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.
IDPGs extend RDPGs with a Poisson process for random latent positions.
New algorithms improve community detection and parameter estimation for PABM.
Extends random dot product graph model to handle multiple graphs.
Convex optimization method infers latent structure in random dot product graphs.
The random dot product graph (RDPG) is an independent-edge random graph that is analytically tractable and, simultaneously, either encompasses or can successfully approximate a wide range of random graphs, from relatively simple stochastic block models to complex latent position graphs. In this survey paper, we describ…
The paper examines how well node similarities are preserved by random projections in graph embeddings.
We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology outlined in \citet{sussman2012universally} to construct consistent estimates for the …
Paper explores embedding methods for detecting pseudo-cliques in random graphs, showing limitations and potential.
The paper extends RDPG model to handle weighted graphs, enabling better analysis of network data.
In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate latent positions for random dot product graphs provided the latent positions are i.i.d. from some distribution. If class labels are observed for a number of vertices tending to infinity, then we show that the …
New method uses manifold learning to infer latent positions of 1D submanifolds in random dot product graphs.
Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network model known as the random dot product graph, to allow interpretation of those vector representations as latent position estimates. The general…
New method recovers graph latent positions under edge differential privacy.
OmniMatch algorithm perfectly matches graphs without edge correlation.
Online CPD for weighted and directed graphs using RDPG model.
GraphMoE generates random graphs using neural networks and graphlets.
Vertex clustering in a stochastic blockmodel graph has wide applicability and has been the subject of extensive research. In thispaper, we provide a short proof that the adjacency spectral embedding can be used to obtain perfect clustering for the stochastic blockmodel and the degree-corrected stochastic blockmodel. We…
Improves efficiency of random feature approximations for dot product kernels.
The paper corrects for node degree in spectral clustering using random walk Laplacian.
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear…
Power of network tests degrades when vertices are misaligned.
Linear time algorithm for random walk kernels on sparse graphs.
A latent space model for a family of random graphs assigns real-valued vectors to nodes of the graph such that edge probabilities are determined by latent positions. Latent space models provide a natural statistical framework for graph visualizing and clustering. A latent space model of particular interest is the Rando…
Two types of nonidentifiability in latent position graphs identified and characterized.
New method embeds dynamic networks with stability for node behavior.
Researchers prove inner product recovery is impossible in latent space models.
The paper predicts responses on out-of-sample nodes using latent positions on unknown curves.
We present a method to estimate block membership of nodes in a random graph generated by a stochastic blockmodel. We use an embedding procedure motivated by the random dot product graph model, a particular example of the latent position model. The embedding associates each node with a vector; these vectors are clustere…
We prove a central limit theorem for the components of the eigenvectors corresponding to the largest eigenvalues of the normalized Laplacian matrix of a finite dimensional random dot product graph. As a corollary, we show that for stochastic blockmodel graphs, the rows of the spectral embedding of the normalized La…
Inference for the stochastic blockmodel is currently of burgeoning interest in the statistical community, as well as in various application domains as diverse as social networks, citation networks, brain connectivity networks (connectomics), etc. Recent theoretical developments have shown that spectral embedding of gra…
We present semiparametric spectral modeling of the complete larval Drosophila mushroom body connectome. Motivated by a thorough exploratory data analysis of the network via Gaussian mixture modeling (GMM) in the adjacency spectral embedding (ASE) representation space, we introduce the latent structure model (LSM) for n…
The paper examines deformations of simple dotted graphs made of circles.
Estimates latent norms and Gram matrices for graphs on Euclidean balls.
Tests if vertices in graphs have the same latent positions.
This paper improves GNNs' generalization by adding a Low-Rank Global Attention module.
Estimates kernel eigenvalues for compositional dot-product kernels.
In this paper we study the concentration properties for the eigenvalues of kernel matrices, which are central objects in a wide range of kernel methods and, more recently, in network analysis. We present a set of concentration inequalities tailored for each individual eigenvalue of the kernel matrix with respect to its…
Revisits neural collaborative filtering vs. matrix factorization, showing dot product superiority.
Traditionally, multi-layer neural networks use dot product between the output vector of previous layer and the incoming weight vector as the input to activation function. The result of dot product is unbounded, thus increases the risk of large variance. Large variance of neuron makes the model sensitive to the change o…
Random features enhance control of complex systems.
Many popular dimensionality reduction procedures have out-of-sample extensions, which allow a practitioner to apply a learned embedding to observations not seen in the initial training sample. In this work, we consider the problem of obtaining an out-of-sample extension for the adjacency spectral embedding, a procedure…
In statistical relational learning, knowledge graph completion deals with automatically understanding the structure of large knowledge graphs---labeled directed graphs---and predicting missing relationships---labeled edges. State-of-the-art embedding models propose different trade-offs between modeling expressiveness, …
The paper analyzes learning curves for kernel ridge regression with dot-product kernels.
Kernel methods form a powerful, versatile, and theoretically-grounded unifying framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the kernel trick to perform pairwise evaluations of a kernel function, which leads to scalability issues for large datasets due …
Given an edge-independent random graph G(n,p), we determine various facts about the cohomology of graph products of groups for the graph G(n,p). In particular, the random graph product of a sequence of finite groups is a rational duality group with probability tending to 1 as n goes to infinity. This includes random ri…
The paper refines transformations of lattice diagrams and introduces dotted diagrams.
Formula derived for spherical growth series of specific groups.
We define analogues of the graphs of free splittings, of cyclic splittings, and of maximally-cyclic splittings of for free products of groups, and show their hyperbolicity. Given a countable group which splits as , where denotes a finitely generated free group, we identify th…