arXiv subjects

Jason Pillay

Publications and source records attributed to Jason Pillay.

4 recordsLinked to original sources

arXiv2026

Handling mild outliers and unobserved values in compositional datasets using finite mixtures of mean-parametrised Dirichlet models

Heterogeneous compositional data may be simultaneously affected by missing values and atypical points, posing challenges for both clustering and outlier detection. We develop a mixture model for incomplete compositional data under Huber's contamination model, with contamination defined directly on the simplex and on observations that may be missing at random. The model provides a principled representation of outliers and allows the distribution of missing parts to be derived while accounting for contamination. We establish that maximisation of the observed log-likelihood constructed from contaminated, mean-parametrised Dirichlet densities is a convex optimisation problem. We then develop a tailored expectation-maximisation. The E-step incorporates the moments from the distribution of the missing parts of the data. Although the resulting parameter estimates are not available in closed form, the maximisation step admits tractable element-wise iterative updates. Numerical experiments demonstrate the performance of the proposed approach under varying percentage of missingness and contamination, and different sample size. An application to the American Time Use Survey identifies two interpretable clusters corresponding to work-intensive and sociable recreational days, while revealing atypical time-use compositions. In contrast, a conventional Dirichlet mixture model identifies four clusters, reflecting the influence of outliers and an artificial splitting of one cluster.

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arXiv2026

Handling Missingness and Censoring in Dirichlet Mixture Models

Incomplete compositional data analysis faces a fundamental limitation: likelihood-based methods for compositional models generally require fully observed compositions, making it difficult to accommodate missing or censored proportions directly on the simplex. Consequently, analysts often discard partially observed compositions or transform the data into unconstrained spaces, potentially sacrificing interpretability and coherence. This paper proposes a likelihood-based method for incomplete compositional data without leaving the simplex. Specifically, we develop an Expectation-Maximisation (EM) type algorithm for fitting finite mixtures of Dirichlet distributions in the presence of missing and censored components. The proposed approach performs parameter estimation and model-based imputation simultaneously while preserving the compositional structure and interpretability of the original variables. A simulation experiment evaluates the performance of the proposed estimators and imputations under increasingly complex coarsening mechanisms. Particular attention is paid to clustering performance, and model selection outcomes. The results showed beneficial clustering performance despite observations being incomplete, and a higher probability of model selection metrics identifying the correct number of clusters compared to current alternative of case-deletion. The practical utility of the method is illustrated using two real datasets with distinct coarsened patterns. Analysis of the xenolith dataset identifies a four-component Dirichlet mixture that reveals interpretable profiles of rock types and speciation methods. Application to PM$_{2.5}$ speciation data from the Air Quality System, containing both left-censored and missing-at-random values, supports a four-component mixture model that characterises compositional parts of particulate matter across the United States.

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arXiv2025

Sleep pattern profiling using a finite mixture of contaminated multivariate skew-normal distributions on incomplete data

Medical data often exhibit characteristics that make cluster analysis particularly challenging, such as missing values, outliers, and cluster features like skewness. Typically, such data would need to be preprocessed -- by cleaning outliers and missing values -- before clustering could be performed. However, these preliminary steps rely on objective functions different from those used in the clustering stage. In this paper, we propose a unified model-based clustering approach that simultaneously handles atypical observations, missing values, and cluster-wise skewness within a single framework. Each cluster is modelled using a contaminated multivariate skew-normal distribution -- a convenient two-component mixture of multivariate skew-normal densities -- in which one component represents the main data (the "bulk") and the other captures potential outliers. From an inferential perspective, we implement and use a variant of the EM algorithm to obtain the maximum likelihood estimates of the model parameters. Simulation studies demonstrate that the proposed model outperforms existing approaches in both clustering accuracy and outlier detection, across low- and high-dimensional settings, even in the presence of substantial missingness. The method is further applied to the Cleveland Children's Sleep and Health Study (CCSHS), a dataset characterised by incomplete observations. Without any preprocessing, the proposed approach identifies five distinct groups of sleepers, revealing meaningful differences in sleeper typologies.

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arXiv2025

Clustering data with values missing at random using scale mixtures of multivariate skew-normal distributions

Handling missing data is a major challenge in model-based clustering, especially when the data exhibit skewness and heavy tails. We address this by extending the finite mixture of scale mixtures of multivariate skew-normal (FMSMSN) family to accommodate incomplete data under a missing at random (MAR) mechanism. Unlike previous work that is limited to one of the special cases of the FMSMSN family, our method offers a cluster analysis methodology for the entire family that accounts for skewness and excess kurtosis amidst data with missing values. The multivariate skew-normal distribution, as parameterised by \cite{azzalini1996} and \cite{arnoldbeaver} includes the normal distribution as a special case, which ensures that our method is flexible toward existing symmetric model-based clustering techniques under a normality assumption. We derive the distributional properties of the missing components of the data and propose an augmented EM-type algorithm tailored for incomplete observations. The modified E-step yields closed-form expressions for the conditional expectations of the missing values. The simulation experiments showcase the flexibility of the FMSMSN family in both clustering performance and parameter recovery for varying percentages of missing values, while incorporating the effects of sample size and cluster proximity. Finally, we illustrate the practical utility of the proposed method by applying special cases of the FMSMSN family to global CO2 emissions data.

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