##### Preprints

Ordering-based causal structure learning in the presence of latent variables

D. I. Bernstein, B. Saeed, C. Squires and C. Uhler

Under review

[arXiv]

Keywords: causal inference, algebraic statistics

Permutation-based causal structure learning with unknown intervention targets

C. Squires, Y. Wang and C. Uhler

Under review

[arXiv]

Keywords: causal inference, applications to biology

Overparameterized neural networks can implement associative memory

A. Radhakrishnan, M. Belkin and C. Uhler

Under review

[arXiv]

Keywords: autoencoders, machine learning

Covariance matrix estimation under total positivity for portfolio selection

R. Agrawal, U. Roy and C. Uhler

Under review

[arXiv]

Keywords: total positivity, applications to finance

Learning high-dimensional Gaussian graphical models under total positivity without tuning parameters

Y. Wang, U. Roy and C. Uhler

Under review

[arXiv]

Keywords: total positivity, applications to finance

Anchored causal inference in the presence of measurement error

B. Saeed, A. Belyaeva, Y. Wang and C. Uhler

Under review

[arXiv]

Keywords: causal inference, applications to biology

Total positivity in structured binary distributions

S. Lauritzen, C. Uhler and P. Zwiernik

Under review

[arXiv]

Keywords: total positivity, algebraic statistics

Brownian motion tree models are toric

B. Sturmfels, C. Uhler and P. Zwiernik

Under review

[arXiv]

Keywords: total positivity, algebraic statistics

Autoencoder and optimal transport to infer single-cell trajectories of biological processes

K.D. Yang, K. Damodaran, S. Venkatchalapathy, A.C. Soylemezoglu, G.V Shivashankar and C. Uhler

Under review

[arXiv]

Keywords: autoencoders, application to biology

Maximum likelihood estimation for totally positive log-concave densities

E. Robeva, B. Sturmfels, N. Tran and C. Uhler

Under review

[arXiv]

Keywords: shape-constrained density estimation, total positivity

High-dimensional joint estimation of multiple directed Gaussian graphical models

Y. Wang, S. Segarra and C. Uhler

Under review

[arXiv]

Keywords: causal inference, high-dimensional statistics

Consistency guarantees for permutation-based causal inference algorithms

L. Solus, Y. Wang, L. Matejovicova and C. Uhler

Under review

[arXiv]

Keywords: causal inference, algebraic statistics

##### 2019

Algebraic statistics in practice: Applications to networks

M. Casanellas, S. Petrovic and C. Uhler

To appear in Annual Review of Statistics and its Applications (invited review)

[arXiv]

Keywords: causal inference, algebraic statistics

Maximum likelihood estimation in Gaussian models under total positivity

S. Lauritzen, C. Uhler and P. Zwiernik

Annals of Statistics 47 (2019), pp. 1835-1863.

[arXiv]

Keywords: total positivity, Gaussian graphical models

Multi-domain translation by learning uncoupled autoencoders

K.D. Yang and C. Uhler

Computational Biology Workshop, International Conference on Machine Learning (ICML 2019)

[arXiv]

Keywords: autoencoders, machine learning

Memorization in overparameterized autoencoders

A. Radhakrishnan, K.D. Yang, M. Belkin and C. Uhler

Deep Phenomena Workshop, International Conference on Machine Learning (ICML 2019)

[arXiv]

Keywords: autoencoders, machine learning

ABCD-Strategy: Budgeted experimental design for targeted causal structure discovery

R. Agrawal, C. Squires, K.D. Yang, K. Shanmugam and C. Uhler

Proceedings of Machine Learning Research 89 (AISTATS 2019), pp. 3400-3409

Keywords: causal inference, experimental design

Size of interventional Markov equivalence classes in random DAG models

D. Katz-Rogozhnikov,K. Shanmugam, C. Squires and C. Uhler

Proceedings of Machine Learning Research 89 (AISTATS 2019), pp. 3234-3243

Keywords: causal inference

Scalable unbalanced optimal transport using generative adversarial networks

K.D. Yang and C. Uhler

International Conference on Learning Representations (ICLR 2019)

