arXiv subjects

Iryna Zabarianska

Publications and source records attributed to Iryna Zabarianska.

3 recordsLinked to original sources

arXiv2026

Discrete Bridges for Mutual Information Estimation

Diffusion bridge models in both continuous and discrete state spaces have recently become powerful tools in the field of generative modeling. In this work, we leverage the discrete state space formulation of bridge matching models to address another important problem in machine learning and information theory: the estimation of the mutual information (MI) between discrete random variables. By neatly framing MI estimation as a domain transfer problem, we construct a Discrete Bridge Mutual Information (DBMI) estimator suitable for discrete data, which poses difficulties for conventional MI estimators. We showcase the performance of our estimator on two MI estimation settings: low-dimensional and image-based.

cs.LG↗

arXiv2025

Coalescing Force of Group Pressure: Consensus in Nonlinear Opinion Dynamics

This work extends the recent opinion dynamics model from Cheng et al., emphasizing the role of group pressure in consensus formation. We generalize the findings to incorporate social influence algorithms with general time-varying, opinion-dependent weights and multidimensional opinions, beyond bounded confidence dynamics. We demonstrate that, with uniformly positive conformity levels, group pressure consistently drives consensus and provide a tighter estimate for the convergence rate. Unlike previous models, the common public opinion in our framework can assume arbitrary forms within the convex hull of current opinions, offering flexibility applicable to real-world scenarios such as opinion polls with random participant selection. This analysis provides deeper insights into how group pressure mechanisms foster consensus under diverse conditions.

physics.soc-ph↗

arXiv2024

Opinion Dynamics with Set-Based Confidence: Convergence Criteria and Periodic Solutions

This paper introduces a new multidimensional extension of the Hegselmann-Krause (HK) opinion dynamics model, where opinion proximity is not determined by a norm or metric. Instead, each agent trusts opinions within the Minkowski sum $ξ+\mathcal{O}$, where $ξ$ is the agent's current opinion and $\mathcal{O}$ is the confidence set defining acceptable deviations. During each iteration, agents update their opinions by simultaneously averaging the trusted opinions. Unlike traditional HK systems, where $\mathcal{O}$ is a ball in some norm, our model allows the confidence set to be non-convex and even unbounded. We demonstrate that the new model, referred to as SCOD (Set-based Confidence Opinion Dynamics), can exhibit properties absent in the conventional HK model. Some solutions may converge to non-equilibrium points in the state space, while others oscillate periodically. These ``pathologies'' disappear if the set $\mathcal{O}$ is symmetric and contains zero in its interior: similar to the usual HK model, SCOD then converges in a finite number of iterations to one of the equilibrium points. The latter property is also preserved if one agent is "stubborn" and resists changing their opinion, yet still influences the others; however, two stubborn agents can lead to oscillations.

cs.MA↗