Related papers: Asymptotic Theory for Two-Way Clustering
A probabilistic expert system emulates the decision-making ability of a human expert through a directional graphical model. The first step in building such systems is to understand data generation mechanism. To this end, one may try to…
In this article, we consider a sequence $(N_n)_{n \geq 1}$ of point processes, whose points lie in a subset $E$ of $\bR \verb2\2 \{0\}$, and satisfy an asymptotic independence condition. Our main result gives some necessary and sufficient…
We propose a novel method for multiple clustering that assumes a co-clustering structure (partitions in both rows and columns of the data matrix) in each view. The new method is applicable to high-dimensional data. It is based on a…
Asymptotic homogenisation is considered for problems with integral constraints imposed on a slowly-varying microstructure; an insulator with an array of perfectly dielectric inclusions of slowly varying size serves as a paradigm. Although…
The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…
Traditional statistical inference in cluster randomized trials typically invokes the asymptotic theory that requires the number of clusters to approach infinity. In this article, we propose an alternative conformal causal inference…
Recent work by Gao et al. (JASA 2022) has laid the foundations for post-clustering inference, establishing a theoretical framework allowing to test for differences between means of estimated clusters. Additionally, they studied the…
Clustering algorithms start with a fixed divergence, which captures the possibly asymmetric distance between a sample and a centroid. In the mixture model setting, the sample distribution plays the same role. When all attributes have the…
This paper presents a neural network-based end-to-end clustering framework. We design a novel strategy to utilize the contrastive criteria for pushing data-forming clusters directly from raw data, in addition to learning a feature embedding…
We present a clustering method and provide a theoretical analysis and an explanation to a phenomenon encountered in the applied statistical literature since the 1990's. This phenomenon is the natural adaptability of the order when using a…
Understanding causal heterogeneity is essential for scientific discovery in domains such as biology and medicine. However, existing methods lack causal awareness, with insufficient modeling of heterogeneity, confounding, and observational…
We consider a discrete latent variable model for two-way data arrays, which allows one to simultaneously produce clusters along one of the data dimensions (e.g. exchangeable observational units or features) and contiguous groups, or…
We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for observables of compact group extensions of nonuniformly…
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
The global clustering coefficient serves as a powerful metric for the structural analysis and comparison of complex networks. Random geometric graphs offer a realistic framework for representing the spatial constraints and geometry often…
I introduce a generic method for inference about a scalar parameter in research designs with a finite number of heterogeneous clusters where only a single cluster received treatment. This situation is commonplace in…
In this work we present a coupled-cluster theory for the propagation of multireference electronic systems initiating at general quantum mechanical states. Our formalism is based on the infinitesimal analysis of modified cluster operators,…
A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…
Weights and directionality of the edges carry a large part of the information we can extract from a complex network. However, many network measures were formulated initially for undirected binary networks. The necessity to incorporate…
Standard clustering techniques assume a common configuration for all features in a dataset. However, when dealing with multi-view or longitudinal data, the clusters' number, frequencies, and shapes may need to vary across features to…