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Convex clustering has recently garnered increasing interest due to its attractive theoretical and computational properties, but its merits become limited in the face of high-dimensional data. In such settings, pairwise affinity terms that rely on $k$-nearest neighbors become poorly specified and Euclidean measures of fit provide weaker discriminating power. To surmount these issues, we propose to modify the convex clustering objective so that feature weights are optimized jointly with the centroids. The resulting problem becomes biconvex, and as such remains well-behaved statistically and algorithmically. In particular, we derive a fast algorithm with closed form updates and convergence guarantees, and establish finite-sample bounds on its prediction error. Under interpretable regularity conditions, the error bound analysis implies consistency of the proposed estimator. Biconvex clustering performs feature selection throughout the clustering task: as the learned weights change the effective feature representation, pairwise affinities can be updated adaptively across iterations rather than precomputed within a dubious feature space. We validate the contributions on real and simulated data, showing that our method effectively addresses the challenges of dimensionality while reducing dependence on carefully tuned heuristics typical of existing approaches.

The safety of medical products due to adverse events (AE) from drugs, therapeutic biologics, and medical devices is a major public health concern worldwide. Likelihood ratio test (LRT) approaches to pharmacovigilance constitute a class of rigorous statistical tools that permit objective identification of AEs of a specific drug and/or a class of drugs cataloged in spontaneous reporting system databases. However, the existing LRT approaches encounter certain theoretical and computational challenges when an underlying Poisson model assumption is violated, including in cases of zero-inflated data. We briefly review existing LRT approaches and propose a novel class of (pseudo-) LRT methods to address these challenges. Our approach uses an alternative parametrization to formulate a unified framework with a common test statistic that can handle both Poisson and zero-inflated Poisson (ZIP) models. The proposed framework is computationally efficient, and it reveals deeper insights into the comparative behaviors of the Poisson and the ZIP models for handling AE data. Our extensive simulation studies document notably superior performances of the proposed methods over existing approaches particularly under zero-inflation, both in terms of statistical (eg, much better control of the nominal level and false discovery rate with substantially enhanced power) and computational (

Cell migration, the process by which cells move from one location to another, plays crucial roles in many biological events. While much research has been devoted to understand the process, most statistical cell migration models rely on using time-lapse microscopy data from cell trajectories alone. However, the cell and its associated nucleus work together to orchestrate cell movement, which motivates a joint analysis of coupled cell-nucleus trajectories. In this paper, we propose a Bayesian hierarchical model for analyzing cell migration. We incorporate a bivariate angular distribution to handle the coupled cell-nucleus trajectories and introduce latent motility status indicators to model a cell's motility as a time-dependent characteristic. A Markov chain Monte Carlo algorithm is provided for practical implementation of our model, which is used on real experimental data from MDA-MB-231 and NIH 3T3 cells. Through the fitted models, deeper insights into the migratory patterns of these experimental cell populations are gained and their differences are quantified.

Statistical analyses of directional or angular data have applications in a variety of fields, such as geology, meteorology and bioinformatics. There is substantial literature on descriptive and inferential techniques for univariate angular data, with the bivariate (or more generally, multivariate) cases receiving more attention in recent years. More specifically, the bivariate wrapped normal, von Mises sine and von Mises cosine distributions, and mixtures thereof, have been proposed for practical use. However, there is a lack of software implementing these distributions and the associated inferential techniques. In this article, we introduce BAMBI, an R package for analyzing bivariate (and univariate) angular data. We implement random data generation, density evaluation, and computation of theoretical summary measures (variances and correlation coefficients) for the three aforementioned bivariate angular distributions, as well as two univariate angular distributions: the univariate wrapped normal and the univariate von Mises distribution. The major contribution of BAMBI to statistical computing is in providing Bayesian methods for modeling angular data using finite mixtures of these distributions. We also provide functions for visual and numerical diagnostics and Bayesian inference for the fitted models. In this article, we first provide a brief review of the distributions and techniques used in BAMBI, then describe the capabilities of the package, and finally conclude with demonstrations of mixture model fitting using BAMBI on the two real data sets included in the package, one univariate and one bivariate.

