Related papers: A Geometric Statistic for Quantifying Correlation …
Family members' satisfaction with one another is central to creating healthy and supportive family environments. In this work, we propose and implement a novel computational technique aimed at exploring the possible relationship between the…
Scatter plots are widely recognized as fundamental tools for illustrating the relationship between two numerical variables. Despite this, based on solid theoretical foundations, scatter plots generated from pairs of continuous random…
In this work, we study the correlation between attribute sets and the occurrence of dense subgraphs in large attributed graphs, a task we call structural correlation pattern mining. A structural correlation pattern is a dense subgraph…
Large graphs abound in machine learning, data mining, and several related areas. A useful step towards analyzing such graphs is that of obtaining certain summary statistics - e.g., or the expected length of a shortest path between two…
Approximating complex probability distributions, such as Bayesian posterior distributions, is of central interest in many applications. We study the expressivity of geometric Gaussian approximations. These consist of approximations by…
We introduce a geometric scaling relation that characterizes the local scale behavior of correlations using the informational distance $d_E = K_0/\sqrt{I}$, where $I$ is the mutual information. We define a geometric conversion factor, $G…
Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric…
Structural features are important features in a geometrical graph. Although there are some correlation analysis of features based on covariance, there is no relevant research on structural feature correlation analysis with graph neural…
Gaussian graphical models are used throughout the natural sciences, social sciences, and economics to model the statistical relationships between variables of interest in the form of a graph. We here provide a pedagogic introduction to…
'Big' high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality-reduction step that inherently distorts the data structure. For the same purpose, clustering methods are also often used. These methods…
Motivated by alignment of correlated sparse random graphs, we introduce a hypothesis testing problem of deciding whether or not two random trees are correlated. We obtain sufficient conditions under which this testing is impossible or…
To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…
Random forests are considered one of the best out-of-the-box classification and regression algorithms due to their high level of predictive performance with relatively little tuning. Pairwise proximities can be computed from a trained…
To obtain a probabilistic model for a dependent variable based on some set of explanatory variables, a distributional approach is often adopted where the parameters of the distribution are linked to regressors. In many classical models this…
Background: We study the statistical properties of fragment coverage in genome sequencing experiments. In an extension of the classic Lander-Waterman model, we consider the effect of the length distribution of fragments. We also introduce…
Using a generating function approach, the correlation coefficients of four different graph-theoretical indices, namely the number of independent vertex subsets, the number of matchings, the number of subtrees and the Wiener index, are…
A new synthesis scheme is proposed to effectively generate a random vector with prescribed joint density that induces a (latent) Gaussian tree structure. The quality of synthesis is measured by total variation distance between the…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
We consider geometrical clusters (i.e. domains of parallel spins) in the square lattice random field Ising model by varying the strength of the Gaussian random field, $\Delta$. In agreement with the conclusion of previous investigation…
This paper addresses the statistical significance of structures in random data: Given a set of vectors and a measure of mutual similarity, how likely does a subset of these vectors form a cluster with enhanced similarity among its elements?…