Graphical Models for Complex Multivariate Data

Faithlessness in Gaussian graphical models

Author(s): Mathias Drton, Leonard Henckel, Benjamin Hollering, Pratik Misra
Published in: Bernoulli, Issue 32, 2026, Page(s) 638-663, ISSN 1350-7265
Publisher: Chapman & Hall
DOI: 10.3150/25-bej1873

Rational maximum likelihood estimators of Kronecker covariance matrices

Author(s): Mathias Drton, Alexandros Grosdos, Andrew McCormack
Published in: Algebraic Statistics, Issue 15, 2024, Page(s) 145-164, ISSN 2693-3004
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/astat.2024.15.145

Confidence Sets for Causal Orderings

Author(s): Y. Samuel Wang, Mladen Kolar, Mathias Drton
Published in: Journal of the American Statistical Association, Issue 121, 2026, Page(s) 690-703, ISSN 0162-1459
Publisher: American Statistical Association
DOI: 10.1080/01621459.2025.2542552

Partial Homoscedasticity in Causal Discovery with Linear Models

Author(s): Jun Wu, Mathias Drton
Published in: IEEE Journal on Selected Areas in Information Theory, 2023, ISSN 2641-8770
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
DOI: 10.1109/jsait.2023.3328476

Learning Linear Gaussian Polytree Models With Interventions

Author(s): Daniele Tramontano, Leonard Waldmann, Mathias Drton, Eliana Duarte
Published in: IEEE Journal on Selected Areas in Information Theory, 2023, ISSN 2641-8770
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
DOI: 10.1109/jsait.2023.3328429

Half-Trek Criterion for Identifiability of Latent Variable Models

Author(s): Rina Foygel Barber, Mathias Drton, Nils Sturma, Luca Weihs
Published in: The Annals of Statistics, Issue 50, 2022, Page(s) 3174-3196, ISSN 0090-5364
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/22-aos2221

On weak convergence of Gaussian conditional distributions

Author(s): Sarah Lumpp, Mathias Drton
Published in: Statistics & Probability Letters, Issue 226, 2026, Page(s) 110497, ISSN 0167-7152
Publisher: Elsevier BV
DOI: 10.1016/j.spl.2025.110497

On the choice of the splitting ratio for the split likelihood ratio test

Author(s): David Strieder, Mathias Drton
Published in: Electronic Journal of Statistics, Issue 16, 2022, Page(s) 6631-6650, ISSN 1935-7524
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/22-ejs2099

Causal Structural Learning via Local Graphs

Author(s): Wenyu Chen, Mathias Drton, Ali Shojaie
Published in: SIAM Journal on Mathematics of Data Science, Issue 5(2), 2023, Page(s) 280-305, ISSN 2577-0187
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1362796

"Discussion of ""A note on universal inference"" by Timmy Tse and Anthony Davison"

Author(s): Mathias Drton, Hongjian Shi, David Strieder
Published in: Stat, Issue 12(1), 2023, Page(s) e574, ISSN 2049-1573
Publisher: Wiley
DOI: 10.1002/sta4.572

Mixtures of discrete decomposable graphical models

Author(s): Yulia Alexandr, Jane Ivy Coons, Nils Sturma
Published in: Algebraic Statistics, Issue 15, 2024, Page(s) 269-293, ISSN 2693-3004
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/astat.2024.15.269

On Azadkia–Chatterjee’s conditional dependence coefficient

Author(s): Hongjian Shi, Mathias Drton, Fang Han
Published in: Bernoulli, Issue 30, 2024, ISSN 1350-7265
Publisher: Chapman & Hall
DOI: 10.3150/22-bej1529

Identifiability of homoscedastic linear structural equation models using algebraic matroids

Author(s): Mathias Drton, Benjamin Hollering, Jun Wu
Published in: Advances in Applied Mathematics, Issue 163, 2024, Page(s) 102794, ISSN 0196-8858
Publisher: Academic Press
DOI: 10.1016/j.aam.2024.102794

