Related papers: Using Gaussian Boson Sampling to Find Dense Subgra…
We define a proportionally dense subgraph (PDS) as an induced subgraph of a graph with the property that each vertex in the PDS is adjacent to proportionally as many vertices in the subgraph as in the graph. We prove that the problem of…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
Photonics is a promising platform for demonstrating a quantum computational advantage (QCA) by outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing proposals and…
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…
Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…
Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More…
Given a graph and an integer $k$, Densest $k$-Subgraph is the algorithmic task of finding the subgraph on $k$ vertices with the maximum number of edges. This is a fundamental problem that has been subject to intense study for decades, with…
Gaussian Boson Sampling is a promising method for experimental demonstrations of quantum advantage because it is easier to implement than other comparable schemes. While most of the properties of Gaussian Boson Sampling are understood to…
Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order…
We show how phase-space simulations of Gaussian quantum states in a photonic network permit verification of measurable correlations of Gaussian boson sampling (GBS) quantum computers. Our results agree with experiments for up to 100-th…
We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…
We establish that in the large degree limit, the value of certain optimization problems on sparse random hypergraphs is determined by an appropriate Gaussian optimization problem. This approach was initiated in Dembo et. al.(2016) for…
A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…
Gaussian boson sampling is a promising candidate for showing experimental quantum advantage. While there is evidence that noiseless Gaussian boson sampling is hard to efficiently simulate using a classical computer, the current Gaussian…
Dense subgraph discovery is an important problem in graph mining and network analysis with several applications. Two canonical problems here are to find a maxcore (subgraph of maximum min degree) and to find a densest subgraph (subgraph of…
Gaussian boson sampling (GBS) is a promising candidate for an experimental demonstration of quantum advantage using photons. However, sufficiently large noise might hinder a GBS implementation from entering the regime where quantum speedup…
As a fundamental topic in graph mining, Densest Subgraph Discovery (DSD) has found a wide spectrum of real applications. Several DSD algorithms, including exact and approximation algorithms, have been proposed in the literature. However,…
Gaussian boson sampling (GBS) is a prominent candidate for the experimental demonstration of quantum advantage. However, while the current implementations of GBS are unavoidably subject to noise, the robustness of the classical…
With the emergence of graph databases, the task of frequent subgraph discovery has been extensively addressed. Although the proposed approaches in the literature have made this task feasible, the number of discovered frequent subgraphs is…
In this work, we describe a method that determines an exact map from a finite set of subgraph densities to the parameters of a stochastic block model (SBM) matching these densities. Given a number $K$ of blocks, the subgraph densities of a…