Related papers: Non-adaptive Learning of Random Hypergraphs with Q…
In the Generalized Mastermind problem, there is an unknown subset $H$ of the hypercube $\{0,1\}^d$ containing $n$ points. The goal is to learn $H$ by making a few queries to an oracle, which, given a point $q$ in $\{0,1\}^d$, returns the…
Hypergraphs (i.e., sets of hyperedges) naturally represent group relations (e.g., researchers co-authoring a paper and ingredients used together in a recipe), each of which corresponds to a hyperedge (i.e., a subset of nodes). Predicting…
We investigate extremal problems for quasirandom hypergraphs. We say that a $3$-uniform hypergraph $H=(V,E)$ is $(d,\eta)$-quasirandom if for any subset $X\subseteq V$ and every set of pairs $P\subseteq V\times V$ the number of pairs…
Representation learning has overcome the often arduous and manual featurization of networks through (unsupervised) feature learning as it results in embeddings that can apply to a variety of downstream learning tasks. The focus of…
Modern data analysis pipelines are becoming increasingly complex due to the presence of multi-view information sources. While graphs are effective in modeling complex relationships, in many scenarios a single graph is rarely sufficient to…
Since their introduction by Kipf and Welling in $2017$, a primary use of graph convolutional networks is transductive node classification, where missing labels are inferred within a single observed graph and its feature matrix. Despite the…
Theoretical analyses for graph learning methods often assume a complete observation of the input graph. Such an assumption might not be useful for handling any-size graphs due to the scalability issues in practice. In this work, we develop…
Hypergraph structure learning, which aims to learn the hypergraph structures from the observed signals to capture the intrinsic high-order relationships among the entities, becomes crucial when a hypergraph topology is not readily available…
How efficiently can we find an unknown graph using distance or shortest path queries between its vertices? Let $G = (V,E)$ be an unweighted, connected graph of bounded degree. The edge set $E$ is initially unknown, and the graph can be…
We study the problem of extracting a selective connector for a given set of query vertices $Q \subseteq V$ in a graph $G = (V,E)$. A selective connector is a subgraph of $G$ which exhibits some cohesiveness property, and contains the query…
We consider space-efficient algorithms for two-coloring $n$-uniform hypergraphs $H=(V,E)$ in the streaming model, when the hyperedges arrive one at a time. It is known that any such hypergraph with at most $0.7 \sqrt{\frac{n}{\ln n}} 2^n$…
Given a directed graph, G=(V,E), a path query, path(u,v), returns whether there is a directed path from u to v in G, for u,v vertices in V. Given only V, exactly learning all the edges in G using path queries is often impossible, since path…
Many real-world problems can be represented as graph-based learning problems. In this paper, we propose a novel framework for learning spatial and attentional convolution neural networks on arbitrary graphs. Different from previous…
This paper aims for set-to-hypergraph prediction, where the goal is to infer the set of relations for a given set of entities. This is a common abstraction for applications in particle physics, biological systems, and combinatorial…
Suppose that there is a family of $n$ random points $X_v$ for $v \in V$, independently and uniformly distributed in the square $\left[-\sqrt{n}/2,\sqrt{n}/2\right]^2$ of area $n$. We do not see these points, but learn about them in one of…
We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information…
Hypergraphs provide a natural way of representing group relations, whose complexity motivates an extensive array of prior work to adopt some form of abstraction and simplification of higher-order interactions. However, the following…
Hypergraphs are generalisation of graphs in which a hyperedge can connect any number of vertices. It can describe n-ary relationships and high-order information among entities compared to conventional graphs. In this paper, we study the…
We study an issue commonly seen with graph data analysis: many real-world complex systems involving high-order interactions are best encoded by hypergraphs; however, their datasets often end up being published or studied only in the form of…
When we try to solve a system of linear equations, we can consider a simple iterative algorithm in which an equation including only one variable is chosen at each step, and the variable is fixed to the value satisfying the equation. The…