[arXiv]

Keywords: optimal transport, applications to biology

Geometry of discrete copulas

E. Perrone, L. Solus and C. Uhler

Journal of Multivariate Analsysis 172 (2019), pp. 162-179

[arXiv]

Keywords: algebraic statistics

Loading monotonicity of weighted premiums, and total positivity properties of weight functions

D. Richards and C. Uhler

Journal of Mathematical Analysis and Applications, 475 (2019), pp. 532-553.

[arXiv]

Keywords: mathematical statistics, total positivity

Generalized Fréchet bounds for cell entries in multidimensional contingency tables

C. Uhler and D. Richards

Journal of Algebraic Statistics 10 (special issue for Stephen E. Fienberg) (2019), pp. 1-12

[arXiv]

Keywords: mathematical statistics, total positivity

Geometry of log-concave density estimation

E. Robeva, B. Sturmfels and C. Uhler

Discrete & Computational Geometry 61 (2019), pp. 136-160

[arXiv]

Keywords: shape-constrained density estimation, algebraic statistics

##### 2018

Direct estimation of differences in causal graphs

Y. Wang, C. Squires, A. Belyaeva and C. Uhler

Advances in Neural Information Processing Systems 31 (2018)

[arXiv]

Keywords: causal inference, applications to biology

PatchNet: Interpretable neural networks for image classification

A. Radhakrishnan, C. Durham, A. Soylemezoglu and C. Uhler

Machine Learning for Health (ML4H) Workshop, Neural Information Processing Systems (2018)

[arXiv]

Keywords: neural nets, applications to biology

Minimal I-MAP MCMC for scalable structure discovery in causal DAG models

R. Agrawal, T. Broderick and C. Uhler

Proceedings of Machine Learning Research 80 (ICML 2018), pp. 89-98

[arXiv]

Keywords: causal inference, Bayesian statistics, applications to biology

Characterizing and learning equivalence classes of causal DAGs under interventions

K. D. Yang, A. Katcoff and C. Uhler

Proceedings of Machine Learning Research 80 (ICML 2018), pp. 5537-5546

[arXiv]

Keywords: causal inference, applications to biology

Learning directed acyclic graphs based on sparsest permutations

G. Raskutti and C. Uhler

Stat 7 (2018), e183

[arXiv]

Keywords: causal inference, algebraic statistics

Counting Markov equivalence classes for DAG models on trees

A. Radhakrishnan, L. Solus and C. Uhler

Discrete Applied Mathematics 244 (2018), pp. 170-185

[arXiv]

Keywords: causal inference, algebraic statistics

Nuclear mechanopathology and cancer diagnosis

C. Uhler and G.V. Shivashankar

Trends in Cancer 4 (2018), pp. 320-331 (invited review)

[journal]

Keywords: applications to biology, chromosome packing

Generalized permutohedra from probabilistic graphical models

F. Mohammadi, C. Uhler, C. Wang and J. Yu

SIAM Journal on Discrete Mathematics 32 (2018), pp. 64-93

[arXiv]

Keywords: causal inference, algebraic statistics

Exact formulas for the normalizing constants of Wishart distributions for graphical models

C. Uhler, A. Lenkoski and D. Richards

Annals of Statistics 46 (2018), pp. 90-118

[arXiv]

Keywords: Gaussian graphical models, Bayesian statistics

Gaussian graphical models: An algebraic and geometric perspective

C. Uhler

Chapter for Handbook on Graphical Models (editors: M. Drton, S. Lauritzen, M. Maathuis and M. Wainwright)

[arXiv]

Keywords: Gaussian graphical models, algebraic statistics

##### 2017

Machine learning for nuclear mechano-morphometric biomarkers in cancer diagnosis

A. Radhakrishnan, D. Damodaran, A. Soylemezoglu, C. Uhler, and G.V. Shivashankar

Scientific Reports 7 (2017), article nr. 17946.

