown to consistently estimate causal direction assuming linear or some type of…
Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of…