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.
Spectral algorithms solve optimal community detection and related problems.
problem Optimal detection of community structures and related substructures.
method Spectral algorithms applied to various planted substructures.
result Spectral algorithms achieve optimal performance for a wide range of planted substructures.
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.
Polynomial-time test for detecting dense subgraphs in heterogeneous networks.
problem Detecting a planted community in heterogeneous networks.
method Proposes a polynomial-time test with a standard normal distribution null limiting distribution.
result The test is efficient and performs well in both simulations and real data.
Detects dense subhypergraphs in random hypergraphs using low-degree polynomials.
problem Detecting a planted dense subhypergraph in a random hypergraph model.
method Degree-n^o(1) polynomials of adjacency tensor entries.
result Thresholds for detection in different density regimes.
Spectral clustering is robust to helpful model changes but not to random changes.
problem Robustness of spectral clustering in the presence of semirandom adversaries.
method Analysis of spectral clustering algorithms under semirandom adversaries.
result Spectral clustering with unnormalized Laplacian is strongly consistent under semirandom adversaries.
This paper studies the problem of detecting the presence of a small dense community planted in a large Erdős-Rényi random graph G(N,q), where the edge probability within the community exceeds q by a constant factor. Assuming the hardness of the planted clique detection problem, we show that the computatio…
We formalize the problem of detecting a community in a network into testing whether in a given (random) graph there is a subgraph that is unusually dense. We observe an undirected and unweighted graph on N nodes. Under the null hypothesis, the graph is a realization of an Erdös-Rényi graph with probability p0. Under th…
Paper tackles dense subgraph discovery with noisy feedback.
problem Discover dense subgraphs in edge-weighted graphs with noisy feedback.
method Proposes polynomial-time and scalable algorithms for dense subgraph discovery.
result Polynomial-time algorithm obtains nearly-optimal solution with high probability.
Paper explores limits of high-order clustering with planted structures.
problem Statistical and computational limits of high-order clustering with planted structures.
method Developed methods for detection and recovery of clusters, identified signal-to-noise ratio boundaries.
result Sharp boundaries of signal-to-noise ratio for statistical and computational feasibility.
A new algorithm reduces graph complexity for better dense subgraph analysis.
problem Mining dense subgraphs in large graphs for better analysis.
method Multi-stage graph peeling algorithm (M-PA) with two-stage data screening.
result M-PA produces similar dense subgraphs to the previous PA but with reduced graph complexity.
Study on detecting and recovering hidden dense cycles in random graphs.
problem Detecting and recovering hidden dense cycles in random graphs.
method Information-theoretic analysis of thresholds for detection and recovery.
result Characterization of information-theoretic thresholds for detection and recovery.
New findings on computational limits for estimating hidden structures.
problem Estimating hidden structures in noisy data.
method Use of low-degree polynomials as a restricted model of computation.
result Established low-degree hardness of recovery problems for easy detection problems.
The binary symmetric stochastic block model deals with a random graph of n vertices partitioned into two equal-sized clusters, such that each pair of vertices is connected independently with probability p within clusters and q across clusters. In the asymptotic regime of p=alogn/n and q=blogn/n for fixe…
Detection of dense cycles in graphs reveals a gap between easy detection and hard recovery.
problem Detecting and recovering dense cycles in Erdős-Rényi graphs.
method Characterization of computational thresholds for detection and recovery using low-degree polynomial algorithms.
result A gap exists between the detection and recovery thresholds for certain parameter regimes.
Method finds interestingly dense subgroup connections in graphs.
problem Understanding patterns in graph connectivity based on node attributes.
method Information-theoretic definition of interestingness for subgroup connections.
result Identifies pairs of node subgroups with high or low edge density.
