no code implementations • 3 Mar 2021 • Vishesh Jain, Ashwin Sah, Mehtaab Sawhney
Let $M_n$ be a random $n\times n$ matrix with i. i. d.
Probability Combinatorics
no code implementations • 16 Feb 2021 • Vishesh Jain, Huy Tuan Pham, Thuy-Duong Vuong
(3) Satisfying assignments of general atomic constraint satisfaction problems with $p\cdot \Delta^{7. 043} \lesssim 1.$ The constant $7. 043$ improves upon the previously best-known constant of $350$ [Feng, He, Yin; STOC 2021].
Data Structures and Algorithms Combinatorics Probability
no code implementations • 19 Jan 2021 • Vishesh Jain, Ashwin Sah, Mehtaab Sawhney
Let $\vec{w} = (w_1,\dots, w_n) \in \mathbb{R}^{n}$.
Combinatorics Data Structures and Algorithms Probability
no code implementations • 24 May 2019 • Vishesh Jain, Frederic Koehler, Jingbo Liu, Elchanan Mossel
The analysis of Belief Propagation and other algorithms for the {\em reconstruction problem} plays a key role in the analysis of community detection in inference on graphs, phylogenetic reconstruction in bioinformatics, and the cavity method in statistical physics.
no code implementations • 22 Aug 2018 • Vishesh Jain, Frederic Koehler, Andrej Risteski
More precisely, we show that the mean-field approximation is within $O((n\|J\|_{F})^{2/3})$ of the free energy, where $\|J\|_F$ denotes the Frobenius norm of the interaction matrix of the Ising model.
no code implementations • 16 Feb 2018 • Vishesh Jain, Frederic Koehler, Elchanan Mossel
The mean field approximation to the Ising model is a canonical variational tool that is used for analysis and inference in Ising models.
no code implementations • 16 Feb 2018 • Vishesh Jain, Frederic Koehler, Elchanan Mossel
Results in graph limit literature by Borgs, Chayes, Lov\'asz, S\'os, and Vesztergombi show that for Ising models on $n$ nodes and interactions of strength $\Theta(1/n)$, an $\epsilon$ approximation to $\log Z_n / n$ can be achieved by sampling a randomly induced model on $2^{O(1/\epsilon^2)}$ nodes.
no code implementations • 5 Nov 2017 • Vishesh Jain, Frederic Koehler, Elchanan Mossel
One exception is recent results by Risteski (2016) who considered dense graphical models and showed that using variational methods, it is possible to find an $O(\epsilon n)$ additive approximation to the log partition function in time $n^{O(1/\epsilon^2)}$ even in a regime where correlation decay does not hold.