On the power of Chatterjee’s rank correlation

Author(s): Hongjian Shi, Mathias Drton, Fang Han
Published in: Biometrika, 2021, ISSN 0006-3444
Publisher: Oxford University Press
DOI: 10.1093/biomet/asab028

Algebraic Sparse Factor Analysis

Author(s): Mathias Drton, Alexandros Grosdos, Irem Portakal, Nils Sturma
Published in: SIAM Journal on Applied Algebra and Geometry, Issue 9, 2025, Page(s) 279-309, ISSN 2470-6566
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/23m1626517

Goodness-of-fit tests for linear non-Gaussian structural equation models

Author(s): D Schkoda, M Drton
Published in: Biometrika, Issue 112, 2026, Page(s) asaf046, ISSN 0006-3444
Publisher: Oxford University Press
DOI: 10.1093/biomet/asaf046

Homaloidal polynomials and Gaussian models of maximum likelihood degree 1

Author(s): Shelby Cox, Pratik Misra, Pardis Semnani
Published in: Algebraic Statistics, Issue 15, 2024, Page(s) 167-198, ISSN 2693-3004
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/astat.2024.15.167

Testing many constraints in possibly irregular models using incomplete <i>U</i>-statistics

Author(s): Nils Sturma, Mathias Drton, Dennis Leung
Published in: Journal of the Royal Statistical Society Series B: Statistical Methodology, Issue 86, 2024, Page(s) 987-1012, ISSN 1369-7412
Publisher: Blackwell Publishing Inc.
DOI: 10.1093/jrsssb/qkae022

Cross-validating causal discovery via Leave-One-Variable-Out

Author(s): Daniela Schkoda; Philipp Michael Faller; Patrick Blöbaum; Dominik Janzing
Published in: Proceedings of the Fourth Conference on Causal Learning and Reasoning, Issue 275, 2025, Page(s) 659-692, ISSN 2640-3498
Publisher: PMLR
DOI: 10.48550/arxiv.2411.05625

Third-Order Moment Varieties of Linear Non-Gaussian Graphical Models

Author(s): Carlos Améndola, Mathias Drton, Alexandros Grosdos, Roser Homs, Elina Robeva
Published in: Information and Inference. A Journal of the IMA, Issue 12(3), 2023, Page(s) iaad007, ISSN 2049-8764
Publisher: Oxford University Press
DOI: 10.1093/imaiai/iaad007

Confidence in causal inference under structure uncertainty in linear causal models with equal variances

Author(s): David Strieder, Mathias Drton
Published in: Journal of Causal Inference, Issue 11, 2024, Page(s) 20230030, ISSN 2193-3685
Publisher: Walter de Gruyter GmbH
DOI: 10.1515/jci-2023-0030

On universally consistent and fully distribution-free rank tests of vector independence

Author(s): Hongjian Shi, Marc Hallin, Mathias Drton, Fang Han
Published in: The Annals of Statistics, Issue 50, 2022, Page(s) 1933-1959, ISSN 0090-5364
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/21-aos2151

Causal inference on process graphs: Causal structure and effect identification

Author(s): Nicolas-Domenic Reiter, Jonas Wahl, Andreas Gerhardus, Jakob Runge
Published in: Bernoulli, Issue 32, 2026, Page(s) 1356-1382, ISSN 1350-7265
Publisher: Chapman & Hall
DOI: 10.3150/25-bej1909

High-dimensional undirected graphical models for arbitrary mixed data

Author(s): Konstantin Göbler, Mathias Drton, Sach Mukherjee, Anne Miloschewski
Published in: Electronic Journal of Statistics, Issue 18, 2024, ISSN 1935-7524
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/24-ejs2254

Parameter identification in linear non-Gaussian causal models under general confounding

Author(s): Daniele Tramontano, Mathias Drton, Jalal Etesami
Published in: The Annals of Statistics, Issue 54, 2026, Page(s) 957-981, ISSN 0090-5364
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/25-aos2597

