339 citations · 551 across the 39 of their papers we have counts for
41 papers
Born Discrete, Made Smooth: Variational Formulation of Shallow Neural Networks
Matej Benko, Pierre Bousquet, Iwona Chlebicka +1
Although neural networks are remarkably effective, their underlying optimization principles remain theoretically elusive, often characterized by non-convex landscapes and stochasti…
Lipschitz stability for Bayesian inference in porous medium tissue growth models
Tomasz Dębiec, Piotr Gwiazda, Błażej Miasojedow +3
We consider a macroscopic model for the dynamics of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Given a power-law constitutive rela…
Operator splitting algorithm for structured population models on metric spaces
Carolin Lindow, Christian Düll, Piotr Gwiazda +2
In this paper, we propose a numerical scheme for structured population models defined on a separable and complete metric space. In particular, we consider a generalized version of…
Convergence of projected stochastic approximation algorithm
Michał Borowski, Błażej Miasojedow
We study the Robbins-Monro stochastic approximation algorithm with projections on a hyperrectangle and prove its convergence. This work fills a gap in the convergence proof of the…
Langevin Monte Carlo Beyond Lipschitz Gradient Continuity
Matej Benko, Iwona Chlebicka, Jørgen Endal +1
We present a significant advancement in the field of Langevin Monte Carlo (LMC) methods by introducing the Inexact Proximal Langevin Algorithm (IPLA). This novel algorithm broadens…
Discarding Lavrentiev's Gap in Non-autonomous and Non-Convex Variational Problems
Michał Borowski, Pierre Bousquet, Iwona Chlebicka +2
We establish that the Lavrentiev gap between Sobolev and Lipschitz maps does not occur for a scalar variational problem of the form: \[ \textrm{to minimize} \qquad u \mapsto \int_Ω…
Convergence rates of particle approximation of forward-backward splitting algorithm for granular medium equations
Matej Benko, Iwona Chlebicka, Jørgen Endal +1
We study the spatially homogeneous granular medium equation \[\partial_tμ=\rm{div}(μ\nabla V)+\rm{div}(μ(\nabla W \ast μ))+Δμ\,,\] within a large and natural class of the confineme…
Stability of solutions of the porous medium equation with growth with respect to the diffusion exponent
Tomasz Dębiec, Piotr Gwiazda, Błażej Miasojedow +1
We consider a macroscopic model for the growth of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Assuming a power-law relation between…
Solidarity of Gibbs Samplers: the spectral gap
Iwona Chlebicka, Krzysztof Łatuszyński, Błażej Miasojedow
Gibbs samplers are preeminent Markov chain Monte Carlo algorithms used in computational physics and statistical computing. Yet, their most fundamental properties, such as relations…
Absence and presence of Lavrentiev's phenomenon for double phase functionals upon every choice of exponents
Michał Borowski, Iwona Chlebicka, Filomena De Filippis +1
We study classes of weights ensuring the absence and presence of the Lavrentiev's phenomenon for double phase functionals upon every choice of exponents. We introduce a new sharp s…
Absence of Lavrentiev's gap for anisotropic functionals
Michał Borowski, Iwona Chlebicka, Błażej Miasojedow
We establish the absence of the Lavrentiev gap between Sobolev and smooth maps for a non-autonomous variational problem of a general structure, where the integrand is assumed to be…
Boundedness of Wolff-type potentials and applications to PDEs
Michał Borowski, Iwona Chlebicka, Błażej Miasojedow
We provide a short proof of a sharp rearrangement estimate for a generalized version of a potential of Wolff--Havin--Maz'ya type. As a consequence, we prove a reduction principle f…
Predicting the redshift of gamma-ray loud AGNs using supervised machine learning
Maria Giovanna Dainotti, Malgorzata Bogdan, Aditya Narendra +8
AGNs are very powerful galaxies characterized by extremely bright emissions coming out from their central massive black holes. Knowing the redshifts of AGNs provides us with an opp…
Convergence of the EBT method for a non-local model of cell proliferation with discontinuous interaction kernel
Piotr Gwiazda, Błażej Miasojedow, Jakub Skrzeczkowski +1
We consider the EBT algorithm (a particle method) for the non-local equation with a discontinuous interaction kernel. The main difficulty lies in the low regularity of the kernel w…
Bayesian inference of a non-local proliferation model
Zuzanna Szymańska, Jakub Skrzeczkowski, Błażej Miasojedow +1
From a systems biology perspective the majority of cancer models, although interesting and providing a qualitative explanation of some problems, have a major disadvantage in that t…
Structure learning for CTBN's via penalized maximum likelihood methods
Maryia Shpak, Błażej Miasojedow, Wojciech Rejchel
The continuous-time Bayesian networks (CTBNs) represent a class of stochastic processes, which can be used to model complex phenomena, for instance, they can describe interactions…
Adaptive Bayesian SLOPE -- High-dimensional Model Selection with Missing Values
Wei Jiang, Malgorzata Bogdan, Julie Josse +3
We consider the problem of variable selection in high-dimensional settings with missing observations among the covariates. To address this relatively understudied problem, we propo…
Gamma-ray Bursts as distance indicators through a machine learning approach
Maria Dainotti, Vahé Petrosian, Malgorzata Bogdan +7
Gamma-ray bursts (GRBs) are spectacularly energetic events, with the potential to inform on the early universe and its evolution, once their redshifts are known. Unfortunately, det…
Jaccard/Tanimoto similarity test and estimation methods
Neo Christopher Chung, Błażej Miasojedow, Michał Startek +1
Binary data are used in a broad area of biological sciences. Using binary presence-absence data, we can evaluate species co-occurrences that help elucidate relationships among orga…
Non-asymptotic Analysis of Biased Stochastic Approximation Scheme
Belhal Karimi, Blazej Miasojedow, Eric Moulines +1
Stochastic approximation (SA) is a key method used in statistical learning. Recently, its non-asymptotic convergence analysis has been considered in many papers. However, most of t…
Asymptotics of maximum likelihood estimators based on Markov chain Monte Carlo methods
Błażej Miasojedow, Wojciech Niemiro, Wojciech Rejchel
In many complex statistical models maximum likelihood estimators cannot be calculated. In the paper we solve this problem using Markov chain Monte Carlo approximation of the true l…
Analysis of nonsmooth stochastic approximation: the differential inclusion approach
Szymon Majewski, Błażej Miasojedow, Eric Moulines
In this paper we address the convergence of stochastic approximation when the functions to be minimized are not convex and nonsmooth. We show that the "mean-limit" approach to the…
Analysis of Langevin Monte Carlo via convex optimization
Alain Durmus, Szymon Majewski, Błażej Miasojedow
In this paper, we provide new insights on the Unadjusted Langevin Algorithm. We show that this method can be formulated as a first order optimization algorithm of an objective func…
Assigning peaks and modeling ETD in top-down mass spectrometry
Mateusz Krzysztof Łącki, Frederik Lermyte, Błażej Miasojedow +5
Among many techniques of modern mass spectrometry, the top down methods are becoming continuously more popular in the overall strive to describe the proteome. These techniques are…