Related papers: Detecting Planted Structure in Circular Data
Planted dense cycles are a type of latent structure that appears in many applications, such as small-world networks in social sciences and sequence assembly in computational biology. We consider a model where a dense cycle with expected…
We study a random graph model for small-world networks which are ubiquitous in social and biological sciences. In this model, a dense cycle of expected bandwidth $n \tau$, representing the hidden one-dimensional geometry of vertices, is…
The paper discusses fundamental detectability properties associated with the problem of distributed state estimation using networked observers. The main result of the paper establishes connections between detectability of the plant through…
Multilayer networks are used to represent the interdependence between the relational data of individuals interacting with each other via different types of relationships. To study the information-theoretic phase transitions in detecting the…
To understand how hidden information can be extracted from statistical networks, planted models in random graphs have been the focus of intensive study in recent years. In this work, we consider the detection of a planted matching, i.e., an…
We study the problem of detecting whether an inhomogeneous random graph contains a planted community. Specifically, we observe a single realization of a graph. Under the null hypothesis, this graph is a sample from an inhomogeneous random…
The phase diagram, ($T,\rho$), of a finite, constrained, and classical system is built from the analysis of cluster distributions in phase and configurational space. The obtained phase diagram can be split in three regions. One, low density…
We study the problem of recovering a known cluster structure in a sparse network, also known as the planted partitioning problem, by means of statistical mechanics. We find a sharp transition from un-recoverable to recoverable structure as…
We study the problem of recovering a planted hierarchy of partitions in a network. The detectability of a single planted partition has previously been analysed in detail and a phase transition has been identified below which the partition…
Motivated by some cutting edge circular data such as from Smart Home technologies and roulette spins from online and casino, we construct some new rich classes of discrete distributions on the circle. We give four new general methods of…
We consider the statistical inference problem of recovering an unknown perfect matching, hidden in a weighted random graph, by exploiting the information arising from the use of two different distributions for the weights on the edges…
We use a well known model (T. Vicsek et al. Phys Rev Lett 15, 1226 (1995)) for flocking to test mutual information as a tool for detecting order-disorder transitions, in particular when observations of the system are limited. We show that…
The planted bisection model is a random graph model in which the nodes are divided into two equal-sized communities and then edges are added randomly in a way that depends on the community membership. We establish necessary and sufficient…
Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…
We consider the task of detecting a hidden bipartite subgraph in a given random graph. This is formulated as a hypothesis testing problem, under the null hypothesis, the graph is a realization of an Erd\H{o}s-R\'{e}nyi random graph over $n$…
We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture model, sparse PCA, and submatrix localization. Each of these problems is…
Statistical significance of network clustering has been an unresolved problem since it was observed that community detection algorithms produce false positives even in random graphs. After a phase transition between undetectable and…
Continuous standard windowing is revisited and a new taper shape is introduced, which is based on the normal circular distribution by von Mises. Continuous-time windows are considered and their spectra obtained. A brief comparison with…
Modeling non-stationary data is a challenging problem in the field of continual learning, and data distribution shifts may result in negative consequences on the performance of a machine learning model. Classic learning tools are often…
We consider several detection situations where, under the alternative hypothesis, the signal admits a low complexity model and, under both the null and the alternative hypotheses, the distribution of the background noise is {unknown}. We…