It is increasingly common clinically for cancer specimens to be examined using techniques that identify somatic mutations. In principle these mutational profiles can be used to diagnose the tissue of origin, a critical task for the 3-5% of tumors that have an unknown primary site. Diagnosis of primary site is also critical for screening tests that employ circulating DNA. However, most mutations observed in any new tumor are very rarely occurring mutations, and indeed the preponderance of these may never have been observed in any previous recorded tumor. To create a viable diagnostic tool we need to harness the information content in this "hidden genome" of variants for which no direct information is available. To accomplish this we propose a multi-level meta-feature regression to extract the critical information from rare variants in the training data in a way that permits us to also extract diagnostic information from any previously unobserved variants in the new tumor sample. A scalable implementation of the model is obtained by combining a high-dimensional feature screening approach with a group-lasso penalized maximum likelihood approach based on an equivalent mixed-effect representation of the multilevel model. We apply the method to the Cancer Genome Atlas whole-exome sequencing data set including 3702 tumor samples across 7 common cancer sites. Results show that our multi-level approach can harness substantial diagnostic information from the hidden genome., Comment: 24 pages, 4 figures, 2 tables

We propose a simple variable (feature) weight learning strategy for the Gaussian means algorithm which can automatically determine the number of clusters in a dataset as well. We investigate some important theoretical properties and convergence behavior of the proposed algorithm.

Bi-clustering refers to the task of partitioning the rows and columns of a data matrix simultaneously. Although empirically useful, the theoretical aspects of bi-clustering techniques have not been studied in-depth. We present a framework for investigating the statistical guarantees behind the sparse bi-clustering algorithm by using the Vapnik–Chervonenkis (VC) theory.

Optimal Transport (OT) distances result in a powerful technique to compare the probability distributions. Defining a similarity measure between clusters has been an open problem in Statistics. This paper introduces a hierarchical clustering algorithm using the OT based distance measures and analyzes the performance of the proposed algorithm on standard datasets with respect to the existing and popular hierarchical clustering methods.

This paper studies circular correlations for the bivariate von Mises sine and cosine distributions. These are two simple and appealing models for bivariate angular data with five parameters each that have interpretations comparable to those in the ordinary bivariate normal model. However, the variability and association of the angle pairs cannot be easily deduced from the model parameters unlike the bivariate normal. Thus to compute such summary measures, tools from circular statistics are needed. We derive analytic expressions and study the properties of the Jammalamadaka-Sarma and Fisher-Lee circular correlation coefficients for the von Mises sine and cosine models. Likelihood-based inference of these coefficients from sample data is then presented. The correlation coefficients are illustrated with numerical and visual examples, and the maximum likelihood estimators are assessed on simulated and real data, with comparisons to their non-parametric counterparts. Implementations of these computations for practical use are provided in our R package BAMBI., Comment: 29 pages, 3 figures, 5 tables

The Bayesian probit regression model (Albert and Chib (1993)) is popular and widely used for binary regression. While the improper flat prior for the regression coefficients is an appropriate choice in the absence of any prior information, a proper normal prior is desirable when prior information is available or in modern high dimensional settings where the number of coefficients ($p$) is greater than the sample size ($n$). For both choices of priors, the resulting posterior density is intractable and a Data Dugmentation (DA) Markov chain is used to generate approximate samples from the posterior distribution. Establishing geometric ergodicity for this DA Markov chain is important as it provides theoretical guarantees for constructing standard errors for Markov chain based estimates of posterior quantities. In this paper, we first show that in case of proper normal priors, the DA Markov chain is geometrically ergodic *for all* choices of the design matrix $X$, $n$ and $p$ (unlike the improper prior case, where $n \geq p$ and another condition on $X$ are required for posterior propriety itself). We also derive sufficient conditions under which the DA Markov chain is trace-class, i.e., the eigenvalues of the corresponding operator are summable. In particular, this allows us to conclude that the Haar PX-DA sandwich algorithm (obtained by inserting an inexpensive extra step in between the two steps of the DA algorithm) is strictly better than the DA algorithm in an appropriate sense., 40 pages, 6 figures; typos corrected

Markov chain Monte Carlo is widely used in a variety of scientific applications to generate approximate samples from intractable distributions. A thorough understanding of the convergence and mixing properties of these Markov chains can be obtained by studying the spectrum of the associated Markov operator. While several methods to bound/estimate the second largest eigenvalue are available in the literature, very few general techniques for consistent estimation of the entire spectrum have been proposed. Existing methods for this purpose require the Markov transition density to be available in closed form, which is often not true in practice, especially in modern statistical applications. In this paper, we propose a novel method to consistently estimate the entire spectrum of a general class of Markov chains arising from a popular and widely used statistical approach known as Data Augmentation. The transition densities of these Markov chains can often only be expressed as intractable integrals. We illustrate the applicability of our method using real and simulated data., Comment: 43 pages (including Appendix), 3 figures; final version