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The data mining technique of time series clustering is well established in many fields. However, as an unsupervised learning method, it requires making choices that are nontrivially influenced by the nature of the data involved. The aim of…

Central limit theorems play an important role in the study of statistical inference for stochastic processes. However, when the nonparametric local polynomial threshold estimator, especially local linear case, is employed to estimate the…

Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…

We provide a systematic approach to stable central limit theorems for d-dimensional martingale difference arrays and martingale difference sequences. The conditions imposed are straightforward extensions of the univariate case.

We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random…

Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…

In urgent decision making applications, ensemble simulations are an important way to determine different outcome scenarios based on currently available data. In this paper, we will analyze the output of ensemble simulations by considering…

Time series clustering is an essential machine learning task with applications in many disciplines. While the majority of the methods focus on time series taking values on the real line, very few works consider time series defined on the…

There is a long history of research into time series clustering using distance-based partitional clustering. Many of the most popular algorithms adapt k-means (also known as Lloyd's algorithm) to exploit time dependencies in the data by…

We analyze the fluctuations of incomplete $U$-statistics over a triangular array of independent random variables. We give criteria for a Central Limit Theorem (CLT, for short) to hold in the sense that we prove that an appropriately scaled…

We improve current instability-based methods for the selection of the number of clusters $k$ in cluster analysis by developing a normalized cluster instability measure that corrects for the distribution of cluster sizes, a previously…

This paper considers metric spaces where distances between a pair of nodes are represented by distance intervals. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a…

The Latent Block Model (LBM) is a model-based method to cluster simultaneously the $d$ columns and $n$ rows of a data matrix. Parameter estimation in LBM is a difficult and multifaceted problem. Although various estimation strategies have…

Identifying possible clusters in datasets and estimating their overall modularity are central tasks in pattern recognition. In the present work, concepts and methodologies are described for performing these tasks while considering only the…

We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it…

The main approach to inference for multivariate extremes consists in approximating the joint upper tail of the observations by a parametric family arising in the limit for extreme events. The latter may be expressed in terms of…

In the past few decades considerable effort has been expended in characterizing and modeling financial time series. A number of stylized facts have been identified, and volatility clustering or the tendency toward persistence has emerged as…

Time series data is prevalent in a wide variety of real-world applications and it calls for trustworthy and explainable models for people to understand and fully trust decisions made by AI solutions. We consider the problem of building…

Spectral clustering has been widely used for community detection in network sciences. While its empirical successes are well-documented, a clear theoretical understanding, particularly for sparse networks where degrees are much smaller than…

This note outlines a method for clustering time series based on a statistical model in which volatility shifts at unobserved change-points. The model accommodates some classical stylized features of returns and its relation to GARCH is…