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The front-door criterion can be used to identify and compute causal effects despite the existence of unmeasured confounders between a treatment and outcome. However, the key assumptions -- (i) the existence of a variable (or set of…
Geometric representations provide a principled framework for structuring the description of latent constructs and clarifying sources of uncertainty in their dimensional characterisation. We introduce a novel geometric representation of…
Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation…
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…
Convex combinations of i.i.d. random variables without a finite mean can behave in a strikingly different way from the finite-mean case: as the weight vector becomes more balanced, the resulting combination may become stochastically larger,…
Addressing selection bias in latent variable causal discovery is important yet underexplored, largely due to a lack of suitable statistical tools: While various tools beyond basic conditional independencies have been developed to handle…
Causal models with unobserved variables impose nontrivial constraints on the distributions over the observed variables. When a common cause of two variables is unobserved, it is impossible to uncover the causal relation between them without…
It is "well known" that in linear models: (1) testable constraints on the marginal distribution of observed variables distinguish certain cases in which an unobserved cause jointly influences several observed variables; (2) the technique of…
Latent variable models are popularly used to measure latent factors (e.g., abilities and personalities) from large-scale assessment data. Beyond understanding these latent factors, the covariate effect on responses controlling for latent…
Causal inference methods based on conditional independence construct Markov equivalent graphs, and cannot be applied to bivariate cases. The approaches based on independence of cause and mechanism state, on the contrary, that causal…
Linear causal disentanglement is a recent method in causal representation learning to describe a collection of observed variables via latent variables with causal dependencies between them. It can be viewed as a generalization of both…
In unsupervised causal representation learning for sequential data with time-delayed latent causal influences, strong identifiability results for the disentanglement of causally-related latent variables have been established in stationary…
How should one assess the credibility of assumptions weaker than statistical independence, like quantile independence? In the context of identifying causal effects of a treatment variable, we argue that such deviations should be chosen…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
Inferring causal relationships from observed data is an important task, yet it becomes challenging when the data is subject to various external interferences. Most of these interferences are the additional effects of external factors on…
This paper studies the challenging problem of estimating causal effects from observational data, in the presence of unobserved confounders. The two-stage least square (TSLS) method and its variants with a standard instrumental variable (IV)…
Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…
Testing for the conditional independence structure in data is a fundamental and critical task in statistics and machine learning, which finds natural applications in causal discovery - a highly relevant problem to many scientific…
Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation is effective for capturing linear dependency, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns.…
This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some…