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.
Tree++ graph kernel captures similarities at multiple granularities.
We consider the problem of path inference: given a path prefix, i.e., a partially observed sequence of nodes in a graph, we want to predict which nodes are in the missing suffix. In particular, we focus on natural paths occurring as a by-product of the interaction of an agent with a network---a driver on the transporta…
In this thesis, we study the problem of feature learning on heterogeneous knowledge graphs. These features can be used to perform tasks such as link prediction, classification and clustering on graphs. Knowledge graphs provide rich semantics encoded in the edge and node types. Meta-paths consist of these types and abst…
PathNNs improve graph neural networks by distinguishing non-isomorphic graphs.
In this paper we use a time-evolving graph which consists of a sequence of graph snapshots over time to model many real-world networks. We study the path classification problem in a time-evolving graph, which has many applications in real-world scenarios, for example, predicting path failure in a telecommunication netw…
Convolution operations designed for graph-structured data usually utilize the graph Laplacian, which can be seen as message passing between the adjacent neighbors through a generic random walk. In this paper, we propose PAN, a new graph convolution framework that involves every path linking the message sender and recei…
PAN uses path integrals for graph convolution and pooling, improving GNN performance.
PathBoost boosts graph-level predictions using path-based features.
Study on Frechet distance properties for paths and graphs.
New method for learning on heterogeneous graphs without meta-paths.
Deep learning approximates shortest path distances in large graphs.
BWFlow improves graph generation by smoothly interpolating graph components.
Proposes a method to improve graph neural networks on heterogeneous graphs using meta-paths.
Landmark-based node embeddings approximate shortest path distances in random graphs.
Generative Flow Networks solve shortest path problems in graphs.
We generalize to tree graphs obtained by connecting path graphs an oracle result obtained for the Fused Lasso over the path graph. Moreover we show that it is possible to substitute in the oracle inequality the minimum of the distances between jumps by their harmonic mean. In doing so we prove a lower bound on the comp…
Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R^d. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges …
We describe unicorn paths in the arc graph and show that they form 1-slim triangles and are invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Considering the same paths in the arc and curve graph, this also shows that all curve graphs are 17-hyperbolic, including closed surfaces.
A framework for hypothesis testing on attributed graphs using sampling.
Much of the recent work on learning molecular representations has been based on Graph Convolution Networks (GCN). These models rely on local aggregation operations and can therefore miss higher-order graph properties. To remedy this, we propose Path-Augmented Graph Transformer Networks (PAGTN) that are explicitly built…
Scalable machine learning with path signatures for time series and graphs.
The notion of friendliness between trees first appeared in solution of Lando's problem on intersection of polyhedra in 3-space. A tree is friendly to a path graph if edges of the tree can be numbered so that for each k,s the path between the edges k and k+1 contains either both or none of the edges k+2s,k+2s+1. Theorem…
Meta-graph is currently the most powerful tool for similarity search on heterogeneous information networks,where a meta-graph is a composition of meta-paths that captures the complex structural information. However, current relevance computing based on meta-graph only considers the complex structural information, but i…
ie-HGCN addresses HIN challenges by efficiently learning node representations.
This work proposes a hybrid method for error detection in noisy Knowledge Graphs.
Study proves hyperfiniteness of mapping class group actions on surface graphs.
A new graph kernel uses LCS and Wasserstein distance for better graph comparisons.
Improved RL for knowledge graph reasoning with entity types.
We consider supervised learning problems where the features are embedded in a graph, such as gene expressions in a gene network. In this context, it is of much interest to automatically select a subgraph with few connected components; by exploiting prior knowledge, one can indeed improve the prediction performance or o…
We extend the notion of unicorn paths between two arcs introduced by Hensel, Przytycki and Webb to the case where we replace one arc with a geodesic asymptotic to a lamination. Using these paths, we give new proofs of the results of Klarreich and Schleimer identifying the Gromov boundaries of the curve graph and the ar…
The classical theorem of Fáry states that every planar graph can be represented by an embedding in which every edge is represented by a straight line segment. We consider generalizations of Fáry's theorem to surfaces equipped with Riemannian metrics. In this setting, we require that every edge is drawn as a shortest pa…
There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation that the above-mentioned common distances in many situations fail to take into ac…
Path queries on a knowledge graph can be used to answer compositional questions such as "What languages are spoken by people living in Lisbon?". However, knowledge graphs often have missing facts (edges) which disrupts path queries. Recent models for knowledge base completion impute missing facts by embedding knowledge…
A regularized optimization problem over a large unstructured graph is studied, where the regularization term is tied to the graph geometry. Typical regularization examples include the total variation and the Laplacian regularizations over the graph. When applying the proximal gradient algorithm to solve this problem, t…
Neural network learns from higher-order connections in molecules.
EntroPath learns manifold geometry from diffusion paths.
For a finite simplicial graph , let denote the right-angled Artin group on the complement graph of . In this article, we introduce the notions of "induced path lifting property" and "semi-induced path lifting property" for immersions between graphs, and obtain graph theoretical criteria for the embedabilit…
This work derives closed-form expressions computing the expectation of co-presence and of number of co-occurrences of nodes on paths sampled from a network according to general path weights (a bag of paths). The underlying idea is that two nodes are considered as similar when they often appear together on (preferably s…
The recently developed bag-of-paths (BoP) framework consists in setting a Gibbs-Boltzmann distribution on all feasible paths of a graph. This probability distribution favors short paths over long ones, with a free parameter (the temperature ) controlling the entropic level of the distribution. This formalism enables…
LG algorithm finds profitable trading paths in decentralized exchanges.
Efficiently searches ancestral graphs using multivariate information.
Study shows saddle connection graph's geometry and quasi-isometry properties.
We present a simple, yet effective, approach to Semi-Supervised Learning. Our approach is based on estimating density-based distances (DBD) using a shortest path calculation on a graph. These Graph-DBD estimates can then be used in any distance-based supervised learning method, such as Nearest Neighbor methods and SVMs…
We show that the Hausdorff distance between any forward and any backward surgery paths in the sphere graph is at most 2. From this it follows that the Hausdorff distance between any two surgery paths with the same initial sphere system and same target sphere system is at most 4. Our proof relies on understanding how su…
Transformer adapts to graphs with adaptive attention and auto-regressive decoding.
Improved bipartite link prediction using 2-hop paths.
Approximates cycles in planar and bounded-genus graphs.
Efficient algorithms decide algebraic constraints of causal graphs.