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### Supervised Classification of Flow Cytometric Samples via the Joint Clustering and Matching (JCM) Procedure

We consider the use of the Joint Clustering and Matching (JCM) procedure for the supervised classification of a flow cytometric sample with respect to a number of predefined classes of such samples. The JCM procedure has been proposed as a method for the unsupervised classification of cells within a sample into a number of clusters and in the case of multiple samples, the matching of these clusters across the samples. The two tasks of clustering and matching of the clusters are performed simultaneously within the JCM framework. In this paper, we consider the case where there is a number of distinct classes of samples whose class of origin is known, and the problem is to classify a new sample of unknown class of origin to one of these predefined classes. For example, the different classes might correspond to the types of a particular disease or to the various health outcomes of a patient subsequent to a course of treatment. We show and demonstrate on some real datasets how the JCM procedure can be used to carry out this supervised classification task. A mixture distribution is used to model the distribution of the expressions of a fixed set of markers for each cell in a sample with the components in the mixture model corresponding to the various populations of cells in the composition of the sample. For each class of samples, a class template is formed by the adoption of random-effects terms to model the inter-sample variation within a class. The classification of a new unclassified sample is undertaken by assigning the unclassified sample to the class that minimizes the Kullback-Leibler distance between its fitted mixture density and each class density provided by the class templates.

### Time-Varying Clusters in Large-Scale Flow Cytometry

Flow cytometers measure the optical properties of particles to classify microbes. Recent innovations have allowed oceanographers to collect flow cytometry data continuously during research cruises, leading to an explosion of data and new challenges for the classification task.The massive scale, time-varying underlying populations, and noisy measurements motivate the development of new classification methods. We describe the problem, the data, and some preliminary results demonstratingthe difficulty with conventional methods.

### Mondrian Processes for Flow Cytometry Analysis

Analysis of flow cytometry data is an essential tool for clinical diagnosis of hematological and immunological conditions. Current clinical workflows rely on a manual process called gating to classify cells into their canonical types. This dependence on human annotation limits the rate, reproducibility, and complexity of flow cytometry analysis. In this paper, we propose using Mondrian processes to perform automated gating by incorporating prior information of the kind used by gating technicians. The method segments cells into types via Bayesian nonparametric trees. Examining the posterior over trees allows for interpretable visualizations and uncertainty quantification - two vital qualities for implementation in clinical practice.

### Mixture modeling on related samples by $\psi$-stick breaking and kernel perturbation

There has been great interest recently in applying nonparametric kernel mixtures in a hierarchical manner to model multiple related data samples jointly. In such settings several data features are commonly present: (i) the related samples often share some, if not all, of the mixture components but with differing weights, (ii) only some, not all, of the mixture components vary across the samples, and (iii) often the shared mixture components across samples are not aligned perfectly in terms of their location and spread, but rather display small misalignments either due to systematic cross-sample difference or more often due to uncontrolled, extraneous causes. Properly incorporating these features in mixture modeling will enhance the efficiency of inference, whereas ignoring them not only reduces efficiency but can jeopardize the validity of the inference due to issues such as confounding. We introduce two techniques for incorporating these features in modeling related data samples using kernel mixtures. The first technique, called $\psi$-stick breaking, is a joint generative process for the mixing weights through the breaking of both a stick shared by all the samples for the components that do not vary in size across samples and an idiosyncratic stick for each sample for those components that do vary in size. The second technique is to imbue random perturbation into the kernels, thereby accounting for cross-sample misalignment. These techniques can be used either separately or together in both parametric and nonparametric kernel mixtures. We derive efficient Bayesian inference recipes based on MCMC sampling for models featuring these techniques, and illustrate their work through both simulated data and a real flow cytometry data set in prediction/estimation, cross-sample calibration, and testing multi-sample differences.

### A fast and efficient Modal EM algorithm for Gaussian mixtures

In the modal approach to clustering, clusters are defined as the local maxima of the underlying probability density function, where the latter can be estimated either non-parametrically or using finite mixture models. Thus, clusters are closely related to certain regions around the density modes, and every cluster corresponds to a bump of the density. The Modal EM algorithm is an iterative procedure that can identify the local maxima of any density function. In this contribution, we propose a fast and efficient Modal EM algorithm to be used when the density function is estimated through a finite mixture of Gaussian distributions with parsimonious component-covariance structures. After describing the procedure, we apply the proposed Modal EM algorithm on both simulated and real data examples, showing its high flexibility in several contexts.