Related papers: Reconstruction of Markov Random Fields from Sample…
In the Graph Reconstruction (GR) problem, the goal is to recover a hidden graph by utilizing some oracle that provides limited access to the structure of the graph. The interest is in characterizing how strong different oracles are when the…
Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges…
In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line…
Given access to the vertex set $V$ of a connected graph $G=(V,E)$ and an oracle that given two vertices $u,v\in V$, returns the shortest path distance between $u$ and $v$, how many queries are needed to reconstruct $E$? Firstly, we show…
Decentralized stochastic gradient method emerges as a promising solution for solving large-scale machine learning problems. This paper studies the decentralized Markov chain gradient descent (DMGD) algorithm - a variant of the decentralized…
We study recovering a 1D order from a noisy, locally sampled pairwise comparison matrix under a tight query budget. We recast the task as reconstructing a sparse, noisy line graph and present, to our knowledge, the first method that…
We provide a general framework to improve trade-offs between the number of full batch and sample queries used to solve structured optimization problems. Our results apply to a broad class of randomized optimization algorithms that…
Inference is a main task in structured prediction and it is naturally modeled with a graph. In the context of Markov random fields, noisy observations corresponding to nodes and edges are usually involved, and the goal of exact inference is…
Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the…
We revisit the asymptotic analysis of probabilistic construction of adjacency matrices of expander graphs proposed in [4]. With better bounds we derived a new reduced sample complexity for the number of nonzeros per column of these…
Motivated by distributed statistical learning over uncertain communication networks, we study distributed stochastic optimization by networked nodes to cooperatively minimize a sum of convex cost functions. The network is modeled by a…
There has been an increased interest in applying machine learning techniques on relational structured-data based on an observed graph. Often, this graph is not fully representative of the true relationship amongst nodes. In these settings,…
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 $k \geq 2$…
The covariance matrix of measurements of Markov random fields (processes) has useful properties that allow to develop effective computational algorithms for many problems in the study of Markov fields on the basis of field observations…
We study the problem of learning the structure and parameters of the Ising model, a fundamental model of high-dimensional data, when observing the evolution of an associated Markov chain. A recent line of work has studied the natural…
Discrete Morse theory has recently been applied in metric graph reconstruction from a given density function concentrated around an (unknown) underlying embedded graph. We propose a new noise model for the density function to reconstruct a…
We propose a conceptually novel method of reconstructing the topology of dynamical networks. By examining the correlation between the variable of one node and the derivative of another node, we derive a simple matrix equation yielding the…
Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications. State-of-the-art methods either use spatial statistics or rely on examples of dense fields in…
In this paper, we aim at recovering an undirected weighted graph of $N$ vertices from the knowledge of a perturbed version of the eigenspaces of its adjacency matrix $W$. For instance, this situation arises for stationary signals on graphs…
We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…