Distribution-free tests of multivariate independence based on center-outward quadrant, Spearman, Kendall, and van der Waerden statistics

Author(s): Hongjian Shi, Mathias Drton, Marc Hallin, Fang Han
Published in: Bernoulli, Issue 31, 2025, Page(s) 106-129, ISSN 1350-7265
Publisher: Chapman & Hall
DOI: 10.3150/24-bej1721

Conditional independence in stationary distributions of diffusions

Author(s): Tobias Boege, Mathias Drton, Benjamin Hollering, Sarah Lumpp, Pratik Misra, Daniela Schkoda
Published in: Stochastic Processes and their Applications, Issue 184, 2025, Page(s) 104604, ISSN 0304-4149
Publisher: Elsevier BV
DOI: 10.1016/j.spa.2025.104604

Causal Discovery with Unobserved Confounding and non-Gaussian Data

Author(s): Y. Samuel Wang, Mathias Drton
Published in: Journal of Machine Learning Research, Issue 271, 2023, Page(s) 1−61, ISSN 1533-7928
Publisher: JMLR, Inc.
DOI: 10.48550/arxiv.2007.11131

Parametric and nonparametric symmetries in graphical models for extremes

Author(s): Frank Röttger, Jane Ivy Coons, Alexandros Grosdos
Published in: Journal of the Royal Statistical Society Series B: Statistical Methodology, 2026, ISSN 1369-7412
Publisher: Blackwell Publishing Inc.
DOI: 10.1093/jrsssb/qkag079

Directed Graphical Models and Causal Discovery for Zero-Inflated Data

Author(s): Shiqing Yu, Mathias Drton, Ali Shojaie
Published in: Proceedings of the Second Conference on Causal Learning and Reasoning, Issue 213, 2023, Page(s) 27-67
Publisher: PMLR

Causal Effect Identification in LiNGAM Models with Latent Confounders

Author(s): Daniele Tramontano, Yaroslav Kivva, Saber Salehkaleybar, Mathias Drton, Negar Kiyavash
Published in: Proceedings of the 41st International Conference on Machine Learning, Issue 235, 2024
Publisher: Proceedings of Machine Learning Research (PMLR)

Unpaired Multi-Domain Causal Representation Learning

Author(s): Nils Sturma, Chandler Squires, Mathias Drton, Caroline Uhler
Published in: Advances in Neural Information Processing Systems (NeurIPS 2023), Issue 36, 2023, Page(s) 34465--34492
Publisher: Curran Associates, Inc.
DOI: 10.48550/arxiv.2302.00993

Interaction Models and Generalized Score Matching for Compositional Data

Author(s): Shiqing Yu, Mathias Drton, and Ali Shojaie
Published in: Proceedings of the Second Learning on Graphs Conference, Issue 231, 2024
Publisher: Proceedings of Machine Learning Research (PMLR)

Root Cause Analysis of Outliers in Unknown Cyclic Graphs

Author(s): Daniela Schkoda, Dominik Janzing
Published in: Proceedings of the 29th International Conference on Artificial Intelligence and Statistics (AISTATS, 2026
Publisher: PMLR

Cost-Aware Optimized Front-Door Experimental Design

Author(s): Leopold Mareis, Mathias Drton
Published in: Proceedings of the Fifth Conference on Causal Learning and Reasoning, Issue 323, 2026, Page(s) 1068-1096
Publisher: PMLR

Causal Effect Identification in lvLiNGAM from Higher-Order Cumulants

Author(s): Daniele Tramontano, Yaroslav Kivva, Saber Salehkaleybar, Negar Kiyavash, Mathias Drton
Published in: Proceedings of the 42nd International Conference on Machine Learning, 2025, Page(s) 59924-59944
Publisher: PMLR

Identifying Total Causal Effects in Linear Models under Partial Homoscedasticity

Author(s): David Strieder, Mathias Drton
Published in: Proceedings of the 12th International Conference on Probabilistic Graphical Models, Issue 246, 2024
Publisher: Proceedings of Machine Learning Research (PMLR)

