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07/25/2023
Likelihood Geometry of Determinantal Point Processes
We study determinantal point processes (DPP) through the lens of algebra...
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04/03/2023
Taylor Polynomials of Rational Functions
A Taylor variety consists of all fixed order Taylor polynomials of ratio...
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01/22/2023
Moment Varieties for Mixtures of Products
The setting of this article is nonparametric algebraic statistics. We st...
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08/31/2022
Four-Dimensional Lie Algebras Revisited
The projective variety of Lie algebra structures on a 4-dimensional vect...
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05/23/2022
Recovery of Plane Curves from Branch Points
We recover plane curves from their branch points under projection onto a...
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04/13/2022
Bayesian Integrals on Toric Varieties
We explore the positive geometry of statistical models in the setting of...
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02/03/2022
Toric Geometry of Entropic Regularization
Entropic regularization is a method for large-scale linear programming. ...
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01/14/2022
Geometry of Dependency Equilibria
An n-person game is specified by n tensors of the same format. We view i...
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12/19/2021
Marginal Independence Models
We impose rank one constraints on marginalizations of a tensor, given by...
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08/21/2021
Beyond Linear Algebra
Our title challenges the reader to venture beyond linear algebra in desi...
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06/26/2021
Recovery from Power Sums
We study the problem of recovering a collection of n numbers from the ev...
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04/20/2021
Linear PDE with Constant Coefficients
We discuss practical methods for computing the space of solutions to an ...
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12/09/2020
Likelihood Equations and Scattering Amplitudes
We relate scattering amplitudes in particle physics to maximum likelihoo...
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10/21/2020
Tangent Quadrics in Real 3-Space
We examine quadratic surfaces in 3-space that are tangent to nine given ...
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06/17/2020
Bad Projections of the PSD Cone
The image of the cone of positive semidefinite matrices under a linear m...
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03/15/2020
Wasserstein Distance to Independence Models
An independence model for discrete random variables is a Segre-Veronese ...
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12/01/2019
Algebraic Analysis of Rotation Data
We develop algebraic tools for statistical inference from samples of rot...
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10/03/2019
D-Modules and Holonomic Functions
In algebraic geometry, one studies the solutions to polynomial equations...
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09/02/2019
Estimating linear covariance models with numerical nonlinear algebra
Numerical nonlinear algebra is applied to maximum likelihood estimation ...
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03/14/2019
Discrete Statistical Models with Rational Maximum Likelihood Estimator
A discrete statistical model is a subset of a probability simplex. Its m...
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02/26/2019
Brownian motion tree models are toric
Felsenstein's classical model for Gaussian distributions on a phylogenet...
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11/20/2018
Voronoi Cells of Varieties
Every real algebraic variety determines a Voronoi decomposition of its a...
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09/05/2018
Learning Paths from Signature Tensors
Matrix congruence extends naturally to the setting of tensors. We apply ...
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06/26/2018
Maximum Likelihood Estimation for Totally Positive Log-Concave Densities
We study nonparametric density estimation for two classes of multivariat...
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04/05/2018
The Geometry of SDP-Exactness in Quadratic Optimization
Consider the problem of minimizing a quadratic objective subject to quad...
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10/19/2017
The Geometry of Gaussoids
A gaussoid is a combinatorial structure that encodes independence in pro...
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07/06/2017
Changing Views on Curves and Surfaces
Visual events in computer vision are studied from the perspective of alg...
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03/15/2017
A clever elimination strategy for efficient minimal solvers
We present a new insight into the systematic generation of minimal solve...
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12/04/2016
General models for rational cameras and the case of two-slit projections
The rational camera model recently introduced in [19] provides a general...
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10/06/2016
Distortion Varieties
The distortion varieties of a given projective variety are parametrized ...
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08/21/2016
Congruences and Concurrent Lines in Multi-View Geometry
We present a new framework for multi-view geometry in computer vision. A...
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03/21/2016
Nearest Points on Toric Varieties
We determine the Euclidean distance degree of a projective toric variety...
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10/06/2015
On the Existence of Epipolar Matrices
This paper considers the foundational question of the existence of a fun...
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09/10/2015
Rigid Multiview Varieties
The multiview variety from computer vision is generalized to images by n...
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08/28/2015
Computing the Chow variety of quadratic space curves
Quadrics in the Grassmannian of lines in 3-space form a 19-dimensional p...
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07/21/2014
Certifying the Existence of Epipolar Matrices
Given a set of point correspondences in two images, the existence of a f...
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12/12/2012
Factorization of Discrete Probability Distributions
We formulate necessary and sufficient conditions for an arbitrary discre...
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07/14/2011