[journal]

Keywords: neural nets, applications to biology

Permutation-based causal inference algorithms with interventions

Y. Wang, L. Solus, K.D. Yang and C. Uhler

Advances in Neural Information Processing (NIPS 2017)

[arXiv]

Keywords: causal inference, algebraic statistics

Network analysis identifies chromosome intermingling regions as regulatory hotspots for transcription

A. Belyaeva, S. Venkatachalapathy, M. Nagarajan, G.V. Shivashankar and C. Uhler

Proceedings of the National Academy of Sciences, U.S.A. 114 (2017), pp. 13714-13719.

[journal]

Keywords: chromosome packing, applications to biology

Regulation of genome organization and gene expression by nuclear mechanotransduction

C. Uhler and G.V. Shivashankar

Nature Reviews Molecular Cell Biology 18 (2017), pp. 717-727 (invited review).

[journal]

Keywords: applications to biology, chromosome packing

Chromosome intermingling: Mechanical hotspots for genome regulation

C. Uhler and G.V. Shivashankar

Trends in Cell Biology 27 (2017), pp. 810-819 (invited review)

[journal]

Keywords: chromosome packing, applications to biology

Orientation and repositioning of chromosomes correlate with cell geometry-dependent gene expression

Y. Wang, M. Nagarajan, C. Uhler and G.V. Shivashankar

Molecular Biology of the Cell 28 (2017), pp. 1997-2009

[journal]

Keywords: chromosome packing, applications to biology

Maximum likelihood estimation for linear Gaussian covariance models

P. Zwiernik, C. Uhler and D. Richards

Journal of the Royal Statistical Society, Series B 79 (2017), pp. 1269-1292

[arXiv]

Keywords: Gaussian models, covariance estimation, optimization

Counting Markov equivalence classes by number of immoralities

A. Radhakrishnan, L. Solus and C. Uhler

Proceedings of the Thirty-Third Conference on Uncertainty in Artificial Intelligence (UAI 2017)

[arXiv]

Keywords: causal inference, algebraic statistics

Total positivity in Markov structures

S. Fallat, L. Lauritzen, K. Sadeghi, C. Uhler, N. Wermuth and P. Zwiernik

Annals of Statistics 45 (2017), pp. 1152-1184

[arXiv]

Keywords: total positivity, mathematical statistics

Exact goodness-of-fit testing for the Ising model

A. Martin del Campo, S. Cepeda and C. Uhler

Scandinavian Journal of Statistics 44 (2017), pp. 285-306

[arXiv]

Keywords: hypothesis testing, algebraic statistics

##### 2016

Extremal positive semidefinite matrices for graphs without K5 minors

L. Solus, C. Uhler and R. Yoshida

Linear Algebra and its Applications 509 (2016), pp. 247-275

[arXiv]

Keywords: Gaussian graphical models, algebraic statistics

Geometric control and modeling of genome reprogramming

C. Uhler and G.V. Shivashankar

BioArchitecture 6 (2016), pp. 76-84

[journal]

Keywords: chromosome packing, applications to biology

M. Michalek, B. Sturmfels, C. Uhler and P. Zwiernik

Proceedings of the London Mathematical Society 112 (2016), pp. 27-56

[arXiv]

Keywords: Gaussian graphical models, algebraic statistics

##### 2015

Faithfulness and learning of hypergraphs from discrete distributions

A. Klimova, C. Uhler and T. Rudas

Journal of Computational Statistics and Data Analysis 87 (2015), pp. 57-72.