Rank-Based Causal Discovery for Post-Nonlinear Models

Author(s): Grigor Keropyan, David Strieder, Mathias Drton
Published in: Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, 2023, Page(s) 7849-7870
Publisher: PMLR Proceedings of Machine Learning Research

Definite Non-Ancestral Relations and Structure Learning

Author(s): Wenyu Chen, Mathias Drton, Ali Shojaie
Published in: 8th Causal Inference Workshop at UAI, 2021, Page(s) "Paper #2"
Publisher: causalUAI2021

Efficient Learning of Stationary Diffusions with Stein-type Discrepancies

Author(s): Fabian Bleile, Sarah Lumpp, Mathias Drton
Published in: The 29th International Conference on Artificial Intelligence and Statistics, 2026
Publisher: PMLR

Robust Score Matching

Author(s): Richard Schwank, Andrew McCormack, Mathias Drton
Published in: Proceedings of the 28th International Conference on Artificial Intelligence and Statistics (AISTATS), 2025
Publisher: Proceedings of Machine Learning Research (PMLR)

On the Lasso for Graphical Continuous Lyapunov Models

Author(s): Philipp Dettling, Mathias Drton, Mladen Kolar
Published in: Proceedings of the 3rd Conference on Causal Learning and Reasoning, Issue 236, 2024, Page(s) 514-550
Publisher: Proceedings of Machine Learning Research (PMLR)
DOI: 10.48550/arxiv.2208.13572

Causal Discovery for Linear Non-Gaussian Models with Disjoint Cycles

Author(s): Mathias Drton, Marina Garrote-López, Niko Nikov, Elina Robeva, Y. Samuel Wang
Published in: Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, Issue 286, 2025, Page(s) 1064-1083
Publisher: PMLR

Learning Linear Non-Gaussian Polytree Models

Author(s): Daniele Tramontano, Anthea Monod, Mathias Drton
Published in: Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, Issue Proceedings of Machine Learning Research 180, 2022, Page(s) 1960-1969
Publisher: PMLR
DOI: 10.48550/arxiv.2208.06701

Semiparametric Inference for Half-Trek Estimators in Linear Structural Equation Models

Author(s): Leopold Mareis, Nils Sturma, Mathias Drton
Published in: The 13th International Conference on Probabilistic Graphical Models, 2026
Publisher: PMLR

Confidence in Causal Discovery with Linear Causal Models

Author(s): David Strieder, Tobias Freidling, Stefan Haffner, Mathias Drton
Published in: Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, Issue PMLR 161, 2021, Page(s) 1217-1226
Publisher: Proceedings of Machine Learning Research

Dual Likelihood for Causal Inference under Structure Uncertainty

Author(s): David Strieder, Mathias Drton
Published in: Proceedings of the 3rd Conference on Causal Learning and Reasoning, Issue 236, 2024
Publisher: Proceedings of Machine Learning Research (PMLR)

Coarsening causal DAG models

Author(s): Francisco Madaleno, Pratik Misra, Alex Markham
Published in: 5th Conference on Causal Learning and Reasoning (CLeaR), 2026
Publisher: PMLR

Center-Outward Sign- and Rank-Based Quadrant, Spearman, and Kendall Tests for Multivariate Independence

Author(s): Hongjian Shi, Mathias Drton, Marc Hallin, Fang Han
Published in: OT-SDM 2022: The 1st International Workshop on Optimal Transport and Structured Data Modeling, 2022
Publisher: AAAI 2022

Graphical Representations for Algebraic Constraints of Linear Structural Equations Models

Author(s): Thijs van Ommen, Mathias Drton
Published in: Proceedings of The 11th International Conference on Probabilistic Graphical Models, Issue 186, 2022, Page(s) 409-420
Publisher: Proceedings of Machine Learning Research (PMLR)
DOI: 10.48550/arxiv.2208.00926

