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Learning directed acyclic graphs based on sparsest permutations [article]

Garvesh Raskutti, Caroline Uhler
2019 arXiv   pre-print
We consider the problem of learning a Bayesian network or directed acyclic graph (DAG) model from observational data.  ...  In this paper, we propose the sparsest permutation (SP) algorithm. This algorithm is based on finding the causal ordering of the variables that yields the sparsest DAG.  ...  While there are a number of challenges involved with inferring directional relations amongst several variables, a useful simplification is to assume that the causal structure is modeled by a directed acyclic  ... 
arXiv:1307.0366v4 fatcat:eopveag3dfcx7epwykjrwcf5qq

Learning directed acyclic graph models based on sparsest permutations

Garvesh Raskutti, Caroline Uhler
2018 Stat  
Our contributions In the following, we propose and analyze a score-based method for learning the Markov equivalence class of the underlying DAG based on observational data.  ...  While there are a number of challenges involved with inferring directional relations amongst several variables, a useful simplification is to assume that the causal structure is modeled by a directed acyclic  ...  By applying one last time the contraction axiom to the CI relations (5) and (6) we get that X π(i) ⊥ ⊥ X π(j) | X pa(π(i)) .  ... 
doi:10.1002/sta4.183 fatcat:rl3jsylabff6zpih2ppjipazbe

Ordering-Based Causal Structure Learning in the Presence of Latent Variables [article]

Daniel Irving Bernstein, Basil Saeed, Chandler Squires, Caroline Uhler
2020 arXiv   pre-print
We consider the task of learning a causal graph in the presence of latent confounders given i.i.d. samples from the model.  ...  While current algorithms for causal structure discovery in the presence of latent confounders are constraint-based, we here propose a score-based approach.  ...  Basil Saeed was partially supported by the Abdul Latif Jameel Clinic for Machine Learning in Health at MIT.  ... 
arXiv:1910.09014v2 fatcat:mbphnu7nl5am5fgrkum2juspjm

Causal Structure Learning: a Combinatorial Perspective [article]

Chandler Squires, Caroline Uhler
2022 arXiv   pre-print
In particular, we focus on approaches for learning directed acyclic graphs (DAGs) and various generalizations which allow for some variables to be unobserved in the available data.  ...  Second, we discuss the structure of equivalence classes over causal graphs, i.e., sets of graphs which represent what can be learned from observational data alone, and how these equivalence classes can  ...  Caroline Uhler was partially supported by NSF (DMS-1651995), ONR (N00014-17-1-2147 and N00014-22-1-2116), the MIT-IBM Watson AI Lab, MIT J-Clinic for Machine Learning and Health, the Eric and Wendy Schmidt  ... 
arXiv:2206.01152v1 fatcat:k7bha6htu5cwlmhh2haquuja7m

Consistency Guarantees for Greedy Permutation-Based Causal Inference Algorithms [article]

Liam Solus, Yuhao Wang, Caroline Uhler
2021 arXiv   pre-print
As the space of directed acyclic graphs on p nodes and the associated space of Markov equivalence classes are both much larger than the space of permutations, it is desirable to consider permutation-based  ...  Since the basic task of learning such a model from data is NP-hard, a standard approach is greedy search over the space of directed acyclic graphs or Markov equivalence classes of directed acyclic graphs  ...  Introduction Bayesian networks, or directed acyclic graph (DAG) models, are widely used to model complex causal systems arising, for example, in computational biology, epidemiology, or sociology [7, 20  ... 
arXiv:1702.03530v4 fatcat:ydvrljejezdjrdemzbanjxibi4

Greedy Relaxations of the Sparsest Permutation Algorithm [article]

Wai-Yin Lam, Bryan Andrews, Joseph Ramsey
2022 arXiv   pre-print
There has been an increasing interest in methods that exploit permutation reasoning to search for directed acyclic causal models, including the "Ordering Search" of Teyssier and Kohler and GSP of Solus  ...  We extend the methods of the latter by a permutation-based operation, tuck, and develop a class of algorithms, namely GRaSP, that are efficient and pointwise consistent under increasingly weaker assumptions  ...  A directed acyclic graph (DAG) is a directed graph where no vertex can have a unidirectional directed path to itself. Denote E(G) as the set of directed edges in G.  ... 
arXiv:2206.05421v1 fatcat:nt6lv4wnvjcitlwiz5lufl6d2i

Robustness Metric for Quantifying Causal Model Confidence and Parameter Uncertainty [article]

Garrett Waycaster, Christian Bes, Volodymyr Bilotkach, Christian Gogu, Raphael Haftka, Nam-Ho Kim
2016 arXiv   pre-print
The use of this metric is demonstrated on both numerically simulated data and a case study from existing causal model literature.  ...  Figure 1 . 1 Directed acyclic graph for a Bayesian network. (From Chen and Chihying [2]) , is defined as a vector of the observed data as described in equation( 2.4 ).  ...  However in many cases, experimentally manipulating variables is not feasible; for these cases many methods have been developed for learning causal models based on observational data.  ... 
arXiv:1602.02198v1 fatcat:vquovsmzunbkhblc2546lxkk4m

Permutation-Based Causal Structure Learning with Unknown Intervention Targets [article]

