Mixtures of Regression Models for Time-Course Gene Expression Data: Evaluation of Initialization and Random Effects

Finite mixture models are routinely applied to time course microarray data. Due to the complexity and size of this type of data the choice of good starting values plays an important role. So far initialization strategies have only been investigated for data from a mixture of multivariate normal distributions. In this work several initialization procedures are evaluated for mixtures of regression models with and without random effects in an extensive simulation study on different artificial datasets. Finally these procedures are also applied to a real dataset from E. coli

Parsimonious Time Series Clustering

We introduce a parsimonious model-based framework for clustering time course data. In these applications the computational burden becomes often an issue due to the number of available observations. The measured time series can also be very noisy and sparse and a suitable model describing them can be hard to define. We propose to model the observed measurements by using P-spline smoothers and to cluster the functional objects as summarized by the optimal spline coefficients. In principle, this idea can be adopted within all the most common clustering frameworks. In this work we discuss applications based on a k-means algorithm. We evaluate the accuracy and the efficiency of our proposal by simulations and by dealing with drosophila melanogaster gene expression data

Comparison of Clustering Methods for Time Course Genomic Data: Applications to Aging Effects

Time course microarray data provide insight about dynamic biological processes. While several clustering methods have been proposed for the analysis of these data structures, comparison and selection of appropriate clustering methods are seldom discussed. We compared $3$ probabilistic based clustering methods and $3$ distance based clustering methods for time course microarray data. Among probabilistic methods, we considered: smoothing spline clustering also known as model based functional data analysis (MFDA), functional clustering models for sparsely sampled data (FCM) and model-based clustering (MCLUST). Among distance based methods, we considered: weighted gene co-expression network analysis (WGCNA), clustering with dynamic time warping distance (DTW) and clustering with autocorrelation based distance (ACF). We studied these algorithms in both simulated settings and case study data. Our investigations showed that FCM performed very well when gene curves were short and sparse. DTW and WGCNA performed well when gene curves were medium or long ($>=10$ observations). SSC performed very well when there were clusters of gene curves similar to one another. Overall, ACF performed poorly in these applications. In terms of computation time, FCM, SSC and DTW were considerably slower than MCLUST and WGCNA. WGCNA outperformed MCLUST by generating more accurate and biological meaningful clustering results. WGCNA and MCLUST are the best methods among the 6 methods compared, when performance and computation time are both taken into account. WGCNA outperforms MCLUST, but MCLUST provides model based inference and uncertainty measure of clustering results

Measuring Cluster Stability for Bayesian Nonparametrics Using the Linear Bootstrap

Clustering procedures typically estimate which data points are clustered together, a quantity of primary importance in many analyses. Often used as a preliminary step for dimensionality reduction or to facilitate interpretation, finding robust and stable clusters is often crucial for appropriate for downstream analysis. In the present work, we consider Bayesian nonparametric (BNP) models, a particularly popular set of Bayesian models for clustering due to their flexibility. Because of its complexity, the Bayesian posterior often cannot be computed exactly, and approximations must be employed. Mean-field variational Bayes forms a posterior approximation by solving an optimization problem and is widely used due to its speed. An exact BNP posterior might vary dramatically when presented with different data. As such, stability and robustness of the clustering should be assessed. A popular mean to assess stability is to apply the bootstrap by resampling the data, and rerun the clustering for each simulated data set. The time cost is thus often very expensive, especially for the sort of exploratory analysis where clustering is typically used. We propose to use a fast and automatic approximation to the full bootstrap called the "linear bootstrap", which can be seen by local data perturbation. In this work, we demonstrate how to apply this idea to a data analysis pipeline, consisting of an MFVB approximation to a BNP clustering posterior of time course gene expression data. We show that using auto-differentiation tools, the necessary calculations can be done automatically, and that the linear bootstrap is a fast but approximate alternative to the bootstrap.Comment: 9 pages, NIPS 2017 Advances in Approximate Bayesian Inference Worksho

Modelling time course gene expression data with finite mixtures of linear additive models

Summary: A model class of finite mixtures of linear additive models is presented. The component-specific parameters in the regression models are estimated using regularized likelihood methods. The advantages of the regularization are that (i) the pre-specified maximum degrees of freedom for the splines is less crucial than for unregularized estimation and that (ii) for each component individually a suitable degree of freedom is selected in an automatic way. The performance is evaluated in a simulation study with artificial data as well as on a yeast cell cycle dataset of gene expression levels over time

Joint Clustering and Registration of Functional Data

Curve registration and clustering are fundamental tools in the analysis of functional data. While several methods have been developed and explored for either task individually, limited work has been done to infer functional clusters and register curves simultaneously. We propose a hierarchical model for joint curve clustering and registration. Our proposal combines a Dirichlet process mixture model for clustering of common shapes, with a reproducing kernel representation of phase variability for registration. We show how inference can be carried out applying standard posterior simulation algorithms and compare our method to several alternatives in both engineered data and a benchmark analysis of the Berkeley growth data. We conclude our investigation with an application to time course gene expression

M-quantile regression analysis of temporal gene expression data

In this paper, we explore the use of M-regression and M-quantile coefficients to detect statistical differences between temporal curves that belong to different experimental conditions. In particular, we consider the application of temporal gene expression data. Here, the aim is to detect genes whose temporal expression is significantly different across a number of biological conditions. We present a new method to approach this problem. Firstly, the temporal profiles of the genes are modelled by a parametric M-quantile regression model. This model is particularly appealing to small-sample gene expression data, as it is very robust against outliers and it does not make any assumption on the error distribution. Secondly, we further increase the robustness of the method by summarising the M-quantile regression models for a large range of quantile values into an M-quantile coefficient. Finally, we employ a Hotelling T2-test to detect significant differences of the temporal M-quantile profiles across conditions. Simulated data shows the increased robustness of M-quantile regression methods over standard regression methods. We conclude by using the method to detect differentially expressed genes from time-course microarray data on muscular dystrophy