Related papers: Distributional limits of graph cuts on discretized…
For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian…
We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…
In this paper, we study the problem of approximating the minimum cut in a distributed message-passing model, the CONGEST model. The minimum cut problem has been well-studied in the context of centralized algorithms. However, there were no…
Exchangeable random graphs, which include some of the most widely studied network models, have emerged as the mainstay of statistical network analysis in recent years. Graphons, which are the central objects in graph limit theory, provide a…
Functional Gaussian graphical models (GGM) used for analyzing multivariate functional data customarily estimate an unknown graphical model representing the conditional relationships between the functional variables. However, in many…
Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity,…
We study the tradeoff between the statistical error and communication cost of distributed statistical estimation problems in high dimensions. In the distributed sparse Gaussian mean estimation problem, each of the $m$ machines receives $n$…
Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial structure. A prototypical example is the random geometric…
Spectral clustering (SC) and graph-based semi-supervised learning (SSL) algorithms are sensitive to how graphs are constructed from data. In particular if the data has proximal and unbalanced clusters these algorithms can lead to poor…
We consider the distributed optimization problem for the sum of convex functions where the underlying communications network connecting agents at each time is drawn at random from a collection of directed graphs. Building on an earlier work…
Graph construction is a crucial step in spectral clustering (SC) and graph-based semi-supervised learning (SSL). Spectral methods applied on standard graphs such as full-RBF, $\epsilon$-graphs and $k$-NN graphs can lead to poor performance…
In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…
In 1996, Karger [Kar96] gave a startling randomized algorithm that finds a minimum-cut in a (weighted) graph in time $O(m\log^3n)$ which he termed near-linear time meaning linear (in the size of the input) times a polylogarthmic factor. In…
Attributed graph clustering or community detection which learns to cluster the nodes of a graph is a challenging task in graph analysis. In this paper, we introduce a contrastive learning framework for learning clustering-friendly node…
We consider the number of crossings in a random embedding of a graph, $G$, with vertices in convex position. We give explicit formulas for the mean and variance of the number of crossings as a function of various subgraph counts of $G$.…
We develop a factor analysis for mixed continuous and binary observed variables. To this end, we utilized a recently developed multivariate probability distribution for mixed-type random variables, the Gaussian-Grassmann distribution. In…
This paper proposes a new family of lower and upper bounds on the minimum mean squared error (MMSE). The key idea is to minimize/maximize the MMSE subject to the constraint that the joint distribution of the input-output statistics lies in…
The {\sc $c$-Balanced Separator} problem is a graph-partitioning problem in which given a graph $G$, one aims to find a cut of minimum size such that both the sides of the cut have at least $cn$ vertices. In this paper, we present new…
We propose a Greedy strategy to solve the problem of Graph Cut, called GGC. It starts from the state where each data sample is regarded as a cluster and dynamically merges the two clusters which reduces the value of the global objective…