161 citations · 1k across the 69 of their papers we have counts for
20 papers · 1 filter
Positivity in Linear Gaussian Structural Equation Models
Asad Lodhia, Jan-Christian Hütter, Caroline Uhler +1
We study a notion of positivity of Gaussian directed acyclic graphical models corresponding to a non-negativity constraint on the coefficients of the associated structural equation…
Ordering-Based Causal Structure Learning in the Presence of Latent Variables
Daniel Irving Bernstein, Basil Saeed, Chandler Squires +1
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 i…
Algebraic Statistics in Practice: Applications to Networks
Marta Casanellas, Sonja Petrović, Caroline Uhler
Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra and computational algebra), geometry and combinatorics to provide insight int…
Brownian motion tree models are toric
Bernd Sturmfels, Caroline Uhler, Piotr Zwiernik
Felsenstein's classical model for Gaussian distributions on a phylogenetic tree is shown to be a toric variety in the space of concentration matrices. We present an exact semialgeb…
Maximum Likelihood Estimation for Totally Positive Log-Concave Densities
Elina Robeva, Bernd Sturmfels, Ngoc Tran +1
We study nonparametric maximum likelihood estimation for two classes of multivariate distributions that imply strong forms of positive dependence; namely log-supermodular (MTP)…
High-Dimensional Joint Estimation of Multiple Directed Gaussian Graphical Models
Yuhao Wang, Santiago Segarra, Caroline Uhler
We consider the problem of jointly estimating multiple related directed acyclic graph (DAG) models based on high-dimensional data from each graph. This problem is motivated by the…
Geometry of Discrete Copulas
Elisa Perrone, Liam Solus, Caroline Uhler
Multivariate distributions are fundamental to modeling. Discrete copulas can be used to construct diverse multivariate joint distributions over random variables from estimated univ…
Generalized Fréchet Bounds for Cell Entries in Multidimensional Contingency Tables
Caroline Uhler, Donald Richards
We consider the lattice, , of all subsets of a multidimensional contingency table and establish the properties of monotonicity and supermodularity for the marginalizat…
Gaussian Graphical Models: An Algebraic and Geometric Perspective
Caroline Uhler
Gaussian graphical models are used throughout the natural sciences, social sciences, and economics to model the statistical relationships between variables of interest in the form…
Consistency Guarantees for Greedy Permutation-Based Causal Inference Algorithms
Liam Solus, Yuhao Wang, Caroline Uhler
Directed acyclic graphical models, or DAG models, are widely used to represent complex causal systems. Since the basic task of learning such a model from data is NP-hard, a standar…
Generalized Permutohedra from Probabilistic Graphical Models
Fatemeh Mohammadi, Caroline Uhler, Charles Wang +1
A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a sim…
Total positivity in Markov structures
Shaun Fallat, Steffen Lauritzen, Kayvan Sadeghi +3
We discuss properties of distributions that are multivariate totally positive of order two (MTP2) related to conditional independence. In particular, we show that any independence…
Exact goodness-of-fit testing for the Ising model
Abraham Martin del Campo, Sarah Cepeda, Caroline Uhler
The Ising model is one of the simplest and most famous models of interacting systems. It was originally proposed to model ferromagnetic interactions in statistical physics and is n…
Maximum Likelihood Estimation for Linear Gaussian Covariance Models
Piotr Zwiernik, Caroline Uhler, Donald Richards
We study parameter estimation in linear Gaussian covariance models, which are -dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood e…
Exact formulas for the normalizing constants of Wishart distributions for graphical models
Caroline Uhler, Alex Lenkoski, Donald Richards
Gaussian graphical models have received considerable attention during the past four decades from the statistical and machine learning communities. In Bayesian treatments of this mo…
Learning directed acyclic graphs based on sparsest permutations
Garvesh Raskutti, Caroline Uhler
We consider the problem of learning a Bayesian network or directed acyclic graph (DAG) model from observational data. A number of constraint-based, score-based and hybrid algorithm…
Hypersurfaces and their singularities in partial correlation testing
Shaowei Lin, Caroline Uhler, Bernd Sturmfels +1
An asymptotic theory is developed for computing volumes of regions in the parameter space of a directed Gaussian graphical model that are obtained by bounding partial correlations.…
Geometry of the faithfulness assumption in causal inference
Caroline Uhler, Garvesh Raskutti, Peter Bühlmann +1
Many algorithms for inferring causality rely heavily on the faithfulness assumption. The main justification for imposing this assumption is that the set of unfaithful distributions…
Geometry of maximum likelihood estimation in Gaussian graphical models
Caroline Uhler
We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to find exact lower bounds on the n…
Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic Geometry
Bernd Sturmfels, Caroline Uhler
We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the pro…