Related papers: Testing versus estimation of graph properties, rev…
Consider a graph $G=(V,E)$ without isolated edges and with maximum degree $\Delta$. Given a colouring $c:E\to\{1,2,\ldots,k\}$, the weighted degree of a vertex $v\in V$ is the sum of its incident colours, i.e., $\sum_{e\ni v}c(e)$. For any…
Random geometric graphs are widely used in modeling geometry and dependence structure in networks. In a random geometric graph, nodes are independently generated from some probability distribution $F$ over a metric space, and edges link…
We study which property testing and sublinear time algorithms can be transformed into graph streaming algorithms for random order streams. Our main result is that for bounded degree graphs, any property that is constant-query testable in…
Notions of graph similarity provide alternative perspective on the graph isomorphism problem and vice-versa. In this paper, we consider measures of similarity arising from mismatch norms as studied in Gervens and Grohe: the edit distance…
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…
Approximate Bayesian computation (ABC) is a likelihood-free inference method that has been employed in various applications. However, ABC can be sensitive to outliers if a data discrepancy measure is chosen inappropriately. In this paper,…
This paper considers a natural fault-tolerant shortest paths problem: for some constant integer $f$, given a directed weighted graph with no negative cycles and two fixed vertices $s$ and $t$, compute (either explicitly or implicitly) for…
Given Boolean functions \( f, g : \mathbb{F}_2^n \to \{-1,+1\} \), we say they are {\em linearly isomorphic} if there exists \( A \in \mathrm{GL}_n(\mathbb{F}_2) \) such that \( f(x)=g(Ax) \) for all \( x \). We study this problem in the…
We prove a robust version of a graph embedding theorem of Sauer and Spencer. To state this sparser analogue, we define $G(p)$ to be a random subgraph of $G$ obtained by retaining each edge of $G$ independently with probability $p \in…
Given an undirected and connected graph $G$ on $T$ vertices, suppose each vertex $t$ has a latent signal $x_t \in \mathbb{R}^n$ associated to it. Given partial linear measurements of the signals, for a potentially small subset of the…
We consider a novel multivariate nonparametric two-sample testing problem where, under the alternative, distributions $P$ and $Q$ are separated in an integral probability metric over functions of bounded total variation (TV IPM). We propose…
Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
The framework of distribution testing is currently ubiquitous in the field of property testing. In this model, the input is a probability distribution accessible via independently drawn samples from an oracle. The testing task is to…
Graphs are versatile tools for representing structured data. As a result, a variety of machine learning methods have been studied for graph data analysis. Although many such learning methods depend on the measurement of differences between…
A mapping $\alpha : V(G) \to V(H)$ from the vertex set of one graph $G$ to another graph $H$ is an isometric embedding if the shortest path distance between any two vertices in $G$ equals the distance between their images in $H$. Here, we…
As graphical summaries for topological spaces and maps, Reeb graphs are common objects in the computer graphics or topological data analysis literature. Defining good metrics between these objects has become an important question for…
A common method for deriving non-parametric tests is to reformulate a parametric test in terms of sample ranks. Despite being distribution free (even in finite samples), the resulting tests often display remarkable asymptotic power…
In this paper, we consider several property testing problems and ask how the query complexity depends on the distance parameter $\eps$. We achieve new lower bounds in this setting for the problems of testing whether a function is monotone…
Several works in implicit and explicit generative modeling empirically observed that feature-learning discriminators outperform fixed-kernel discriminators in terms of the sample quality of the models. We provide separation results between…