A tutorial on using MDL for graph analysis, focusing on clique size.
problem Analyzing the size of the largest clique in graphs.
method MDL principle applied to graph analysis.
result Interpretation of MDL results and common pitfalls.
On-device research index
arXiv research
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.
169,051 papers · 148 categories
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48 results for “clique size”
Sublinear algorithms detect cliques in graphs with high probability.
problem Detecting a planted clique in random graphs efficiently.
method Non-adaptive low-degree polynomial queries of adjacency matrix entries.
result Sublinear time detection is possible for a specific range of clique sizes.
Paper explores embedding methods for detecting pseudo-cliques in random graphs, showing limitations and potential.
problem Detecting planted pseudo-cliques in random dot product graphs.
method Adjacency Spectral Embedding (ASE) and Graph Encoder Embedding (GEE).
result These methods can localize pseudo-cliques with additional clean network data, but not without it.
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…
Deep nets learn structured densities without dimensionality issues.
problem Learning structured densities in high dimensions.
method Simple -minimizing loss for neural networks.
result Dimension-independent convergence rates for neural networks.
Learning Clique Forestsstat.ML
MFCF algorithm learns conditional dependency structure from sparse data.
problem Learning conditional dependency structure from sparse and noisy data.
method Repeated application of clique expansion to produce clique forest and MRF.
result MFCF outperforms Graphical Lasso for covariance selection models.
Maximal knotless graphsmath.GT
Maximal knotless graphs have at least 74% of their vertices' edges.
problem Characterizing maximal knotless graphs and understanding their edge constraints.
method Analyzing edge maximality and constructing graphs to meet constraints.
result There exists an infinite family of maximal knotless graphs with fewer edges than previously thought.
Develops a method to efficiently learn causal DAGs using directed clique trees.
problem Efficiently learning causal DAGs in the presence of large cliques.
method Decomposes DAGs into independently orientable components using directed clique trees and designs a two-phase intervention algorithm.
result Proves that the number of single-node interventions necessary to orient any DAG in an EC is at least the sum of half the size of the largest cliques in each chain component of the essential graph.
Estimates log-concave densities in graphical models using tent functions.
problem Maximum likelihood estimation of log-concave densities in undirected graphs.
method MLE as product of tent functions corresponding to maximal cliques.
result MLE can be found via convex optimization.
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…
The maximum number of maximum cliques in a graph is determined for graphs with at least 15 vertices.
problem Determining the maximum number of maximum cliques in a graph with n vertices.
method Defining prime and composite graphs, analyzing edge bounds, and using combinatorial arguments.
result For graphs with at least 15 vertices, the graph with the maximum number of maximum cliques is composite.
Solves partial assignment problems using random clique complexes.
problem Partial assignment problems, especially with severe occlusions and distortions.
method Formulate as matching random clique complexes, analyze k-skeletons, match adjacency matrices, consider geometric neighbourhoods.
result Outperforms diverse matching algorithms significantly.
Infinite clique of rays in plane minus Cantor set.
problem Understanding the mapping class group of plane minus Cantor set.
method Using a graph of loops and cliques of high-filling rays.
result Construction of an infinite clique of high-filling rays.
Improved Graph Clusteringstat.ML
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this problem is the stochastic block model, also referred to as the planted partition model…
Reduces average-case complexity of sparse PCA from weak PC conjectures.
problem Characterizing the average-case complexity of sparse PCA.
method Reduction from planted clique conjecture to spiked covariance model.
result First full characterization of computational barrier in spiked covariance model, providing tight lower bounds at all sparsities.
Novel Machine Learning Algorithms for Centrality and Cliques Detection in Youtube Social Networkscs.LG
Research uses machine learning to find central nodes and cliques in YouTube social networks.
problem Identifying central nodes and cliques in YouTube social networks.
method Unsupervised machine learning, Python programming, Bron-Kerbosch algorithm.
result Successfully found central nodes through clique-centrality and degree centrality.
Tackles the computational hardness of HPC detection, conjecturing equivalence to PC detection.
problem Computational hardness of hypergraphic planted clique detection.
method No specific method mentioned; focuses on conjecturing equivalence.
result Equivalence of computational hardness between HPC and PC detection.
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…
New insights link diverse statistical problems via secret leakage planted clique.
problem Statistical-computational gaps in inference problems.
method Secret leakage planted clique as a new hardness assumption for reductions.
result Establishes tight statistical-computational tradeoffs for various problems.
Proposes clique pooling for graph classification.
problem Graph classification challenges.
method Clique-based graph pooling within GCN and GraphSAGE.
result Competitive performance on graph classification benchmarks.
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…
Artin groups not free of infinity are shown to have finite centers.
problem Characterizing Artin groups with finite centers.
method Reduced clique-cube complexes and actions on them.
result Artin groups not free of infinity have finite centers, and are trivial in many cases.
Study evaluates methods for expanding communities in hypergraphs using random walks.
problem Expanding communities in hypergraphs using random walks.
method Clique-expansion and tensor methods evaluated; hybrid method proposed.
result Parameter regimes identified where methods outperform each other.
