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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…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
Identification theory for causal effects in causal models associated with hidden variable directed acyclic graphs (DAGs) is well studied. However, the corresponding algorithms are underused due to the complexity of estimating the…
Regularization improves generalization of supervised models to out-of-sample data. Prior works have shown that prediction in the causal direction (effect from cause) results in lower testing error than the anti-causal direction. However,…
In this paper, we introduce a novel class of graphical models for representing time lag specific causal relationships and independencies of multivariate time series with unobserved confounders. We completely characterize these graphs and…
In observational studies, the true causal model is typically unknown and needs to be estimated from available observational and limited experimental data. In such cases, the learned causal model is commonly represented as a partially…
Causal DAGs (also known as Bayesian networks) are a popular tool for encoding conditional dependencies between random variables. In a causal DAG, the random variables are modeled as vertices in the DAG, and it is stipulated that every…
Causal discovery aims to infer causal relationships among variables from observational data, typically represented by a directed acyclic graph (DAG). Most existing methods assume independent and identically distributed observations, an…
Multivariate time series (MTS) data such as time course gene expression data in genomics are often collected to study the dynamic nature of the systems. These data provide important information about the causal dependency among a set of…
We present a novel perspective and algorithm for learning directed acyclic graphs (DAGs) from data generated by a linear structural equation model (SEM). First, we show that a linear SEM can be viewed as a linear transform that, in prior…
The causal revolution has stimulated interest in understanding complex relationships in various fields. Most of the existing methods aim to discover causal relationships among all variables within a complex large-scale graph. However, in…
Artificial Neural Networks (ANNs), including fully-connected networks and transformers, are highly flexible and powerful function approximators, widely applied in fields like computer vision and natural language processing. However, their…
Causal graphs, such as directed acyclic graphs (DAGs) and partial ancestral graphs (PAGs), represent causal relationships among variables in a model. Methods exist for learning DAGs and PAGs from data and for converting DAGs to PAGs.…
Graphical causal models are an important tool for knowledge discovery because they can represent both the causal relations between variables and the multivariate probability distributions over the data. Once learned, causal graphs can be…
The ultimate goal of most scientific studies is to understand the underlying causal mechanism between the involved variables. Structural causal models (SCMs) are widely used to represent such causal mechanisms. Given an SCM, causal queries…
Recent work on causal abstraction, in particular graphical approaches focusing on causal structure between clusters of variables, aims to summarize a high-dimensional causal structure in terms of a low-dimensional one. Existing methods for…
A growing body of work has begun to study intervention design for efficient structure learning of causal directed acyclic graphs (DAGs). A typical setting is a causally sufficient setting, i.e. a system with no latent confounders, selection…
We give a selective review of some recent developments in causal inference, intended for researchers who are not familiar with graphical models and causality, and with a focus on methods that are applicable to large data sets. We mainly…
This article surveys the variety of ways in which a directed acyclic graph (DAG) can be used to represent a problem of probabilistic causality. For each of these we describe the relevant formal or informal semantics governing that…
Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Chickering (1995) provided a transformational characterization of…