45 citations · 105 across the 23 of their papers we have counts for
29 papers
Discrete-time, discrete-state multistate Markov models from the perspective of algebraic statistics
Dario Gasbarra, Kaie Kubjas, Sangita Kulathinal +3
We study discrete-time, discrete-state multistate Markov models from the perspective of algebraic statistics. These models are widely studied in event history analysis, and are cha…
Geometry of low nonnegative rank matrix completion
Kaie Kubjas, Lilja Metsälampi
We study completion of partial matrices with nonnegative entries to matrices of nonnegative rank at most for some . Most of our results are for . We…
Uniqueness of size-2 positive semidefinite matrix factorizations
Kristen Dawson, Serkan Hoşten, Kaie Kubjas +1
We characterize when a size-2 positive semidefinite (psd) factorization of a positive matrix of rank 3 and psd rank 2 is unique. The characterization is obtained using tools from r…
Single-cell 3D genome reconstruction in the haploid setting using rigidity theory
Sean Dewar, Georg Grasegger, Kaie Kubjas +2
This article considers the problem of 3-dimensional genome reconstruction for single-cell data, and the uniqueness of such reconstructions in the setting of haploid organisms. We c…
Colored Gaussian directed acyclic graphical models
Tobias Boege, Kaie Kubjas, Pratik Misra +1
We study submodels of Gaussian DAG models defined by partial homogeneity constraints imposed on the model error variances and structural coefficients. We represent these models wit…
Geometry of Polynomial Neural Networks
Kaie Kubjas, Jiayi Li, Maximilian Wiesmann
We study the expressivity and learning process for polynomial neural networks (PNNs) with monomial activation functions. The weights of the network parametrize the neuromanifold. I…
On the uniqueness of collections of pennies and marbles
Sean Dewar, Georg Grasegger, Kaie Kubjas +2
In this note we study the uniqueness problem for collections of pennies and marbles. More generally, consider a collection of unit -spheres that may touch but not overlap. Given…
3D genome reconstruction from partially phased Hi-C data
Diego Cifuentes, Jan Draisma, Oskar Henriksson +2
The 3-dimensional (3D) structure of the genome is of significant importance for many cellular processes. In this paper, we study the problem of reconstructing the 3D structure of c…
Log-concave density estimation in undirected graphical models
Kaie Kubjas, Olga Kuznetsova, Elina Robeva +2
We study the problem of maximum likelihood estimation of densities that are log-concave and lie in the graphical model corresponding to a given undirected graph . We show that t…
Algebraic degree of optimization over a variety with an application to -norm distance degree
Kaie Kubjas, Olga Kuznetsova, Luca Sodomaco
We study an optimization problem with the feasible set being a real algebraic variety and whose parametric objective function is gradient-solvable with respect to the par…
Identifying 3D Genome Organization in Diploid Organisms via Euclidean Distance Geometry
Anastasiya Belyaeva, Kaie Kubjas, Lawrence J. Sun +1
The spatial organization of the DNA in the cell nucleus plays an important role for gene regulation, DNA replication, and genomic integrity. Through the development of chromosome c…
Exact solutions in low-rank approximation with zeros
Kaie Kubjas, Luca Sodomaco, Elias Tsigaridas
Low-rank approximation with zeros aims to find a matrix of fixed rank and with a fixed zero pattern that minimizes the Euclidean distance to a given data matrix. We study the criti…
The Model-Specific Markov Embedding Problem for Symmetric Group-Based Models
Muhammad Ardiyansyah, Dimitra Kosta, Kaie Kubjas
We study model embeddability, which is a variation of the famous embedding problem in probability theory, when apart from the requirement that the Markov matrix is the matrix expon…
Exact Solutions in Log-Concave Maximum Likelihood Estimation
Alexandros Grosdos, Alexander Heaton, Kaie Kubjas +3
We study probability density functions that are log-concave. Despite the space of all such densities being infinite-dimensional, the maximum likelihood estimate is the exponential…
Maximum Likelihood Estimation of Toric Fano Varieties
Carlos Améndola, Dimitra Kosta, Kaie Kubjas
We study the maximum likelihood estimation problem for several classes of toric Fano models. We start by exploring the maximum likelihood degree for all -dimensional Gorenstein…
Uniqueness of nonnegative matrix factorizations by rigidity theory
Robert Krone, Kaie Kubjas
Nonnegative matrix factorizations are often encountered in data mining applications where they are used to explain datasets by a small number of parts. For many of these applicatio…
Tensor network complexity of multilinear maps
Per Austrin, Petteri Kaski, Kaie Kubjas
We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. These capture any algorithm based on low border rank tensor decompositions, such as $…
Maximum likelihood estimation of the Latent Class Model through model boundary decomposition
Elizabeth S. Allman, Hector Baños Cervantes, Robin Evans +5
The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees…
Geometry of symmetric group-based models
Dimitra Kosta, Kaie Kubjas
Phylogenetic models have polynomial parametrization maps. For symmetric group-based models, Matsen studied the polynomial inequalities that characterize the joint probabilities in…
How to flatten a soccer ball
Kaie Kubjas, Pablo A. Parrilo, Bernd Sturmfels
This is an experimental case study in real algebraic geometry, aimed at computing the image of a semialgebraic subset of 3-space under a polynomial map into the plane. For general…
The geometry of rank-one tensor completion
Thomas Kahle, Kaie Kubjas, Mario Kummer +1
The geometry of the set of restrictions of rank-one tensors to some of their coordinates is studied. This gives insight into the problem of rank-one completion of partial tensors.…
Positive semidefinite rank and nested spectrahedra
Kaie Kubjas, Elina Robeva, Richard Z. Robinson
The set of matrices of given positive semidefinite rank is semialgebraic. In this paper we study the geometry of this set, and in small cases we describe its boundary. For general…
Algebraic boundary of matrices of nonnegative rank at most three
Rob H. Eggermont, Emil Horobet, Kaie Kubjas
The Zariski closure of the boundary of the set of matrices of nonnegative rank at most 3 is reducible. We give a minimal generating set for the ideal of each irreducible component.…
Matrix Completion for the Independence Model
Kaie Kubjas, Zvi Rosen
We investigate the problem of completing partial matrices to rank-one matrices in the standard simplex. The motivation for studying this problem comes from statistics: A lack of el…