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.
Tackles the computational hardness of HPC detection, conjecturing equivalence to PC detection.
New insights link diverse statistical problems via secret leakage planted clique.
Sublinear algorithms detect cliques in graphs with high probability.
This paper develops several average-case reduction techniques to show new hardness results for three central high-dimensional statistics problems, implying a statistical-computational gap induced by robustness, a detection-recovery gap and a universality principle for these gaps. A main feature of our approach is to ma…
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…
Paper explores embedding methods for detecting pseudo-cliques in random graphs, showing limitations and potential.
Statistical query algorithms and low-degree tests are nearly equivalent in high-dimensional hypothesis testing.
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 …
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…
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…
Paper explores limits of high-order clustering with planted structures.
In the past decade, sparse principal component analysis has emerged as an archetypal problem for illustrating statistical-computational tradeoffs. This trend has largely been driven by a line of research aiming to characterize the average-case complexity of sparse PCA through reductions from the planted clique (PC) con…
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…
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…
In the context of sparse principal component detection, we bring evidence towards the existence of a statistical price to pay for computational efficiency. We measure the performance of a test by the smallest signal strength that it can detect and we propose a computationally efficient method based on semidefinite prog…
Many high dimensional sparse learning problems are formulated as nonconvex optimization. A popular approach to solve these nonconvex optimization problems is through convex relaxations such as linear and semidefinite programming. In this paper, we study the statistical limits of convex relaxations. Particularly, we con…
In this paper, we propose a general framework for tensor singular value decomposition (tensor SVD), which focuses on the methodology and theory for extracting the hidden low-rank structure from high-dimensional tensor data. Comprehensive results are developed on both the statistical and computational limits for tensor …
The maximum number of maximum cliques in a graph is determined for graphs with at least 15 vertices.
Infinite clique of rays in plane minus Cantor set.
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…
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 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…
The goal of this research project is to analyze the dynamics of social networks using machine learning techniques to locate maximal cliques and to find clusters for the purpose of identifying a target demographic. Unsupervised machine learning techniques are designed and implemented in this project to analyze a dataset…
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…
Develops a method to efficiently learn causal DAGs using directed clique trees.
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.
Spectral algorithms solve optimal community detection and related problems.
Exact partitioning of high-order planted models achieved through convex optimization.
The paper uses VGG-19 for plant species classification from leaf images.
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 …
Maximal knotless graphs have at least 74% of their vertices' edges.
New computational lower bounds for clustering and related problems.
We study methods for aggregating pairwise comparison data in order to estimate outcome probabilities for future comparisons among a collection of n items. Working within a flexible framework that imposes only a form of strong stochastic transitivity (SST), we introduce an adaptivity index defined by the indifference se…
Plants monitor their surrounding environment and control their physiological functions by producing an electrical response. We recorded electrical signals from different plants by exposing them to Sodium Chloride (NaCl), Ozone (O3) and Sulfuric Acid (H2SO4) under laboratory conditions. After applying pre-processing tec…
Estimates log-concave densities in graphical models using tent functions.
Privacy improves robustness in statistical estimation.
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…
Study connects database alignment and planted matching using Gaussian features.
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.
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…
Chemical plants are complex and dynamical systems consisting of many components for manipulation and sensing, whose state transitions depend on various factors such as time, disturbance, and operation procedures. For the purpose of supporting human operators of chemical plants, we are developing an AI system that can s…
Hydropower plants are one of the most convenient option for power generation, as they generate energy exploiting a renewable source, they have relatively low operating and maintenance costs, and they may be used to provide ancillary services, exploiting the large reservoirs of available water. The recent advances in In…
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…
We describe the first known mean-field study of landing probabilities for random walks on hypergraphs. In particular, we examine clique-expansion and tensor methods and evaluate their mean-field characteristics over a class of random hypergraph models for the purpose of seed-set community expansion. We describe paramet…
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…