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.
Polynomial-time algorithm estimates edge density of random graphs with privacy and robustness.
In this paper, we present a novel way to summarize the structure of large graphs, based on non-parametric estimation of edge density in directed multigraphs. Following coclustering approach, we use a clustering of the vertices, with a piecewise constant estimation of the density of the edges across the clusters, and ad…
New graph properties inherited by Frechet mean and median.
The paper defines and studies discrete p-density and compression-radius profiles of lattice knots.
Paper characterizes optimal graph clustering limits under a new model.
Edge augmentation connects disconnected graphs by elevating eigenvalues.
This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know whether or not there is an edge. We want to organize the nodes into disjoint cl…
DIF extends NF with stochastic discrete latent variables for better density estimation.
Mean curvature flow of clusters of n-dimensional surfaces in R^{n+k} that meet in triples at equal angles along smooth edges and higher order junctions on lower dimensional faces is a natural extension of classical mean curvature flow. We call such a flow a mean curvature flow with triple edges. We show that if a smoot…
We reconcile between two classical models of edge-dislocations in solids. The first model, dating from the early 1900s models isolated edge-dislocations as line singularities in locally-Euclidean manifolds. The second model, dating from the 1950s, models continuously-distributed edge-dislocations as smooth manifolds en…
New algorithm estimates edge density of random graphs robustly, achieving optimal breakdown point.
pAElla detects malware in DCs/SCs with high accuracy.
Estimating dimension from sparse random geometric graphs.
We introduce a new random group model called the square model: we quotient a free group on generators by a random set of relations, each of which is a reduced word of length four. We prove, as in the Gromov density model, that for densities a random group in the square model is trivial with overwhel…
Adaptive kernel density estimation improves accuracy in high dimensions.
Polynomial-time algorithm matches correlated random graphs with non-vanishing correlation.
Study fully augmented links in thickened torus, generalizing results.
Low-rank training improves neural network training on edge devices with non-volatile memory.
Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attain low classification errors. The resulting classifier is linear in the log-transformed univariate and b…
Derives continuum model from discrete -graphs with connectivity functional.
New method calibrates probabilistic linear solver for online coverage guarantees.
Recovering edge activities from node activity data in temporal networks.
Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among brain regions. In this paper, we develop a non-asymptotic theory for regularize…
The Mutual Information (MI) is an often used measure of dependency between two random variables utilized in information theory, statistics and machine learning. Recently several MI estimators have been proposed that can achieve parametric MSE convergence rate. However, most of the previously proposed estimators have th…
Lipid-bilayers are the fundamental constituents of the walls of most living cells and lipid vesicles, giving them shape and compartment. The formation and growing of pores in a lipid bilayer have attracted considerable attention from an energetic point of view in recent years. Such pores permit targeted delivery of dru…
The vast majority of the neural network literature focuses on predicting point values for a given set of response variables, conditioned on a feature vector. In many cases we need to model the full joint conditional distribution over the response variables rather than simply making point predictions. In this paper, we …
Novel flows generate molecules without post-processing.
Proposes DISCO, the first CVI for density-based clustering with noise.
Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting output. We prove that kernel smoothing biases the moments of the spectral density.…
Study of straight-line flows on a unique infinite surface.
Higher-order motif structures and multi-vertex interactions are becoming increasingly important in studies that aim to improve our understanding of functionalities and evolution patterns of networks. To elucidate the role of higher-order structures in community detection problems over complex networks, we introduce the…
The paper studies knot densities under various constraints and degenerations.
The study evaluates forecast risk-adjusted performance using various metrics.
Physics-informed ML models improve turbulence understanding in fusion plasmas.
There is a recent surge of interest in identifying the sharp recovery thresholds for cluster recovery under the stochastic block model. In this paper, we address the more refined question of how many vertices that will be misclassified on average. We consider the binary form of the stochastic block model, where ver…
We consider the densest -subgraph problem, which seeks to identify the -node subgraph of a given input graph with maximum number of edges. This problem is well-known to be NP-hard, by reduction to the maximum clique problem. We propose a new convex relaxation for the densest -subgraph problem, based on a nucle…
New method predicts neural network performance using free probability theory.
Graph clustering is a basic technique in machine learning, and has widespread applications in different domains. While spectral techniques have been successfully applied for clustering undirected graphs, the performance of spectral clustering algorithms for directed graphs (digraphs) is not in general satisfactory: the…
Improved manifold-adaptive dimension estimator for better data complexity assessment.
Much of the focus in the design of deep neural networks has been on improving accuracy, leading to more powerful yet highly complex network architectures that are difficult to deploy in practical scenarios, particularly on edge devices such as mobile and other consumer devices given their high computational and memory …
Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In this paper, we introduce stable graphical (SG) models, a class of multivariate st…
Self-supervised VAEs improve data compression and generation.
Exchangeable graphs arise via a sampling procedure from measurable functions known as graphons. A natural estimation problem is how well we can recover a graphon given a single graph sampled from it. One general framework for estimating a graphon uses step-functions obtained by partitioning the nodes of the graph accor…
Graphs from features improve classification accuracy in tasks.
New model captures time series dependence across and within blocks.
Clustering is fundamental for gaining insights from complex networks, and spectral clustering (SC) is a popular approach. Conventional SC focuses on second-order structures (e.g., edges connecting two nodes) without direct consideration of higher-order structures (e.g., triangles and cliques). This has motivated SC ext…
The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and hobbies. The connectivity of a graph can thus possibly be understood in terms of patte…
We study the problem of learning sparse structure changes between two Markov networks and . Rather than fitting two Markov networks separately to two sets of data and figuring out their differences, a recent work proposed to learn changes \emph{directly} via estimating the ratio between two Markov network models…