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We consider graphs that represent pairwise marginal independencies amongst a set of variables (for instance, the zero entries of a covariance matrix for normal data). We characterize the directed acyclic graphs (DAGs) that faithfully…

Artificial Intelligence · Computer Science 2015-08-04 Johannes Textor , Alexander Idelberger , Maciej Liśkiewicz

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…

Machine Learning · Computer Science 2024-02-14 Davin Choo , Kirankumar Shiragur

Graphical models have been popularly used for capturing conditional independence structure in multivariate data, which are often built upon independent and identically distributed observations, limiting their applicability to complex…

Methodology · Statistics 2025-07-03 Yuwen Wang , Changyu Liu , Xin He , Junhui Wang

Conditions are presented for different types of identifiability of discrete variable models generated over an undirected graph in which one node represents a binary hidden variable. These models can be seen as extensions of the latent class…

Methodology · Statistics 2013-12-12 Elena Stanghellini , Barbara Vantaggi

Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for…

Machine Learning · Statistics 2014-01-17 Le Song , Han Liu , Ankur Parikh , Eric Xing

In this review, we discuss approaches for learning causal structure from data, also called causal discovery. In particular, we focus on approaches for learning directed acyclic graphs (DAGs) and various generalizations which allow for some…

Methodology · Statistics 2022-12-20 Chandler Squires , Caroline Uhler

We consider the setting where a collection of time series, modeled as random processes, evolve in a causal manner, and one is interested in learning the graph governing the relationships of these processes. A special case of wide interest…

Machine Learning · Computer Science 2016-08-30 Hossein Hosseini , Sreeram Kannan , Baosen Zhang , Radha Poovendran

We extend the framework of variational autoencoders to represent transformations explicitly in the latent space. In the family of hierarchical graphical models that emerges, the latent space is populated by higher order objects that are…

Machine Learning · Computer Science 2020-04-24 Giorgio Giannone , Saeed Saremi , Jonathan Masci , Christian Osendorfer

Temporally causal representation learning aims to identify the latent causal process from time series observations, but most methods require the assumption that the latent causal processes do not have instantaneous relations. Although some…

Machine Learning · Computer Science 2026-01-21 Zijian Li , Yifan Shen , Kaitao Zheng , Ruichu Cai , Xiangchen Song , Mingming Gong , Guangyi Chen , Kun Zhang

It is known that from purely observational data, a causal DAG is identifiable only up to its Markov equivalence class, and for many ground truth DAGs, the direction of a large portion of the edges will be remained unidentified. The golden…

Machine Learning · Computer Science 2019-10-15 AmirEmad Ghassami , Saber Salehkaleybar , Negar Kiyavash

Causal representation learning seeks to uncover causal relationships among high-level latent variables from low-level, entangled, and noisy observations. Existing approaches often either rely on deep neural networks, which lack…

Methodology · Statistics 2026-03-27 Wenjin Zhang , Yixin Wang , Yuqi Gu

The assumption of independence between observations (units) in a dataset is prevalent across various methodologies for learning causal graphical models. However, this assumption often finds itself in conflict with real-world data, posing…

Machine Learning · Computer Science 2024-12-31 Alex Chen , Qing Zhou

A key goal of unsupervised learning is to go beyond density estimation and sample generation to reveal the structure inherent within observed data. Such structure can be expressed in the pattern of interactions between explanatory latent…

Machine Learning · Computer Science 2022-11-11 Changmin Yu , Hugo Soulat , Neil Burgess , Maneesh Sahani

Causal discovery aims to recover causal structures or models underlying the observed data. Despite its success in certain domains, most existing methods focus on causal relations between observed variables, while in many scenarios the…

Machine Learning · Computer Science 2020-11-19 Feng Xie , Ruichu Cai , Biwei Huang , Clark Glymour , Zhifeng Hao , Kun Zhang

We consider continuous-time survival or more general event-history settings, where the aim is to infer the causal effect of a time-dependent treatment process. This is formalised as the effect on the outcome event of a (possibly…

Methodology · Statistics 2024-04-23 Kjetil Røysland , Pål Ryalen , Mari Nygård , Vanessa Didelez

We consider the problem of learning the structure of a causal directed acyclic graph (DAG) model in the presence of latent variables. We define latent factor causal models (LFCMs) as a restriction on causal DAG models with latent variables,…

Methodology · Statistics 2022-07-06 Chandler Squires , Annie Yun , Eshaan Nichani , Raj Agrawal , Caroline Uhler

The ability to learn disentangled representations that split underlying sources of variation in high dimensional, unstructured data is important for data efficient and robust use of neural networks. While various approaches aiming towards…

Machine Learning · Statistics 2019-05-15 Raphael Suter , Đorđe Miladinović , Bernhard Schölkopf , Stefan Bauer

One critical challenge of time-series modeling is how to learn and quickly correct the model under unknown distribution shifts. In this work, we propose a principled framework, called LiLY, to first recover time-delayed latent causal…

Machine Learning · Statistics 2022-02-25 Weiran Yao , Guangyi Chen , Kun Zhang

In longitudinal studies where units are embedded in space or a social network, interference may arise, meaning that a unit's outcome can depend on treatment histories of others. The presence of interference poses significant challenges for…

Methodology · Statistics 2025-08-26 Ye Wang , Michael Jetsupphasuk

Causal inference with observational data critically relies on untestable and extra-statistical assumptions that have (sometimes) testable implications. Well-known sets of assumptions that are sufficient to justify the causal interpretation…

Methodology · Statistics 2024-02-20 Pablo Geraldo Bastías