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1. Evaluating methods for addressing skewness in clustering: a focus on generalized hyperbolic mixture models

   https://doi.org/10.1080/00949655.2025.2502535  

   Tortora, Cristina (May 2025, Journal of Statistical Computation and Simulation)

   In model-based clustering, the population is assumed to be a combination of sub-populations. Typically, each sub-population is modeled by a mixture model component, distributed according to a known probability distribution. Each component is considered a cluster. Two primary approaches have been used in the literature when clusters are skewed: (1) transforming the data within each cluster and applying a mixture of symmetric distributions to the transformed data, and (2) directly modeling each cluster using a skewed distribution. Among skewed distributions, the generalized hyperbolic distribution is notably flexible and includes many other known distributions as special or limiting cases. This paper achieves two goals. First, it extends the flexibility of transformation-based methods as outlined in approach (1) by employing a flexible symmetric generalized hyperbolic distribution to model each transformed cluster. This innovation results in the introduction of two new models, each derived from distinct within-cluster data transformations. Second, the paper benchmarks the approaches listed in (1) and (2) for handling skewness using both simulated and real data. The findings highlight the necessity of both approaches in varying contexts. 

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2. A Dirichlet Mixture Model of Hawkes Processes for Event Sequence Clustering

   Xu, Hongteng; Zha, Hongyuan (January 2017, Advances in neural information processing systems)

   How to cluster event sequences generated via different point processes is an interesting and important problem in statistical machine learning. To solve this problem, we propose and discuss an effective model-based clustering method based on a novel Dirichlet mixture model of a special but significant type of point processes — Hawkes process. The proposed model generates the event sequences with different clusters from the Hawkes processes with different parameters, and uses a Dirichlet distribution as the prior distribution of the clusters. We prove the identifiability of our mixture model and propose an effective variational Bayesian inference algorithm to learn our model. An adaptive inner iteration allocation strategy is designed to accelerate the convergence of our algorithm. Moreover, we investigate the sample complexity and the computational complexity of our learning algorithm in depth. Experiments on both synthetic and real-world data show that the clustering method based on our model can learn structural triggering patterns hidden in asynchronous event sequences robustly and achieve superior performance on clustering purity and consistency compared to existing methods. 

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3. Nonparametric clustering of RNA-sequencing data

   https://doi.org/10.1002/sam.11638  

   Lozano, Gabriel; Atallah, Nadia; Levine, Michael (December 2023, Statistical Analysis and Data Mining: The ASA Data Science Journal)

   Abstract Identification of clusters of co‐expressed genes in transcriptomic data is a difficult task. Most algorithms used for this purpose can be classified into two broad categories: distance‐based or model‐based approaches. Distance‐based approaches typically utilize a distance function between pairs of data objects and group similar objects together into clusters. Model‐based approaches are based on using the mixture‐modeling framework. Compared to distance‐based approaches, model‐based approaches offer better interpretability because each cluster can be explicitly characterized in terms of the proposed model. However, these models present a particular difficulty in identifying a correct multivariate distribution that a mixture can be based upon. In this manuscript, we review some of the approaches used to select a distribution for the needed mixture model first. Then, we propose avoiding this problem altogether by using a nonparametric MSL (maximum smoothed likelihood) algorithm. This algorithm was proposed earlier in statistical literature but has not been, to the best of our knowledge, applied to transcriptomics data. The salient feature of this approach is that it avoids explicit specification of distributions of individual biological samples altogether, thus making the task of a practitioner easier. We performed both a simulation study and an application of the proposed algorithm to two different real datasets. When used on a real dataset, the algorithm produces a large number of biologically meaningful clusters and performs at least as well as several other mixture‐based algorithms commonly used for RNA‐seq data clustering. Our results also show that this algorithm is capable of uncovering clustering solutions that may go unnoticed by several other model‐based clustering algorithms. Our code is publicly available on Github at https://github.com/Matematikoi/non_parametric_clustering 

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4. FedSoft: Soft Clustered Federated Learning with Proximal Local Updating

   https://doi.org/10.1609/aaai.v36i7.20785  

   Ruan, Yichen; Joe-Wong, Carlee (June 2022, Proceedings of the AAAI Conference on Artificial Intelligence)

   Traditionally, clustered federated learning groups clients with the same data distribution into a cluster, so that every client is uniquely associated with one data distribution and helps train a model for this distribution. We relax this hard association assumption to soft clustered federated learning, which allows every local dataset to follow a mixture of multiple source distributions. We propose FedSoft, which trains both locally personalized models and high-quality cluster models in this setting. FedSoft limits client workload by using proximal updates to require the completion of only one optimization task from a subset of clients in every communication round. We show, analytically and empirically, that FedSoft effectively exploits similarities between the source distributions to learn personalized and cluster models that perform well. 

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5. Model Selection for Sparse Microbial Network Inference using Variational Approximation

   Yooseph, Shibu (March 2025, Springer Verlag)

   Microbial communities are often composed of taxa from different taxonomic groups. The associations among the constituent members in a microbial community play an important role in determining the functional characteristics of the community, and these associations can be modeled using an edge weighted graph (microbial network). A microbial network is typically inferred from a sample–taxa matrix that is obtained by sequencing multiple biological samples and identifying the taxa abundance in each sample. Motivated by microbiome studies that involve a large number of samples collected across a range of study parameters, here we consider the computational problem of identifying the number of microbial networks underlying the observed sample-taxa abundance matrix. Specifically, we consider the problem of determing the number of sparse microbial networks in this setting. We use a mixture model framework to address this problem, and present formulations to model both count data and proportion data. We propose several variational approximation based algorithms that allow the incorporation of the sparsity constraint while estimating the number of components in the mixture model. We evaluate these algorithms on a large number of simulated datasets generated using a collection of different graph structures (band, hub, cluster, random, and scale-free). 

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