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…
We define a metric filtration of the Gordian graph by an infinite family of 1-dense subgraphs. The n-th subgraph of this family is generated by all knots whose fundamental groups surject to a symmetric group with parameter at least n, where all meridians are mapped to transpositions. Incidentally, we verify the Meridio…
The stochastic block model is one of the oldest and most ubiquitous models for studying clustering and community detection. In an exciting sequence of developments, motivated by deep but non-rigorous ideas from statistical physics, Decelle et al. conjectured a sharp threshold for when community detection is possible in…
New tests detect communities in dense bipartite graphs with high accuracy.
problem Detecting communities in dense bipartite graphs with high accuracy.
method Non-asymptotic upper and lower bounds, novel minimax-optimal tests, hard-thresholded nonlinear statistics.
result Non-asymptotic upper and lower bounds match for any configuration of graph sizes.
We consider the densest k-subgraph problem, which seeks to identify the k-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 k-subgraph problem, based on a nucle…
Faster algorithm for generalized mean densest subgraph problem.
problem Finding subgraphs with highest average p-th-power degree. method GENPEEL++ algorithm, which yields (2(p+1))1/p-approximation for p∈[1,+∞) with time complexity O(m(logn)). result GENPEEL++ algorithm provides faster and more efficient solution for generalized mean densest subgraph problem.
New method explains computational barriers in high-dimensional statistical models.
problem Understanding detection-recovery gaps in high-dimensional inference.
method Combining algorithmic contiguity and cross-validation reduction to obtain conditional computational lower bounds.
result Mild control of low-degree advantage is sufficient to explain computational barriers for recovery.
We propose a semidefinite programming (SDP) algorithm for community detection in the stochastic block model, a popular model for networks with latent community structure. We prove that our algorithm achieves exact recovery of the latent communities, up to the information-theoretic limits determined by Abbe and Sandon (…
Estimates social network structure from random walk subgraphs.
problem Recovering population structure from random walk subgraphs in stochastic block models.
method Maximum likelihood estimation, SAEM algorithm, de-biasing techniques.
result New de-biased estimator provides more accurate recovery of network structure.
GANs improve anomaly detection in power plants, achieving nearly perfect classification.
problem Anomaly detection in power generation plants to identify irregularities.
method Used Generative Adversarial Networks (GANs) for anomaly detection in power generation plants.
result GANs achieved an accuracy rate of 98.99% in anomaly detection, significantly improved by data augmentation.
Finding "densely connected clusters" in a graph is in general an important and well studied problem in the literature \cite{Schaeffer}. It has various applications in pattern recognition, social networking and data mining \cite{Duda,Mishra}. Recently, Ames and Vavasis have suggested a novel method for finding cliques i…
Sparse neural networks can match dense models on Lipschitz functions.
problem Sparse networks are more efficient but lack theoretical guarantees.
method Formal model of sparse networks, LSH-based routing function, Lipschitz function approximation.
result Sparse networks can approximate dense networks on Lipschitz functions.
We study a semidefinite programming (SDP) relaxation of the maximum likelihood estimation for exactly recovering a hidden community of cardinality K from an n×n symmetric data matrix A, where for distinct indices i,j, Aij∼P if i,j are both in the community and Aij∼Q otherwise, for …
New tools in nonlinear random matrices improve understanding of the Sum of Squares hierarchy.
problem Improving the Sum of Squares (SoS) hierarchy's performance on average-case problems.
method Developed new tools in nonlinear random matrices and applied them to analyze the SoS hierarchy.
result Subexponential-time SoS lower bounds for various problems, offering evidence for the low-degree likelihood ratio hypothesis.
We consider the problem of detecting a tight community in a sparse random network. This is formalized as testing for the existence of a dense random subgraph in a random graph. Under the null hypothesis, the graph is a realization of an Erdös-Rényi graph on N vertices and with connection probability p0; under the …
We study the problem of recovering a hidden community of cardinality K from an n×n symmetric data matrix A, where for distinct indices i,j, Aij∼P if i,j both belong to the community and Aij∼Q otherwise, for two known probability distributions P and Q depending on n. If $P={\r…
New bootstraps improve speed and accuracy for graph count functionals.
problem Efficiently counting subgraphs in large graphs.
method Developed two types of multiplier bootstraps: a fast, approximate linear one and a quadratic one for denser graphs.
result Both bootstraps provide valid inference and higher-order accuracy under different graph sparsity conditions.
