Bartosz Kołodziejek

activity

20122026

most citedThe Lukacs-Olkin-Rubin theorem on symmetric cones without invariance of the "quotient"

15 citations · 67 across the 29 of their papers we have counts for

collaborators

34 papers

stat.ME2026

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…

math.PR2026

Finite free perpetuities

Julia Le Bihan, Bartosz Kołodziejek

We introduce and study finite free perpetuities, defined as monic polynomial solutions of degree $n$ to the affine fixed-point equation \[ p(z) = \mathbb{E}\!\left[ A^{n}\,p\!\left…

math.PR2026

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…

math.ST2026

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…

math.ST2025

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…

math.ST2025

From Graphical Lasso to Atomic Norms: High-Dimensional Pattern Recovery

Piotr Graczyk, Bartosz Kołodziejek, Hideto Nakashima +1

We study high-dimensional precision-matrix estimation with polyhedral atomic-norm penalties on the off-diagonal entries. This framework covers the graphical lasso, $ℓ_{\infty}$ -ty…

math.PR2025

Free Perpetuities I: Existence, Subordination and Tail Asymptotics

Serban Belinschi, Bartosz Kołodziejek, Kamil Szpojankowski

We study the free analogue of the classical affine fixed-point (or perpetuity) equation \[ \mathbb{X} \stackrel{d}{=} \mathbb{A}^{1/2}\mathbb{X}\,\mathbb{A}^{1/2} + \mathbb{B}, \]…

math.PR2025

Perpetuities with light tails and the local dependence measure

Julia Le Bihan, Bartosz Kołodziejek

This work investigates the tail behavior of solutions to the affine stochastic fixed-point equation of the form $X = d A X + B$ , where $X$ and $(A, B)$ are independent. Focus…

math.PR2025

Probability laws associated to the independence preserving quadrirational Yang-Baxter maps -- the ultimate case

Bartosz Kołodziejek, Gérard Letac, Mauro Piccioni +1

A map $F : X \times Y \to U \times V$ is said to be independence preserving (IP) if there exists a pair of independent random variables $(X, Y)$ v…

math.PR2023★ 1 cited

Graphical Negative Multinomial and Multinomial Models with Dirichlet-type priors

Iza Danielewska, Bartosz Kołodziejek, Jacek Wesołowski +1

Bayesian statistical graphical models are typically classified as either continuous and parametric (Gaussian, parameterized by the graph-dependent precision matrix with Wishart-typ…

math.ST2022

Analysis of Conditional Randomisation and Permutation schemes with application to conditional independence testing

Małgorzata Łazęcka, Bartosz Kołodziejek, Jan Mielniczuk

We study properties of two resampling scenarios: Conditional Randomisation and Conditional Permutation schemes, which are relevant for testing conditional independence of discrete…

math.ST2022

Graphical Gaussian models associated to a homogeneous graph with permutation symmetries

Piotr Graczyk, Hideyuki Ishi, Bartosz Kołodziejek

We consider multivariate centered Gaussian models for the random vector $(Z^{1}, \dots, Z^{p})$ , whose conditional structure is described by a homogeneous graph and which is invariant…

math.ST2022

Pattern recovery by SLOPE

Małgorzata Bogdan, Xavier Dupuis, Piotr Graczyk +4

SLOPE is a popular method for dimensionality reduction in the high-dimensional regression. Indeed some regression coefficient estimates of SLOPE can be null (sparsity) or can be eq…

math.ST2022

Pattern recovery and signal denoising by SLOPE when the design matrix is orthogonal

Tomasz Skalski, Piotr Graczyk, Bartosz Kołodziejek +1

Sorted $ℓ_{1}$ Penalized Estimator (SLOPE) is a relatively new convex regularization method for fitting high-dimensional regression models. SLOPE allows to reduce the model dimens…

math.PR2021

A phase transition for tails of the free multiplicative convolution powers

Bartosz Kołodziejek, Kamil Szpojankowski

We study the behavior of the tail of a measure $μ^{⊠ t}$ , where $⊠ t$ is the $t$ -fold free multiplicative convolution power for $t \geq 1$ . We focus on the case wher…

math.PR2020

Stochastic fixed point equation and local dependence measure

Krzysztof Burdzy, Bartosz Kołodziejek, Tvrtko Tadić

We study solutions to the stochastic fixed point equation $X = d A X + B$ where the coefficients $A$ and $B$ are nonnegative random variables. We introduce the ``local depen…

math.ST2020

Model selection in the space of Gaussian models invariant by symmetry

Piotr Graczyk, Hideyuki Ishi, Bartosz Kołodziejek +1

We consider multivariate centered Gaussian models for the random variable $Z = (Z_{1}, \dots, Z_{p})$ , invariant under the action of a subgroup of the group of permutations on $\{1,\ldot…

math.PR2018★ 3 cited

A renewal theorem and supremum of a perturbed random walk

Ewa Damek, Bartosz Kołodziejek

We study tails of the supremum of a perturbed random walk under regime which was not yet considered in the literature. Our approach is based on a new renewal theorem, which is of i…

math.ST2018

Location and scale behaviour of the quantiles of a natural exponential family

Mauro Piccioni, Bartosz Kołodziejek, Gérard Letac

Let $P_{0}$ be a probability on the real line generating a natural exponential family $(P_{t})_{t \in R}$ . Fix $α$ in $(0, 1) .$ We show that the property that $P_t((-\infty,t)…

math.ST2018★ 4 cited

Wishart laws and variance function on homogeneous cones

Piotr Graczyk, Hideyuki Ishi, Bartosz Kołodziejek

We present a systematic study of Riesz measures and their natural exponential families of Wishart laws on a homogeneous cone. We compute explicitly the inverse of the mean map and…

math.PR2018

Inverse Exponential Decay: Stochastic Fixed Point Equation and ARMA Models

Krzysztof Burdzy, Bartosz Kołodziejek, Tvrtko Tadić

We study solutions to the stochastic fixed point equation $X = d A X + B$ when the coefficients are nonnegative and $B$ is an "inverse exponential decay" (IED) random variab…

math.PR2017★ 4 cited

On perpetuities with light tails

Bartosz Kołodziejek

In the paper we consider the asymptotics of logarithmic tails of a perpetuity $$R \stackrel{d}{=}\sum_{j=1}^\infty Q_j \prod_{k=1}^{j-1}M_k,\qquad(M_n,Q_n)_{n=1}^\infty \mbox{ are…

math.PR2017★ 2 cited

A Matsumoto-Yor characterization for Kummer and Wishart random matrices

Bartosz Kołodziejek

In the paper we resolve positively the conjecture on a characterization of matrix Kummer and Wishart laws through independence property, which was posed in [Koudou, Statist. Probab…

math.PR2017

Independence characterization for Wishart and Kummer random matrices

Agnieszka Piliszek, Bartosz Kołodziejek

We generalize the following univariate characterization of the Kummer and Gamma distributions to the cone of symmetric positive definite matrices: let $X$ and $Y$ be independent, n…