A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This paper proposes a web-based visual graph analytics platform for interactive graph mining, visualization, and real-time exploration of networks. GraphVis is fast, intuitive, and flexible, combining interactive visualizations with analytic techniques to reveal important patterns and insights for sense making, reasoni…
This paper explores the recently proposed Graph Convolutional Network architecture proposed in (Kipf & Welling, 2016) The key points of their work is summarized and their results are reproduced. Graph regularization and alternative graph convolution approaches are explored. I find that explicit graph regularization was…
We explore the generalization of scattering transforms from traditional (e.g., image or audio) signals to graph data, analogous to the generalization of ConvNets in geometric deep learning, and the utility of extracted graph features in graph data analysis. In particular, we focus on the capacity of these features to r…
The family of image visibility graphs (IVGs) have been recently introduced as simple algorithms by which scalar fields can be mapped into graphs. Here we explore the usefulness of such operator in the scenario of image processing and image classification. We demonstrate that the link architecture of the image visibilit…
This paper considers the problem of efficient exploration of unseen environments, a key challenge in AI. We propose a `learning to explore' framework where we learn a policy from a distribution of environments. At test time, presented with an unseen environment from the same distribution, the policy aims to generalize …
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques aim to automatically create a low-dimensional representation of a given graph, whi…
Boltzmann exploration is widely used in reinforcement learning to provide a trade-off between exploration and exploitation. Recently, in (Cesa-Bianchi et al., 2017) it has been shown that pure Boltzmann exploration does not perform well from a regret perspective, even in the simplest setting of stochastic multi-armed b…
Zipper logic is a graph rewrite system, consisting in only local rewrites on a class of zipper graphs. Connections with the chemlambda artificial chemistry and with knot diagrammatics based computation are explored in the article.
In graph-based active learning, algorithms based on expected error minimization (EEM) have been popular and yield good empirical performance. The exact computation of EEM optimally balances exploration and exploitation. In practice, however, EEM-based algorithms employ various approximations due to the computational ha…
Time series of graphs are increasingly prevalent in modern data and pose unique challenges to visual exploration and pattern extraction. This paper describes the development and application of matrix factorizations for exploration and time-varying community detection in time-evolving graph sequences. The matrix factori…
Graph convolutional neural networks (GCN) have been the model of choice for graph representation learning, which is mainly due to the effective design of graph convolution that computes the representation of a node by aggregating those of its neighbors. However, existing GCN variants commonly use 1-D graph convolution …
In a talk at the Cornell Topology Festival in 2005, W. Thurston discussed a graph which we call "The Big Dehn Surgery Graph", B. Here we explore this graph, particularly the link of S^3, and prove facts about the geometry and topology of B. We also investigate some interesting subgraphs and pose what we believe are imp…
This thesis explores GNNs, categorizing them into local and global approaches.
problem Understanding the convergence of global GNNs and connecting local and global approaches.
method Categorization of GNNs into local and global, study of Invariant Graph Networks, connecting local and global approaches, and using local MPNN for graph coarsening.
result Established a connection between local and global GNN approaches.
Statistical network modeling has focused on representing the graph as a discrete structure, namely the adjacency matrix, and considering the exchangeability of this array. In such cases, the Aldous-Hoover representation theorem (Aldous, 1981;Hoover, 1979} applies and informs us that the graph is necessarily either dens…
We introduce Graph-Sparse Logistic Regression, a new algorithm for classification for the case in which the support should be sparse but connected on a graph. We val- idate this algorithm against synthetic data and benchmark it against L1-regularized Logistic Regression. We then explore our technique in the bioinformat…
The paper explores stability and generalization of deep GCNs.
problem Understanding the stability and generalization of deep GCNs from a theoretical perspective.
method Theoretical analysis of stability and generalization properties of deep GCNs.
result The stability and generalization of deep GCNs are influenced by the maximum absolute eigenvalue of the graph filter operators and the depth of the network.
We propose a novel graph pooling operation using cliques as the unit pool. As this approach is purely topological, rather than featural, it is more readily interpretable, a better analogue to image coarsening than filtering or pruning techniques, and entirely nonparametric. The operation is implemented within graph con…