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Change point detection algorithms have numerous applications in fields of scientific and economic importance. We consider the problem of change point detection on compositional multivariate data (each sample is a probability mass function), which is a practically important sub-class of general multivariate data. While the problem of change-point detection is well studied in univariate setting, and there are few viable implementations for a general multivariate data, the existing methods do not perform well on compositional data. In this paper, we propose a parametric approach for change point detection in compositional data. Moreover, using simple transformations on data, we extend our approach to handle any general multivariate data. Experimentally, we show that our method performs significantly better on compositional data and is competitive on general data compared to the available state of the art implementations.
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Change-point detection regains much attention recently for analyzing array or sequencing data for copy number variation (CNV) detection. In such applications, the true signals are typically very short and buried in the long data sequence, which makes it challenging to identify the variations efficiently and accurately. In this article, we propose a new change-point detection method, a backward procedure, which is not only fast and simple enough to exploit high-dimensional data but also performs very well for detecting short signals. Although motivated by CNV detection, the backward procedure is generally applicable to assorted change-point problems that arise in a variety of scientific applications. It is illustrated by both simulated and real CNV data that the backward detection has clear advantages over other competing methods especially when the true signal is short.
This manuscript makes two contributions to the field of change-point detection. In a general change-point setting, we provide a generic algorithm for aggregating local homogeneity tests into an estimator of change-points in a time series. Interestingly, we establish that the error rates of the collection of test directly translate into detection properties of the change-point estimator. This generic scheme is then applied to the problem of possibly sparse multivariate mean change-point detection setting. When the noise is Gaussian, we derive minimax optimal rates that are adaptive to the unknown sparsity and to the distance between change-points. For sub-Gaussian noise, we introduce a variant that is optimal in almost all sparsity regimes.
Microbes can affect processes from food production to human health. Such microbes are not isolated, but rather interact with each other and establish connections with their living environments. Understanding these interactions is essential to an understanding of the organization and complex interplay of microbial communities, as well as the structure and dynamics of various ecosystems. A common and essential approach toward this objective involves the inference of microbiome interaction networks. Although network inference methods in other fields have been studied before, applying these methods to estimate microbiome associations based on compositional data will not yield valid results. On the one hand, features of microbiome data such as compositionality, sparsity and high-dimensionality challenge the data normalization and the design of computational methods. On the other hand, several issues like microbial community heterogeneity, external environmental interference and biological concerns also make it more difficult to deal with the network inference. In this paper, we provide a comprehensive review of emerging microbiome interaction network inference methods. According to various assumptions and research targets, estimated networks are divided into four main categories: correlation networks, conditional correlation networks, mixture networks and differential networks. Their scope of applications, advantages and limitations are presented in this review. Since real microbial interactions can be complex and dynamic, no unifying method has captured all the aspects of interest to date. In addition, we discuss the challenges now confronting current microbial associations study and future prospects. Finally, we highlight that the research in microbial network inference requires the joint promotion of statistical computation methods and experimental techniques.
Mass cytometry technology enables the simultaneous measurement of over 40 proteins on single cells. This has helped immunologists to increase their understanding of heterogeneity, complexity, and lineage relationships of white blood cells. Current statistical methods often collapse the rich single-cell data into summary statistics before proceeding with downstream analysis, discarding the information in these multivariate datasets. In this article, our aim is to exhibit the use of statistical analyses on the raw, uncompressed data thus improving replicability, and exposing multivariate patterns and their associated uncertainty profiles. We show that multivariate generative models are a valid alternative to univariate hypothesis testing. We propose two models: a multivariate Poisson log-normal mixed model and a logistic linear mixed model. We show that these models are complementary and that either model can account for different confounders. We use Hamiltonian Monte Carlo to provide Bayesian uncertainty quantification. Our models applied to a recent pregnancy study successfully reproduce key findings while quantifying increased overall protein-to-protein correlations between first and third trimester.
Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often have an interesting theoretical interpretation in real problems. However, standard factor analysis is only applicable when the variables are scaled, which is often inappropriate, for example, in data obtained from questionnaires in the field of psychology,where the variables are often categorical. In this framework, we propose a factor model for the analysis of multivariate ordered and non-ordered polychotomous data. The inference procedure is done under the Bayesian approach via Markov chain Monte Carlo methods. Two Monte-Carlo simulation studies are presented to investigate the performance of this approach in terms of estimation bias, precision and assessment of the number of factors. We also illustrate the proposed method to analyze participants responses to the Motivational State Questionnaire dataset, developed to study emotions in laboratory and field settings.
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