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Found 8 papers, 0 papers with code
Rank deficiency of random matrices
Let $M_n$ be a random $n\times n$ matrix with i. i. d.
Probability Combinatorics
On the sampling Lovász Local Lemma for atomic constraint satisfaction problems
(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
Anticoncentration versus the number of subset sums
Let $\vec{w} = (w_1,\dots, w_n) \in \mathbb{R}^{n}$.
Combinatorics Data Structures and Algorithms Probability
Accuracy-Memory Tradeoffs and Phase Transitions in Belief Propagation
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.
Mean-field approximation, convex hierarchies, and the optimality of correlation rounding: a unified perspective
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.
The Vertex Sample Complexity of Free Energy is Polynomial
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.
The Mean-Field Approximation: Information Inequalities, Algorithms, and Complexity
The mean field approximation to the Ising model is a canonical variational tool that is used for analysis and inference in Ising models.
Approximating Partition Functions in Constant Time
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.