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 …
New method tests causal relationships from data without needing to learn the entire graph.
problem Testing if a causal graph belongs to a specific Markov equivalence class from observational data.
method Established bounds on the number of independence tests required and provided an algorithm that matches these bounds.
result Testing requires exponentially less independence tests compared to learning, especially in graphs with high in-degrees and small clique sizes.
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 …
New algorithm finds minimal causal models for complex latent variables.
problem Learning causal structure in presence of latent variables and measurement dependencies.
method Graph theoretic edge clique cover problem, non-parametric algorithm.
result Minimality in minimal causal models implies specific properties.
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…
Label assignment problems with large state spaces are important tasks especially in computer vision. Often the pairwise interaction (or smoothness prior) between labels assigned at adjacent nodes (or pixels) can be described as a function of the label difference. Exact inference in such labeling tasks is still difficul…
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…
Proposes CLIQUE for improved local variable importance in multi-class classification.
problem Lack of methods to characterize local structure in model loss space.
method CLIQUE (Conditional Local Importance by Quantile Expectations)
result CLIQUE emphasizes locally dependent information and captures interaction behavior.
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…
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…
The study shows acylindrical hyperbolicity for Artin groups not associated with joins or cones.
problem Proving acylindrical hyperbolicity for Artin groups of infinite type not associated with joins or cones.
method Developing and extending the clique-cube complex and action studies of Charney and Morris-Wright.
result Acylindrical hyperbolicity demonstrated for Artin groups of infinite type associated with graphs that are not cones.
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…
New algorithm identifies near-optimal policies in adversarial distributed RL settings.
problem Adversarial agents in distributed RL settings that can collude and report arbitrary data.
method Weighted-Clique algorithm for robust mean estimation from batches, combined with novel distributed algorithms.
result Achieves superior robustness guarantees and near-optimal sample complexities in both offline and online settings.
Efficient algorithm for self-directed learning of convex clusters on graphs.
problem Self-directed classification of nodes on graphs with convex clusters.
method Developed efficient algorithms for (geodesically) convex clusters on graphs.
result Polynomial runtime algorithm with mistakes for graphs with two convex clusters.
This work sets a universal lower bound for learning causal DAGs with atomic interventions.
problem Learning causal DAGs using only observational data results in a Markov equivalence class, requiring interventions to fully orient.
method Developed CBSP orderings and used them to prove a universal lower bound on the number of single-node interventions needed.
result The universal lower bound is within a factor of two of the minimum number of single-node interventions required to fully orient a given Markov equivalence class.
Constrained speaker linkingstat.ML
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…
As a model problem for clustering, we consider the densest k-disjoint-clique problem of partitioning a weighted complete graph into k disjoint subgraphs such that the sum of the densities of these subgraphs is maximized. We establish that such subgraphs can be recovered from the solution of a particular semidefinite re…
This paper studies the problem of detecting the presence of a small dense community planted in a large Erdős-Rényi random graph , where the edge probability within the community exceeds by a constant factor. Assuming the hardness of the planted clique detection problem, we show that the computatio…
Average-Case Lower Bounds for Learning Sparse Mixtures, Robust Estimation and Semirandom Adversariescs.CC
Paper shows statistical-computational gaps in learning sparse mixtures and robust estimation.
problem Statistical-computational gaps in learning sparse mixtures and robust estimation.
method Average-case reduction techniques, Imbalanced Sparse Gaussian Mixtures, and algorithmic change of measure.
result New hardness results for robust sparse mean estimation, semirandom planted dense subgraph, and universality principle for sparse mixture problems.
Paper calculates Gromov-Hausdorff distance between simplexes and 2-distance spaces.
problem Calculating Gromov-Hausdorff distance between simplexes and 2-distance spaces.
method Formulas derived for clique covering number and chromatic number of graphs.
result Complete solution to generalized Borsuk problem for 2-distance spaces.
Compressive Network Analysisstat.ML
Modern data acquisition routinely produces massive amounts of network data. Though many methods and models have been proposed to analyze such data, the research of network data is largely disconnected with the classical theory of statistical learning and signal processing. In this paper, we present a new framework for …
A new hypergraph-based active learning scheme reduces query complexity.
problem Efficiently querying and learning from complex hypergraph structures.
method Developed a novel hypergraph-based active learning scheme that can handle both pointwise and pairwise queries.
result Demonstrated that requires significantly fewer queries than a previously used graph-based method .
The Cartesian subgroup in graph products of groups is studied with bounds and algorithms.
problem Understanding the structure of Cartesian subgroups in graph products of groups.
method Theory of polyhedral products, lower and upper bounds, algorithm for small presentations.
result Bounds on the number of relations and deficiency in presentations of Cartesian groups.
Given a large data matrix , we consider the problem of determining whether its entries are i.i.d. with some known marginal distribution , or instead contains a principal submatrix whose entries have marginal distribution . As …