Structural identifiability of graphical continuous Lyapunov models

Author(s): Carlos Amendola, Tobias Boege, Ben Hollering, Pratik Misra
Published in: 2026
Publisher: arXiv

Asymptotics for Model Selection in Probabilistic Principal Component Analysis

Author(s): Mathias Drton, Andrew McCormack, Daniel Windisch
Published in: 2026
Publisher: arXiv

Non-parametric recovery of causal diffusion mechanisms from steady-state observations

Author(s): Richard Schwank, Mathias Drton
Published in: 2026
Publisher: arXiv

Existence of Direct Density Ratio Estimators

Author(s): Erika Banzato, Mathias Drton, Kian Saraf-Poor, Hongjian Shi
Published in: 2025
Publisher: ArXiv

Identifiability in Graphical Discrete Lyapunov Models

Author(s): Cecilie Olesen Recke, Sarah Lumpp, Nataliia Kushnerchuk, Janike Oldekop, Jiayi Li, Jane Ivy Coons, Elina Robeva
Published in: 2026
Publisher: arXiv

On universal inference in Gaussian mixture models

Author(s): Hongjian Shi, Mathias Drton
Published in: 2024
Publisher: ArXiv
DOI: 10.48550/arxiv.2407.19361

Linear relations of colored Gaussian cycles

Author(s): Hannah Göbel, Pratik Misra
Published in: 2025
Publisher: arXiv

Efficient symbolic computations for identifying causal effects

Author(s): Ben Hollering, Pratik Misra, Nils Sturma
Published in: 2026
Publisher: arXiv

Identifying Direct Causal Effects in Latent Factor Models by Accounting for Unidentified Parents

Author(s): Tom Hochsprung, Nils Sturma, Jakob Runge, Mathias Drton, Andreas Gerhardus
Published in: 2026
Publisher: arXiv

Causal Discovery of Linear Non-Gaussian Causal Models with Unobserved Confounding

Author(s): Daniela Schkoda, Elina Robeva, Mathias Drton
Published in: 2024
Publisher: ArXiv
DOI: 10.48550/arxiv.2408.04907

Coloured Gaussian directed acyclic graphical models

Author(s): Tobias Boege, Kaie Kubjas, Pratik Misra, Liam Solus
Published in: Journal of the Royal Statistical Society Series B: Statistical Methodology, Issue 88(3), 2025, Page(s) 819–875
Publisher: Oxford University Press
DOI: 10.48550/arxiv.2404.04024

Trek-Based Parameter Identification for Linear Causal Models With Arbitrarily Structured Latent Variables

Author(s): Nils Sturma, Mathias Drton
Published in: 2025
Publisher: arXiv

Identifiability and Statistical Inference in Latent Variable Modeling

Author(s): Sturma, Nils B.
Published in: 2024
Publisher: online

Homoscedasticity and Feedback Loops in Graphical Models

Author(s): Wu, Jun
Published in: Issue 5, 2023
Publisher: Technical University of Munich

Graphical Continuous Lyapunov Models

Author(s): Dettling, Philipp Maximilian
Published in: 2024
Publisher: online

Matching Criterion for Identifiability in Sparse Factor Analysis

Author(s): Nils Sturma, Miriam Kranzlmueller, Irem Portakal, Mathias Drton
Published in: Psychometrika, Issue 91, 2026, Page(s) 536-555, ISSN 0033-3123
Publisher: Psychometric Society
DOI: 10.1017/psy.2026.10079

Identifiability in Continuous Lyapunov Models

Author(s): Philipp Dettling, Roser Homs, Carlos Améndola, Mathias Drton, Niels Richard Hansen
Published in: SIAM Journal on Matrix Analysis and Applications, Issue 44, 2023, Page(s) 1799-1821, ISSN 0895-4798
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m1520311

Publications

Download Download the content of the page

Graphical Models for Complex Multivariate Data

Project Results

Publications

Download Download the content of the page