相关论文: QQ plots, Random sets and data from a heavy tailed…

Geometric scale-free random graphs are popular models for networks that exhibit as heavy-tailed degree distributions, small-worldness and high clustering. In these models, vertices have weights that cause the heavy-tailed degrees and are…

We determine, asymptotically in $n$, the distribution and mean of the weight of a minimum-weight $k$-clique (or any strictly balanced graph $H$) in a complete graph $K_n$ whose edge weights are independent random values drawn from the…

A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…

The problem of defining a statistical ensemble of random graphs with an arbitrary connectivity distribution is discussed. Introducing such an ensemble is a step towards uderstanding the geometry of wide classes of graphs independently of…

When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or…

Quantile-Quantile (Q-Q) plots are often difficult to interpret because it is unclear how large the deviation from the theoretical distribution must be to indicate a lack of fit. Most Q-Q plots could benefit from the addition of meaningful…

Angular observations, or observations lying on the unit circle, arise in many disciplines and require special care in their description, analysis, interpretation and visualization. We provide methods to construct concentric circular boxplot…

The threshold network model is a type of finite random graphs. In this paper, we introduce a generalized threshold network model. A pair of vertices with random weights is connected by an edge when real-valued functions of the pair of…

Regular Path Queries (RPQs) are a type of graph query where answers are pairs of nodes connected by a sequence of edges matching a regular expression. We study the techniques to process such queries on a distributed graph of data. While…

We build a sharp approximation of the whole distribution of the sum of iid heavy-tailed random vectors, combining mean and extreme behaviors. It extends the so-called 'normex' approach from a univariate to a multivariate framework. We…

We consider the detection and localization of change points in the distribution of an offline sequence of observations. Based on a nonparametric framework that uses a similarity graph among observations, we propose new test statistics when…

We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…

Borrowing ideas from the relation between simply laced Lie algebras and Dynkin diagrams, a weighted graph theory representation of quantum information is addressed. In this way, the density matrix of a quantum state can be interpreted as a…

We study statistical properties of the truncated flat spot map $f_t(x)$. In particular, we investigate whether for large $n$, the deviations $\sum_{i=0}^{n-1} \left(f_t^i(x_0)-\frac 12\right)$ upon rescaling satisfy a $Q$-Gaussian…

When using the Focused Information Criterion (FIC) for assessing and ranking candidate models with respect to how well they do for a given estimation task, it is customary to produce a so-called FIC plot. This plot has the different point…

One of the classic concerns in statistics is determining if two samples come from thesame population, i.e. homogeneity testing. In this paper, we propose a homogeneitytest in the context of Functional Data Analysis, adopting an idea from…

We provide a distribution-free test that can be used to determine whether any two joint distributions $p$ and $q$ are statistically different by inspection of a large enough set of samples. Following recent efforts from Long et al. [1], we…

Modeling joint probability distributions is an important task in a wide variety of fields. One popular technique for this employs a family of multivariate distributions with uniform marginals called copulas. While the theory of modeling…

We study a class of directed random graphs. In these graphs, the interval [0,x] is the vertex set, and from each y\in [0,x], directed links are drawn to points in the interval (y,x] which are chosen uniformly with density one. We analyze…

Clustering is a fundamental task for analyzing unlabeled data based solely on its underlying distribution. Spectral clustering is a clustering method that represents a dataset as a graph and uses the relationships between data points.…