相关论文: The One-Inclusion Graph Algorithm is not Always Op…

A well-studied challenge that arises in the structure learning problem of causal directed acyclic graphs (DAG) is that using observational data, one can only learn the graph up to a "Markov equivalence class" (MEC). The remaining undirected…

Incorporating graph side information into recommender systems has been widely used to better predict ratings, but relatively few works have focused on theoretical guarantees. Ahn et al. (2018) firstly characterized the optimal sample…

Combinatorial optimization problems are notoriously challenging for neural networks, especially in the absence of labeled instances. This work proposes an unsupervised learning framework for CO problems on graphs that can provide integral…

We initiate the study of deterministic distributed graph algorithms with predictions in synchronous message passing systems. The process at each node in the graph is given a prediction, which is some extra information about the problem…

Causal discovery is a fundamental problem with applications spanning various areas in science and engineering. It is well understood that solely using observational data, one can only orient the causal graph up to its Markov equivalence…

It has long been known that random regular graphs are with high probability good expanders. This was first established in the 1980s by Bollob\'as by directly calculating the probability that a set of vertices has small expansion and then…

The inertia bound, introduced by Cvetkovi\'c in 1971, is a fundamental result in spectral graph theory that provides an upper bound for the independence number of a graph in terms of spectral information about a weighted adjacency matrix of…

The problem of reconciling a prior probability law on paths with data was introduced by E. Schr\"odinger in 1931/32. It represents an early formulation of a maximum likelihood problem. This specific formulation can also be seen as the…

In this paper, we study Dirac-type theorems for an inhomogenous random graph (G) whose edge probabilities are not necessarily all the same. We obtain sufficient conditions for the existence of Hamiltonian paths and perfect matchings, in…

Vizing's celebrated theorem asserts that any graph of maximum degree $\Delta$ admits an edge coloring using at most $\Delta+1$ colors. In contrast, Bar-Noy, Naor and Motwani showed over a quarter century that the trivial greedy algorithm,…

We tackle the network topology inference problem by utilizing Laplacian constrained Gaussian graphical models, which recast the task as estimating a precision matrix in the form of a graph Laplacian. Recent research \cite{ying2020nonconvex}…

Many problems in robotics involve both continuous and discrete components, and modeling them together for estimation tasks has been a long standing and difficult problem. Hybrid Factor Graphs give us a mathematical framework to model these…

The hardcore model on a graph $G$ with parameter $\lambda>0$ is a probability measure on the collection of all independent sets of $G$, that assigns to each independent set $I$ a probability proportional to $\lambda^{|I|}$. In this paper we…

Schaefer's theorem is a complexity classification result for so-called Boolean constraint satisfaction problems: it states that every Boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in…

Link prediction systems (e.g. recommender systems) typically use graph topology as one of their main sources of information. However, automorphisms and related properties of graphs beget inherent limits in predictability. We calculate hard…

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…

We provide an algorithm which, with high probability, maintains a $(1-\epsilon)$-approximate maximum flow on an undirected graph undergoing $m$-edge additions in amortized $m^{o(1)} \epsilon^{-3}$ time per update. To obtain this result, we…

We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…

We study causal effect estimation under interference from network data. We work under the chain-graph formulation pioneered in Tchetgen Tchetgen et. al (2021). Our first result shows that polynomial time evaluation of treatment effects is…

Graph learning problems are typically approached by focusing on learning the topology of a single graph when signals from all nodes are available. However, many contemporary setups involve multiple related networks and, moreover, it is…