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.
Paper calculates Gromov-Hausdorff distance between simplexes and 2-distance spaces.
New algorithm finds minimal causal models for complex latent variables.
The maximum number of maximum cliques in a graph is determined for graphs with at least 15 vertices.
These notes review six lectures given by Prof. Andrea Montanari on the topic of statistical estimation for linear models. The first two lectures cover the principles of signal recovery from linear measurements in terms of minimax risk. Subsequent lectures demonstrate the application of these principles to several pract…
Develops a method to efficiently learn causal DAGs using directed clique trees.
Infinite clique of rays in plane minus Cantor set.
We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters, de ned as well-connected subsets of vertices. The decomposition is based on a s…
We propose a topological learning algorithm for the estimation of the conditional dependency structure of large sets of random variables from sparse and noisy data. The algorithm, named Maximally Filtered Clique Forest (MFCF), produces a clique forest and an associated Markov Random Field (MRF) by generalising Prim's m…
We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields with untied parameters which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for graphs of bounded degree, its complexity is linear in the number of cliques. Unlike…
Paper explores embedding methods for detecting pseudo-cliques in random graphs, showing limitations and potential.
Estimates log-concave densities in graphical models using tent functions.
Cliques, or fully connected subgraphs, are among the most important and well-studied graph motifs in network science. We consider the problem of finding a statisti- cally anomalous clique hidden in a large network. There are two parts to this problem: (1) detection, i.e., determining whether an anomalous clique is pres…
Research uses machine learning to find central nodes and cliques in YouTube social networks.
Tackles the computational hardness of HPC detection, conjecturing equivalence to PC detection.
We introduce the concept of community trees that summarizes topological structures within a network. A community tree is a tree structure representing clique communities from the clique percolation method (CPM). The community tree also generates a persistent diagram. Community trees and persistent diagrams reveal topol…
Sublinear algorithms detect cliques in graphs with high probability.
New insights link diverse statistical problems via secret leakage planted clique.
We present an alternate formulation of the partial assignment problem as matching random clique complexes, that are higher-order analogues of random graphs, designed to provide a set of invariants that better detect higher-order structure. The proposed method creates random clique adjacency matrices for each k-skeleton…
We consider stochastic multi-armed bandit problems with graph feedback, where the decision maker is allowed to observe the neighboring actions of the chosen action. We allow the graph structure to vary with time and consider both deterministic and Erdős-Rényi random graph models. For such a graph feedback model, we fir…
We say a graph has property when it is an induced subgraph of the curve graph of a surface of genus with punctures. Two well-known graph invariants, the chromatic and clique numbers, can provide obstructions to . We introduce a new invariant of a graph, the 'nested complex…
Brain Electroencephalography (EEG) classification is widely applied to analyze cerebral diseases in recent years. Unfortunately, invalid/noisy EEGs degrade the diagnosis performance and most previously developed methods ignore the necessity of EEG selection for classification. To this end, this paper proposes a novel m…
The problem of categorical data analysis in high dimensions is considered. A discussion of the fundamental difficulties of probability modeling is provided, and a solution to the derivation of high dimensional probability distributions based on Bayesian learning of clique tree decomposition is presented. The main contr…
We prove that graph products constructed over infinite graphs with bounded clique number preserve finite asymptotic dimension. We also study the extent to which Dranishnikov's property C, and Dranishnikov and Zarichnyi's straight finite decomposition complexity are preserved by constructions such as unions, free produc…
We study an asynchronous online learning setting with a network of agents. At each time step, some of the agents are activated, requested to make a prediction, and pay the corresponding loss. The loss function is then revealed to these agents and also to their neighbors in the network. Our results characterize how much…
Artin groups not free of infinity are shown to have finite centers.
The Cartesian subgroup in graph products of groups is studied with bounds and algorithms.
Learning to predict solutions to real-valued combinatorial graph problems promises efficient approximations. As demonstrated based on the NP-hard edge clique cover number, recurrent neural networks (RNNs) are particularly suited for this task and can even outperform state-of-the-art heuristics. However, the theoretical…
Study evaluates methods for expanding communities in hypergraphs using random walks.
In financial markets, abnormal trading behaviors pose a serious challenge to market surveillance and risk management. What is worse, there is an increasing emergence of abnormal trading events that some experienced traders constitute a collusive clique and collaborate to manipulate some instruments, thus mislead other …
Estimates joint probability distribution from 1-way marginals using low-rank tensors and random projections.
Maximal knotless graphs have at least 74% of their vertices' edges.
New method improves conditional covariance estimation using targeted groups of assets.
We study the chromatic number of the curve graph of a surface. We show that the chromatic number grows like k log k for the graph of separating curves on a surface of Euler characteristic -k. We also show that the graph of curves that represent a fixed non-zero homology class is uniquely t-colorable, where t denotes it…
Let be an orientable surface with negative Euler characteristic. For , let denote the , whose vertices are isotopy classes of essential simple closed curves on , and whose edges correspond to pairs of curves that can be realized to intersect at most …
Statistical query algorithms and low-degree tests are nearly equivalent in high-dimensional hypothesis testing.
The paper conjectures and proves fixed points for certain group actions on nonpositively curved spaces.
For every orientable surface of finite negative Euler characteristic, we find a right-angled Artin group of cohomological dimension two which does not embed into the associated mapping class group. For a right-angled Artin group on a graph $\gam$ to embed into the mapping class group of a surface , we show that the …
Proposes CLIQUE for improved local variable importance in multi-class classification.
We construct a partial order relation which acts on the set of 3-cliques of a maximal planar graph G and defines a unique hierarchy. We demonstrate that G is the union of a set of special subgraphs, named `bubbles', that are themselves maximal planar graphs. The graph G is retrieved by connecting these bubbles in a tre…
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…
In many domains, there is significant interest in capturing novel relationships between time series that represent activities recorded at different nodes of a highly complex system. In this paper, we introduce multipoles, a novel class of linear relationships between more than two time series. A multipole is a set of t…
A directed acyclic graph (DAG) is the most common graphical model for representing causal relationships among a set of variables. When restricted to using only observational data, the structure of the ground truth DAG is identifiable only up to Markov equivalence, based on conditional independence relations among the v…
The study shows acylindrical hyperbolicity for Artin groups not associated with joins or cones.
We consider two closely related problems: planted clustering and submatrix localization. The planted clustering problem assumes that a random graph is generated based on some underlying clusters of the nodes; the task is to recover these clusters given the graph. The submatrix localization problem concerns locating hid…
Efficient algorithm for self-directed learning of convex clusters on graphs.
New method tests causal relationships from data without needing to learn the entire graph.
New algorithms recover signals robustly against outliers and heavy-tailed noise.
In this paper we study speaker linking (a.k.a.\ partitioning) given constraints of the distribution of speaker identities over speech recordings. Specifically, we show that the intractable partitioning problem becomes tractable when the constraints pre-partition the data in smaller cliques with non-overlapping speakers…