Improved spectral method recovers sparse vectors in random subspaces.
problem Recovering a sparse vector in a random subspace with sub-Gaussian entries.
method Improved spectral method with leave-one-out analysis.
result Spectral method recovers sparse vectors with high probability under certain conditions.
EnsemFDet detects fraud by solving subproblems on small graphs, scaling up e-commerce fraud detection.
problem Detecting and preventing fraud in e-commerce, especially in large-scale bipartite graphs.
method EnsemFDet uses an ensemble approach to decompose the problem into smaller subproblems, solving them in parallel.
result EnsemFDet is up to 100x faster than state-of-the-art methods while maintaining high accuracy.
SubGNN tackles subgraph prediction challenges in graphs.
problem Subgraphs in graphs are challenging to predict due to their internal topology and external connectivity.
method SubGNN introduces a novel subgraph routing mechanism to learn disentangled subgraph representations.
result SubGNN achieves considerable performance gains on subgraph classification tasks, outperforming strong baseline methods.
New algorithms detect and estimate rank-one signals with prior directional information.
problem Detecting and estimating rank-one signals with directional prior information.
method Construct nonlinear Laplacians and examine top eigenvalues and eigenvectors.
result Nonlinear Laplacian algorithms outperform direct spectral methods for biased signals.
The paper introduces subgraph nomination for finding similar subgraphs in networks.
problem Finding similar subgraphs in networks using example subgraphs.
method Formalizes subgraph nomination framework with user-supervised retrieval.
result User-supervised retrieval improves performance in subgraph nomination.
NeuroMatch efficiently matches subgraphs in large graphs using neural networks.
problem Determining the presence and location of a query graph in a large target graph.
method NeuroMatch decomposes graphs into subgraphs, embeds them using graph neural networks, and matches them directly in the embedding space.
result NeuroMatch is 100x faster and 18% more accurate than existing methods.
The paper uses VGG-19 for plant species classification from leaf images.
problem Manual inspection of plant species by botanists is time-consuming.
method Transfer learning with VGG-19 for feature extraction and classification.
result The model achieves 99.70% accuracy in predicting plant species.
Exact partitioning of high-order planted models achieved through convex optimization.
problem Efficiently partitioning hypergraphs generated by high-order planted models.
method Solving a computationally efficient convex optimization problem with a tensor nuclear norm constraint.
result Exact recovery of true underlying cluster structures with high probability.
Unified framework for subgraph-enhanced GNNs, improving prediction accuracy and reducing computation time.
problem Limited understanding of subgraph-enhanced GNNs and their relation to the Weisfeiler-Leman hierarchy.
method Theoretical framework, theoretical expressivity results, and data-driven subgraph sampling methods.
result Data-driven subgraph-enhanced GNNs outperform non-data-driven methods in predictive performance.
Study area-minimizing subgraphs in integer lattices.
problem Finding the most efficient subgraphs in integer lattices.
method Formulated functions of bounded variations, classified subgraphs in 2D, proved properties in higher dimensions.
result Classified area-minimizing subgraphs in 2D integer lattice up to isomorphisms.
A biclustering algorithm finds dense disjoint subgraphs in weighted bipartite graphs.
problem Finding dense disjoint bicliques in a weighted bipartite graph.
method Semidefinite programming-based branch-and-cut algorithm with upper and lower bounds.
result The algorithm can solve much larger instances than general-purpose solvers.
We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be applied to attributed graphs, our approach allows to rate mappings of subgraphs by …
GNNS uses graph neural networks to efficiently estimate subgraph frequency distributions.
problem Efficiently calculating subgraph frequency distributions in large networks.
method Graph Neural Networks (GNNS) for sampling and estimating subgraph frequencies.
result GNNS achieves comparable accuracy with a significant speedup of three orders of magnitude.
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.
Study on visibility properties of spiral sets in higher dimensions.
problem Characterizing density properties of spiral sets.
method Employing visibility concepts from discrete geometry.
result Established conditions for various density properties of spirals.