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Optimal Rates for Estimation of Two-Dimensional Totally Positive Distributions
Jan-Christian Hütter, Cheng Mao, Philippe Rigollet +1
We study minimax estimation of two-dimensional totally positive distributions. Such distributions pertain to pairs of strongly positively dependent random variables and appear freq…
Multi-trek separation in Linear Structural Equation Models
Elina Robeva, Jean-Baptiste Seby
Building on the theory of causal discovery from observational data, we study interactions between multiple (sets of) random variables in a linear structural equation model with non…
Estimation of Monge Matrices
Jan-Christian Hütter, Cheng Mao, Philippe Rigollet +1
Monge matrices and their permuted versions known as pre-Monge matrices naturally appear in many domains across science and engineering. While the rich structural properties of such…
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)…
Duality of Graphical Models and Tensor Networks
Elina Robeva, Anna Seigal
In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor h…
Determinantal Generalizations of Instrumental Variables
Luca Weihs, Bill Robinson, Emilie Dufresne +6
Linear structural equation models relate the components of a random vector using linear interdependencies and Gaussian noise. Each such model can be naturally associated with a mix…