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In todays age of data, discovering relationships between different variables is an interesting and a challenging problem. This problem becomes even more critical with regards to complex dynamical systems like weather forecasting and…
Instrumental variables allow for quantification of cause and effect relationships even in the absence of interventions. To achieve this, a number of causal assumptions must be met, the most important of which is the independence assumption,…
We wish to test whether a real-valued variable $Z$ has explanatory power, in addition to a multivariate variable $X$, for a binary variable $Y$. Thus, we are interested in testing the hypothesis $\mathbb{P}(Y=1\, | \, X,Z)=\mathbb{P}(Y=1\,…
Causal discovery is to learn cause-effect relationships among variables given observational data and is important for many applications. Existing causal discovery methods assume data sufficiency, which may not be the case in many real world…
Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly…
Multivariate time series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the…
Simple correlation coefficients between two variables have been generalized to measure association between two matrices in many ways. Coefficients such as the RV coefficient, the distance covariance (dCov) coefficient and kernel based…
Constraint-based causal discovery methods leverage conditional independence tests to infer causal relationships in a wide variety of applications. Just as the majority of machine learning methods, existing work focuses on studying…
Most existing methods that address out-of-distribution (OOD) generalization for node classification on graphs primarily focus on a specific type of data biases, such as label selection bias or structural bias. However, anticipating the type…
Instrumental variable models allow us to identify a causal function between covariates $X$ and a response $Y$, even in the presence of unobserved confounding. Most of the existing estimators assume that the error term in the response $Y$…
Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding…
In this paper, we define and study the concept of traceable regressions. These are sequences of regressions in joint or single responses for which a corresponding regression graph captures not only an independence structure but represents,…
We propose a sequential, anytime-valid method to test the conditional independence of a response $Y$ and a predictor $X$ given a random vector $Z$. The proposed test is based on e-statistics and test martingales, which generalize likelihood…
We study identifiability in continuous-time linear stationary stochastic differential equations with known causal structure. Unlike existing approaches, we relax the assumption of a known diffusion matrix, thereby respecting the model's…
Two known results on the relationship between conditional and unconditional independence are obtained as a consequence of the main result of this paper, a theorem that uses independence of Markov kernels to obtain a minimal condition which…
The Y-test is a useful tool for detecting missing confounders in the context of a multivariate regression.However, it is rarely used in practice since it requires identifying multiple conditionally independent instruments, which is often…
In the causal learning setting, we wish to learn cause-and-effect relationships between variables such that we can correctly infer the effect of an intervention. While the difference between a cyclic structure and an acyclic structure may…
Causality is receiving increasing attention by the artificial intelligence and machine learning communities. This paper gives an example of modelling a recommender system problem using causal graphs. Specifically, we approached the causal…
Motivated by extreme value theory, max-linear Bayesian networks have been recently introduced and studied as an alternative to linear structural equation models. However, for max-linear systems the classical independence results for…
Estimating causal effects from observational data requires identifying valid adjustment sets. This task is especially challenging in realistic settings where latent confounding and feedback loops are present. Existing approaches typically…