4 papers
Data-Driven Energy-Based Learning via Gibbs Measures on Hierarchical Structures
L. U. Abdullaev, F. Herrera, U. A. Rozikov +1
We introduce a data-driven probabilistic framework for learning systems based on Gibbs measures on hierarchical structures. Unlike standard empirical risk minimization, where a dat…
Ising Models with Hidden Markov Structure: Applications to Probabilistic Inference in Machine Learning
F. Herrera, U. A. Rozikov, M. V. Velasco
In this paper, we investigate tree-indexed Markov chains (Gibbs measures) defined by a Hamiltonian that couples two Ising layers: hidden spins \(s(x) \in \{\pm 1\}\) and observed s…
Coupled Ising-Potts Model: Rich Sets of Critical Temperatures and Translation-Invariant Gibbs Measures
F. H. Haydarov, B. A. Omirov, U. A. Rozikov
We consider a coupled Ising-Potts model on Cayley trees of order . This model involves spin vectors , and generalizes both the Ising and Potts models by inco…
Extreme Gibbs measures for a Hard-Core-SOS model on Cayley trees
R. M. Khakimov, M. T. Makhammadaliev, U. A. Rozikov
We investigate splitting Gibbs measures (SGMs) of a three-state (wand-graph) hardcore SOS model on Cayley trees of order . Recently, this model was studied for the hing…