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Data simulation is fundamental for machine learning and causal inference, as it allows exploration of scenarios and assessment of methods in settings with full control of ground truth. Directed acyclic graphs (DAGs) are well established for…

We consider distributions arising from a mixture of causal models, where each model is represented by a directed acyclic graph (DAG). We provide a graphical representation of such mixture distributions and prove that this representation…

We consider a binary response which is potentially affected by a set of continuous variables. Of special interest is the causal effect on the response due to an intervention on a specific variable. The latter can be meaningfully determined…

We show that every directed graph $G$ with $n$ vertices and $m$ edges admits a directed acyclic graph (DAG) with $m^{1+o(1)}$ edges, called a DAG projection, that can either $(1+1/\text{polylog} (n))$-approximate distances between all pairs…

Causal inference is a critical task across fields such as healthcare, economics, and the social sciences. While recent advances in machine learning, especially those based on the deep-learning architectures, have shown potential in…

Federated learning (FL) aims to collaboratively train a global model while ensuring client data privacy. However, FL faces challenges from the non-IID data distribution among clients. Clustered FL (CFL) has emerged as a promising solution,…

Uncovering hidden graph structures underlying real-world data is a critical challenge with broad applications across scientific domains. Recently, transformer-based models leveraging the attention mechanism have demonstrated strong…

We develop terminology and methods for working with maximally oriented partially directed acyclic graphs (maximal PDAGs). Maximal PDAGs arise from imposing restrictions on a Markov equivalence class of directed acyclic graphs, or…

Ancestral graphs can encode conditional independence relations that arise in directed acyclic graph (DAG) models with latent and selection variables. However, for any ancestral graph, there may be several other graphs to which it is Markov…

This paper considers inference of causal structure in a class of graphical models called "conditional DAGs". These are directed acyclic graph (DAG) models with two kinds of variables, primary and secondary. The secondary variables are used…

Recursive linear structural equation models and the associated directed acyclic graphs (DAGs) play an important role in causal discovery. The classic identifiability result for this class of models states that when only observational data…

Finding a directed acyclic graph (DAG) that best encodes the conditional independence statements observable from data is a central question within causality. Algorithms that greedily transform one candidate DAG into another given a fixed…

To represent the causal relationships between variables, a directed acyclic graph (DAG) is widely utilized in many areas, such as social sciences, epidemics, and genetics. Many causal structure learning approaches are developed to learn the…

When a dynamical system can be modeled as a sequence of observations, Granger causality is a powerful approach for detecting predictive interactions between its variables. However, traditional Granger causal inference has limited utility 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…

This work addresses the NP-Hard problem of acyclic directed acyclic graph (DAG) partitioning problem. The acyclic partitioning problem is defined as partitioning the vertex set of a given directed acyclic graph into disjoint and…

Transformer models have recently gained popularity in graph representation learning as they have the potential to learn complex relationships beyond the ones captured by regular graph neural networks. The main research question is how to…

Assessing the accuracy of the output of causal discovery algorithms is crucial in developing and comparing novel methods. Common evaluation metrics such as the structural Hamming distance are useful for assessing individual links of causal…

Hidden variables are ubiquitous in practical data analysis, and therefore modeling marginal densities and doing inference with the resulting models is an important problem in statistics, machine learning, and causal inference. Recently, a…

It is well known that there may be many causal explanations that are consistent with a given set of data. Recent work has been done to represent the common aspects of these explanations into one representation. In this paper, we address…