Chandler Squires, Yuhao Wang, Caroline Uhler
2020 arXiv   pre-print
We demonstrate the performance of our algorithm on synthetic and biological datasets.  ...  The proposed algorithm greedily searches over the space of permutations to minimize a novel score function.  ...  Typically, the causal model is in the form of a directed acyclic graph (DAG).  ... 
arXiv:1910.09007v2 fatcat:a3eta6lnu5gpxdla2x6p6eqho4

Efficient Permutation Discovery in Causal DAGs [article]

Chandler Squires, Joshua Amaniampong, Caroline Uhler
2020 arXiv   pre-print
The problem of learning a directed acyclic graph (DAG) up to Markov equivalence is equivalent to the problem of finding a permutation of the variables that induces the sparsest graph.  ...  Finally, we show that there exist dense graphs on which our method achieves almost perfect performance, so that unlike most existing causal structure learning algorithms, the situations in which our algorithm  ...  Acknowledgments Chandler Squires was partially supported by an NSF Graduate Fellowship, MIT J-Clinic for Machine Learning and Health, and IBM.  ... 
arXiv:2011.03610v1 fatcat:bnhbaclxrza2vidqbcijcvas6u

Algebraic Statistics in Practice: Applications to Networks

Marta Casanellas, Sonja Petrović, Caroline Uhler
2017 Annual Review of Statistics and Its Application  
In this review, we illustrate this on three problems related to networks: network models for relational data, causal structure discovery, and phylogenetics.  ...  For each problem, we give an overview of recent results in algebraic statistics, with emphasis on the statistical achievements made possible by these tools and their practical relevance for applications  ...  Abbreviation: DAG, directed acyclic graph.  ... 
doi:10.1146/annurev-statistics-031017-100053 fatcat:cmd2g7mbhzgbxpp4erqzf5klfu

Low-variance Black-box Gradient Estimates for the Plackett-Luce Distribution [article]

Artyom Gadetsky, Kirill Struminsky, Christopher Robinson, Novi Quadrianto, Dmitry Vetrov
2019 arXiv   pre-print
We show that our method outperforms competitive relaxation-based optimization methods and is also applicable to non-differentiable score functions.  ...  To illustrate the approach, we consider a variety of causal structure learning tasks for continuous and discrete data.  ...  Causal Structure Learning Through Order Search Directed acyclic graph (DAG) models are popular tools for describing causal relationships and for guiding attempts to learn them from data.  ... 
arXiv:1911.10036v1 fatcat:f7ghfmu2afcq5g7ieb7f5weho4

Optimizing regularized Cholesky score for order-based learning of Bayesian networks [article]

Qiaoling Ye, Arash A. Amini, Qing Zhou
2019 arXiv   pre-print
Bayesian networks are a class of popular graphical models that encode causal and conditional independence relations among variables by directed acyclic graphs (DAGs).  ...  We propose a novel structure learning method, annealing on regularized Cholesky score (ARCS), to search over topological sorts, or permutations of nodes, for a high-scoring Bayesian network.  ...  The GES algorithm outputs a completed partially directed acyclic graph (CPDAG).  ... 
arXiv:1904.12360v1 fatcat:xmutjkkmwnhubgyw2nrc57sofq

Learning Linear Bayesian Networks with Latent Variables

Animashree Anandkumar, Daniel J. Hsu, Adel Javanmard, Sham M. Kakade
2013 International Conference on Machine Learning  
The constraint concerns the expansion properties of the underlying directed acyclic graph (DAG) between observed and unobserved variables in the network, and it is satisfied by many natural families of  ...  This work considers the problem of learning linear Bayesian networks when some of the variables are unobserved.  ...  For a matrix M , diag(M ) is a diagonal matrix with the same diagonal as M . 1 A polytree is a directed acyclic graph where ignoring the directions, the graph is a tree.  ... 
dblp:conf/icml/AnandkumarHJK13 fatcat:a5covt42ungfznbunapgytpxji

Ordering-Based Causal Discovery with Reinforcement Learning [article]

Xiaoqiang Wang, Yali Du, Shengyu Zhu, Liangjun Ke, Zhitang Chen, Jianye Hao, Jun Wang
2021 arXiv   pre-print
However, searching the space of directed graphs and enforcing acyclicity by implicit penalties tend to be inefficient and restrict the existing RL-based method to small scale problems.  ...  Experimental results on both synthetic and real data sets shows that the proposed method achieves a much improved performance over existing RL-based method.  ...  Some recent ordering-based methods such as sparsest permutation [Raskutti and Uhler, 2018] and greedy sparsest permutation [Solus et al., 2017] can guarantee consistency of Markov equivalence class  ... 
arXiv:2105.06631v4 fatcat:urs3qnwpwnez3gzxcm2v4agrx4

Low-Variance Black-Box Gradient Estimates for the Plackett-Luce Distribution

Artyom Gadetsky, Kirill Struminsky, Christopher Robinson, Novi Quadrianto, Dmitry Vetrov
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We show that our method outperforms competitive relaxation-based optimization methods and is also applicable to non-differentiable score functions.  ...  To illustrate the approach, we consider a variety of causal structure learning tasks for continuous and discrete data.  ...  Causal Structure Learning Through Order Search Directed acyclic graph (DAG) models are popular tools for describing causal relationships and for guiding attempts to learn them from data.  ... 
doi:10.1609/aaai.v34i06.6572 fatcat:x2lv7rzfrzd3xi4bbs4cpds7se
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