Related papers: Quantifying Variational Approximation for the Log-…
We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labeled by integers representing their position in the target space, with the SOS constraint that…
We describe a polynomial-time algorithm which, given a graph $G$ with treewidth $t$, approximates the pathwidth of $G$ to within a ratio of $O(t\sqrt{\log t})$. This is the first algorithm to achieve an $f(t)$-approximation for some…
While Graph Neural Networks (GNNs) have demonstrated significant efficacy in node classification tasks, where predictions rely on local neighborhood information, the performance of GNNs often drops when prediction tasks depend on long-range…
The local tree-width of a graph G=(V,E) is the function ltw^G: N -> N that associates with every natural number r the maximal tree-width of an r-neighborhood in G. Our main graph theoretic result is a decomposition theorem for graphs with…
This work describes probabilistic methods for utilizing random spanning trees generated via a random walk process. Goyal et al. showed that the union of random spanning trees approximates the expansion of every cut of a graph. First, we…
We study the parameterized complexity of computing the tree-partition-width, a graph parameter equivalent to treewidth on graphs of bounded maximum degree. On one hand, we can obtain approximations of the tree-partition-width efficiently:…
Gromov-Wasserstein (GW) is a powerful tool to compare probability measures whose supports are in different metric spaces. GW suffers however from a computational drawback since it requires to solve a complex non-convex quadratic program. We…
With applications in distribution systems and communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The…
We give two new approximation algorithms to compute the fractional hypertree width of an input hypergraph. The first algorithm takes as input $n$-vertex $m$-edge hypergraph $H$ of fractional hypertree width at most $\omega$, runs in…
Probabilistic graphical models offer a powerful framework to account for the dependence structure between variables, which is represented as a graph. However, the dependence between variables may render inference tasks intractable. In this…
Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types…
The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…
We present a polynomial-time $(\alpha_{GW} + \varepsilon)$-approximation algorithm for the Maximum Cut problem on interval graphs and split graphs, where $\alpha_{GW} \approx 0.878$ is the approximation guarantee of the Goemans-Williamson…
We propose a scalable Gromov-Wasserstein learning (S-GWL) method and establish a novel and theoretically-supported paradigm for large-scale graph analysis. The proposed method is based on the fact that Gromov-Wasserstein discrepancy is a…
The arboricity $\Gamma$ of a graph is the minimum number of forests its edge set can be partitioned into. Previous approximation schemes were nonconstructive, i.e., they only approximated the arboricity as a value without computing a…
We present a new local approximation algorithm for computing Maximum a Posteriori (MAP) and log-partition function for arbitrary exponential family distribution represented by a finite-valued pair-wise Markov random field (MRF), say $G$.…
Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition…
We propose a new approach to deriving quantitative mean field approximations for any probability measure $P$ on $\mathbb{R}^n$ with density proportional to $e^{f(x)}$, for $f$ strongly concave. We bound the mean field approximation for the…
Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks.…
We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…