The Annals of Applied Statistics

A hierarchical framework for state-space matrix inference and clustering

Chandler Zuo, Kailei Chen, Kyle J. Hewitt, Emery H. Bresnick, and Sündüz Keleş

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Integrative analysis of multiple experimental datasets measured over a large number of observational units is the focus of large numbers of contemporary genomic and epigenomic studies. The key objectives of such studies include not only inferring a hidden state of activity for each unit over individual experiments, but also detecting highly associated clusters of units based on their inferred states. Although there are a number of methods tailored for specific datasets, there is currently no state-of-the-art modeling framework for this general class of problems. In this paper, we develop the MBASIC (Matrix Based Analysis for State-space Inference and Clustering) framework. MBASIC consists of two parts: state-space mapping and state-space clustering. In state-space mapping, it maps observations onto a finite state-space, representing the activation states of units across conditions. In state-space clustering, MBASIC incorporates a finite mixture model to cluster the units based on their inferred state-space profiles across all conditions. Both the state-space mapping and clustering can be simultaneously estimated through an Expectation-Maximization algorithm. MBASIC flexibly adapts to a large number of parametric distributions for the observed data, as well as the heterogeneity in replicate experiments. It allows for imposing structural assumptions on each cluster, and enables model selection using information criterion. In our data-driven simulation studies, MBASIC showed significant accuracy in recovering both the underlying state-space variables and clustering structures. We applied MBASIC to two genome research problems using large numbers of datasets from the ENCODE project. The first application grouped genes based on transcription factor occupancy profiles of their promoter regions in two different cell types. The second application focused on identifying groups of loci that are similar to a GATA2 binding site that is functional at its endogenous locus by utilizing transcription factor occupancy data and illustrated applicability of MBASIC in a wide variety of problems. In both studies, MBASIC showed higher levels of raw data fidelity than analyzing these data with a two-step approach using ENCODE results on transcription factor occupancy data.

Article information

Ann. Appl. Stat., Volume 10, Number 3 (2016), 1348-1372.

Received: May 2015
Revised: January 2016
First available in Project Euclid: 28 September 2016

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Zentralblatt MATH identifier

State-space clustering E-M algorithm transcription factors ChIP-seq


Zuo, