Causal Structure Learning

Heinze‐Deml, Christina; Maathuis, Marloes H.; Meinshausen, Nicolai

doi:10.1146/annurev-statistics-031017-100630

Cited by 134 publications

(114 citation statements)

References 33 publications

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“…Overall, we place our work as a starting effort to better characterize the task of learning the structure of Bayesian Networks from data, which may lead in the future to a more effective application of this approach. In particular, we focused on the more general task of learning the structure of a BN [6], and we did not dwell on several interesting domain-specific topics, which we leave for future investigations [12,13,14].…”

Section: Discussionmentioning

confidence: 99%

Learning the Structure of Bayesian Networks: A Quantitative Assessment of the Effect of Different Algorithmic Schemes

et al. 2018

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One of the most challenging tasks when adopting Bayesian Networks (BNs) is the one of learning their structure from data. This task is complicated by the huge search space of possible solutions, and by the fact that the problem is N P -hard. Hence, full enumeration of all the possible solutions is not always feasible and approximations are often required. However, to the best of our knowledge, a quantitative analysis of the performance and characteristics of the different heuristics to solve this problem has never been done before.For this reason, in this work, we provide a detailed comparison of many different state-of-the-arts methods for structural learning on simulated data considering both BNs with discrete and continuous variables, and with different rates of noise in the data. In particular, we investigate the performance of different widespread scores and algorithmic approaches proposed for the inference and the statistical pitfalls within them.

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Section: Discussionmentioning

confidence: 99%

Learning the Structure of Bayesian Networks: A Quantitative Assessment of the Effect of Different Algorithmic Schemes

et al. 2018

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“…If the underlying DAG G is unknown, it needs to be estimated from data; for a general overview of causal structure learning see for example Heinze‐Deml et al . (). Under a faithfulness assumption (Meek, ), the set of conditional independences in the observational distribution will be exactly those that may be inferred via d ‐separation from G .…”

Section: Conditional Independence Graph Estimation and Causal Structumentioning

confidence: 97%

Right Singular Vector Projection Graphs: Fast High Dimensional Covariance Matrix Estimation under Latent Confounding

Shah

Frot

Thanei

et al. 2020

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary We consider the problem of estimating a high dimensional p×p covariance matrix Σ, given n observations of confounded data with covariance Σ+ΓnormalΓsans-serifT, where Γ is an unknown p×q matrix of latent factor loadings. We propose a simple and scalable estimator based on the projection onto the right singular vectors of the observed data matrix, which we call right singular vector projection (RSVP). Our theoretical analysis of this method reveals that, in contrast with approaches based on the removal of principal components, RSVP can cope well with settings where the smallest eigenvalue of normalΓsans-serifTΓ is relatively close to the largest eigenvalue of Σ, as well as when the eigenvalues of normalΓsans-serifTΓ are diverging fast. RSVP does not require knowledge or estimation of the number of latent factors q, but it recovers Σ only up to an unknown positive scale factor. We argue that this suffices in many applications, e.g. if an estimate of the correlation matrix is desired. We also show that, by using subsampling, we can further improve the performance of the method. We demonstrate the favourable performance of RSVP through simulation experiments and an analysis of gene expression data sets collated by the GTEX consortium.

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“…(), Drton and Maathuis () and Heinze‐Deml et al . () for a more detailed overview and simulation studies.…”

Section: Problem Statement and Suggested Workmentioning

confidence: 99%

“…Structure learning algorithms fall into three main categories that we review here. Since there are many approaches in each of these categories we refer the reader to Han et al (2016), Drton and Maathuis (2017) and Heinze-Deml et al (2018) for a more detailed overview and simulation studies. Score-based approaches assign a score to each structure and aim to identify the one (or ones) that maximizes a scoring function.…”

Section: Previous Workmentioning

confidence: 99%

Robust Causal Structure Learning with Some Hidden Variables

Frot

Nandy

Maathuis

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary We introduce a new method to estimate the Markov equivalence class of a directed acyclic graph (DAG) in the presence of hidden variables, in settings where the underlying DAG among the observed variables is sparse, and there are a few hidden variables that have a direct effect on many of the observed variables. Building on the so‐called low rank plus sparse framework, we suggest a two‐stage approach which first removes the effect of the hidden variables and then estimates the Markov equivalence class of the underlying DAG under the assumption that there are no remaining hidden variables. This approach is consistent in certain high dimensional regimes and performs favourably when compared with the state of the art, in terms of both graphical structure recovery and total causal effect estimation.

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Causal Structure Learning

Cited by 134 publications

References 33 publications

Learning the Structure of Bayesian Networks: A Quantitative Assessment of the Effect of Different Algorithmic Schemes

Learning the Structure of Bayesian Networks: A Quantitative Assessment of the Effect of Different Algorithmic Schemes

Right Singular Vector Projection Graphs: Fast High Dimensional Covariance Matrix Estimation under Latent Confounding

Robust Causal Structure Learning with Some Hidden Variables

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