Related papers: Delta-Closure Structure for Studying Data Distribu…

In this paper, we are revisiting pattern mining and especially itemset mining, which allows one to analyze binary datasets in searching for interesting and meaningful association rules and respective itemsets in an unsupervised way. While a…

For numerous reasons there raises a need for dimension reduction that preserves certain characteristics of data. In this work we focus on data coming from a mixture of Gaussian distributions and we propose a method that preserves…

Classical algebraic structures require exact satisfaction of their defining axioms. We propose similarity algebra, a framework extending algebraic and Lie structures to settings where operations satisfy quantitative bounds up to a tolerance…

Autoencoders are a prominent model in many empirical branches of machine learning and lossy data compression. However, basic theoretical questions remain unanswered even in a shallow two-layer setting. In particular, to what degree does a…

In this paper, we consider the problem of degradation of anonymity upon linkages of anonymized datasets. We work in the setting where an adversary links together $t\geq 2$ anonymized datasets in which a user of interest participates, based…

We consider closure properties in the class of positively decreasing distributions. Our results stem from different types of dependence, but each type belongs in the family of asymptotically independent dependence structure. Namely we…

We introduce a novel statistical significance-based approach for clustering hierarchical data using semi-parametric linear mixed-effects models designed for responses with laws in the exponential family (e.g., Poisson and Bernoulli). Within…

Leveraging on the underlying low-dimensional structure of data, low-rank and sparse modeling approaches have achieved great success in a wide range of applications. However, in many applications the data can display structures beyond simply…

The degree distribution, referred to as the delta-sequence of a network is studied. Using the non-normalized Lorenz curve, we apply a generalized form of the classical majorization partial order. Next, we introduce a new class of small…

In this paper, we test whether two datasets share a common clustering structure. As a leading example, we focus on comparing clustering structures in two independent random samples from two mixtures of multivariate normal distributions.…

Measuring dataset similarity is fundamental in machine learning, particularly for transfer learning and domain adaptation. In the context of supervised learning, most existing approaches quantify similarity of two data sets based on their…

Many high dimensional vector distances tend to a constant. This is typically considered a negative "contrast-loss" phenomenon that hinders clustering and other machine learning techniques. We reinterpret "contrast-loss" as a blessing.…

In recent years, advances in high throughput sequencing technology have led to a need for specialized methods for the analysis of digital gene expression data. While gene expression data measured on a microarray take on continuous values…

We study statistical/computational tradeoffs for the following density estimation problem: given $k$ distributions $v_1, \ldots, v_k$ over a discrete domain of size $n$, and sampling access to a distribution $p$, identify $v_i$ that is…

Statistical data depth plays an important role in the analysis of multivariate data sets. The main outcome is a center-outward ordering of the observations that can be used both to highlight features of the underlying distribution of the…

Clustering methods with dimension reduction have been receiving considerable wide interest in statistics lately and a lot of methods to simultaneously perform clustering and dimension reduction have been proposed. This work presents a novel…

Substructure in galaxy clusters can be quantified with the robust Delta statistics (Dressler and Shectman 1988) which uses velocity kinematics and sky projected positions. We test its sensitivity using dissipationless numerical simulations…

Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…

Nowadays, data are generated massively and rapidly from scientific fields as bioinformatics, neuroscience and astronomy to business and engineering fields. Cluster analysis, as one of the major data analysis tools, is therefore more…

This article establishes the performance of stochastic blockmodels in addressing the co-clustering problem of partitioning a binary array into subsets, assuming only that the data are generated by a nonparametric process satisfying the…