13 papers
Graphical Models for Multivariate Count Data
Iza Danielewska, Bartosz Kołodziejek
The classical multinomial, negative multinomial, hypergeometric, and negative hypergeometric distributions are naturally organized by two features of the sampling scheme: sampling…
Finite free perpetuities
Julia Le Bihan, Bartosz Kołodziejek
We introduce and study finite free perpetuities, defined as monic polynomial solutions of degree to the affine fixed-point equation \[ p(z) = \mathbb{E}\!\left[ A^{n}\,p\!\left…
On the empirical spectral distribution of matrix perpetuities
Bartosz Kołodziejek, Kamil Szpojankowski
We study matrix perpetuities, that is, solutions to affine fixed-point equations of the form \[ \mathbf{X} \stackrel{d}{=} \mathbf{A}\,\mathbf{X} \,\mathbf{A}^\top+\mathbf{B},\qqua…
A new class of colored Gaussian graphical models with explicit normalizing constants
Adam Chojecki, Piotr Graczyk, Hideyuki Ishi +1
We study Bayesian model selection in colored Gaussian graphical models (CGGMs), which combine sparsity of conditional independencies with symmetry constraints encoded by vertex- an…
Identifying Network Hubs with the Partial Correlation Graphical LASSO
Małgorzata Bogdan, Adam Chojecki, Ivan Hejný +2
Graphical LASSO (GLASSO) is a widely used method for estimating sparse precision matrices and learning undirected graphical models in high-dimensional settings. Because GLASSO pena…
From Graphical Lasso to Atomic Norms: High-Dimensional Pattern Recovery
Piotr Graczyk, Bartosz Kołodziejek, Hideto Nakashima +1
Estimating high-dimensional precision matrices is a fundamental problem in modern statistics, with the graphical lasso and its -penalty being a standard approach for recove…