Combinatorial approach for factorization of variance and entropy in spin systems
Z Chen - Proceedings of the 2024 Annual ACM-SIAM …, 2024 - SIAM
We present a simple combinatorial framework for establishing approximate tensorization of
variance and entropy in the setting of spin systems (aka undirected graphical models) based …
variance and entropy in the setting of spin systems (aka undirected graphical models) based …
Improved mixing for the convex polygon triangulation flip walk
D Eppstein, D Frishberg - arXiv preprint arXiv:2207.09972, 2022 - arxiv.org
We prove that the well-studied triangulation flip walk on a convex point set mixes in time O
(n^ 3 log^ 3 n), the first progress since McShine and Tetali's O (n^ 5 log n) bound in 1997. In …
(n^ 3 log^ 3 n), the first progress since McShine and Tetali's O (n^ 5 log n) bound in 1997. In …
Optimal mixing via tensorization for random independent sets on arbitrary trees
We study the mixing time of the single-site update Markov chain, known as the Glauber
dynamics, for generating a random independent set of a tree. Our focus is obtaining optimal …
dynamics, for generating a random independent set of a tree. Our focus is obtaining optimal …
Spectral Independence Beyond Total Influence on Trees and Related Graphs
We study how to establish $\textit {spectral independence} $, a key concept in sampling,
without relying on total influence bounds, by applying an $\textit {approximate inverse} $ of …
without relying on total influence bounds, by applying an $\textit {approximate inverse} $ of …
Time Lower Bounds for the Metropolis Process and Simulated Annealing
The Metropolis process (MP) and Simulated Annealing (SA) are stochastic local search
heuristics that are often used in solving combinatorial optimization problems. Despite …
heuristics that are often used in solving combinatorial optimization problems. Despite …
[图书][B] Flow-Based Decomposition for Geometric and Combinatorial Markov Chain Mixing
D Frishberg - 2023 - search.proquest.com
We prove that the well-studied triangulation flip walk on a convex point set mixes in time O (n
3 log 3 n), the first progress since McShine and Tetali's O (n 5 log n) bound in 1997. In the …
3 log 3 n), the first progress since McShine and Tetali's O (n 5 log n) bound in 1997. In the …