[arXiv]

Keywords: causal inference, algebraic statistics

##### 2014

Hypersurfaces and their singularities in partial correlation testing

S. Lin, C. Uhler, B. Sturmfels and P. Bühlmann

Foundations of Computational Mathematics 14 (2014), pp. 1079-1116

[arXiv]

Keywords: causal inference, algebraic statistics

Differentially private logistic regression for detecting multiple-SNP association in GWAS databases

F. Yu, M. Rybar, C. Uhler and S.E. Fienberg

Privacy in Statistical Databases 8744 (2014), pp. 170-184

[arXiv]

Keywords: differential privacy, applications to biology

Sphere packing with limited overlap

M. Iglesias-Ham, M. Kerber and C. Uhler

Proceedings of the 26th Canadian Conference on Computational Geometry, Halifax, Nova Scotia (2014), pp. 155-161.

[arXiv]

Keywords: sphere packing, applications to biology

Scalable privacy-preserving data sharing methodology for genome-wide association studies

F. Yu, S.E. Fienberg, A. Slavkovic and C. Uhler

Journal of Biomedical Informatics 50 (2014), pp. 133-141

[arXiv]

Keywords: differential privacy, applications to biology

##### 2013

Packing ellipsoids with overlap

C. Uhler and S.J. Wright

SIAM Review 55 (2013), pp. 671-706 (selected as Research Spotlight)

[arXiv]

Keywords: optimization, sphere packing, chromosome packing

Geometry of faithfulness assumption in causal inference

C. Uhler, G. Raskutti, P. Bühlmann and B. Yu

Annals of Statistics 41 (2013), pp. 436-463

[arXiv]

Keywords: causal inference, algebraic statistics

Privacy-preserving data sharing for genome-wide association studies

C. Uhler, S.E. Fienberg and A. Slavkovic

Journal of Privacy and Confidentiality 5 (2013), pp. 137-166

[arXiv]

Keywords: differential privacy, applications to biology

##### 2012

Geometry of maximum likelihood estimation in Gaussian graphical models

C. Uhler

Annals of Statistics 40 (2012), pp. 238-261

[arXiv]

Keywords: Gaussian graphical models, algebraic statistics

##### 2011

Privacy preserving GWAS data sharing

S.E. Fienberg, A. Slavkovic and C. Uhler

Proceedings of the 11th IEEE International Conference on Data Mining, Vancouver, Canada (2011), pp. 628-635

[pdf]

Keywords: differential privacy, applications to biology

Detecting epistasis via Markov bases

A. Malaspinas and C. Uhler

Journal of Algebraic Statistics 2 (2011), pp. 36-53

[arXiv]

Keywords: algebraic statistics, applications to biology

##### 2010

Multivariate Gaussians, semidefinite matrix completion and convex algebraic geometry

B. Sturmfels and C. Uhler

Annals of the Institute of Statistical Mathematics 62 (2010), pp. 603-638

[arXiv]

Keywords: Gaussian graphical models, algebraic statistics

Commuting birth-and-death processes

S. Evans, B. Sturmfels and C. Uhler

Annals of Applied Probability 20 (2010), pp. 238-266

[arXiv]

Keywords: birth-and-death processes, algebraic statistics

##### 2009

C. Uhler

Journal of Agricaltural, Biological, and Environmental Statistics 14 (2009), pp. 79-98

Keywords: differential privacy, applications to biology

##### 2008

A complete Neandertal mitochondrial genome sequence determined by high-throughput sequencing

R.E. Green, A. Malaspinas, J. Krause, A.W. Briggs, P.L. Johnson, C. Uhler, M. Meyer, J.M. Good, T. Maricic, U. Stenzel, K. Prüfer, M. Siebauer, H.A. Burbano, M. Ronan, J.M. Rothberg, M. Egholm, P. Rudan, D. Brajkovic, Z. Kucan, I. Gusic, M. Wikström, L. Laakkonen, J. Kelso, M. Slatkin and S. Pääbo

Cell 134 (2008), pp. 416-426

[journal]

Keywords: applications to biology