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Missing data is a pervasive problem in data analyses, resulting in datasets that contain censored realizations of a target distribution. Many approaches to inference on the target distribution using censored observed data, rely on missing…
Learning causal relationships between variables is a fundamental task in causal inference and directed acyclic graphs (DAGs) are a popular choice to represent the causal relationships. As one can recover a causal graph only up to its Markov…
Causality is important for designing interpretable and robust methods in artificial intelligence research. We propose a local approach to identify whether a variable is a cause of a given target under the framework of causal graphical…
Causal parameters may not be point identified in the presence of unobserved confounding. However, information about non-identified parameters, in the form of bounds, may still be recovered from the observed data in some cases. We develop a…
We present a novel form of Fourier analysis, and associated signal processing concepts, for signals (or data) indexed by edge-weighted directed acyclic graphs (DAGs). This means that our Fourier basis yields an eigendecomposition of a…
Real causal processes may contain feedback loops and change over time. In this paper, we model cycles and non-stationary distributions using a mixture of directed acyclic graphs (DAGs). We then study the conditional independence (CI)…
This paper concerns the assessment of direct causal effects from a combination of: (i) non-experimental data, and (ii) qualitative domain knowledge. Domain knowledge is encoded in the form of a directed acyclic graph (DAG), in which all…
Causal relationships among variables are commonly represented via directed acyclic graphs. There are many methods in the literature to quantify the strength of arrows in a causal acyclic graph. These methods, however, have undesirable…
Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high dimensional settings when the graphs to be learned are not sparse. In this paper, we…
Background: There is increasing interest in approaches for analyzing the effect of exposure mixtures on health. A key issue is how to simultaneously analyze often highly collinear components of the mixture, which can create problems such as…
An important task in data analysis is the discovery of causal relationships between observed variables. For continuous-valued data, linear acyclic causal models are commonly used to model the data-generating process, and the inference of…
The invariance properties of interventional distributions relative to the observational distribution, and how these properties allow us to refine Markov equivalence classes (MECs) of DAGs, is central to causal DAG discovery algorithms that…
Statistical relationships in observed data can arise for several different reasons: the observed variables may be causally related, they may share a latent common cause, or there may be selection bias. Each of these scenarios can be…
We present a generalized linear structural causal model, coupled with a novel data-adaptive linear regularization, to recover causal directed acyclic graphs (DAGs) from time series. By leveraging a recently developed stochastic monotone…
We present a generalized linear structural causal model, coupled with a novel data-adaptive linear regularization, to recover causal directed acyclic graphs (DAGs) from time series. By leveraging a recently developed stochastic monotone…
We study the problem of discovering the simplest latent variable that can make two observed discrete variables conditionally independent. The minimum entropy required for such a latent is known as common entropy in information theory. We…
Social science theories often postulate causal relationships among a set of variables or events. Although directed acyclic graphs (DAGs) are increasingly used to represent these theories, their full potential has not yet been realized in…
Learning a faithful directed acyclic graph (DAG) from samples of a joint distribution is a challenging combinatorial problem, owing to the intractable search space superexponential in the number of graph nodes. A recent breakthrough…
Inference of causality is central in nonlinear time series analysis and science in general. A popular approach to infer causality between two processes is to measure the information flow between them in terms of transfer entropy. Using…
We consider identifying a conditional causal effect when a graph is known up to a maximally oriented partially directed acyclic graph (MPDAG). An MPDAG represents an equivalence class of graphs that is restricted by background knowledge and…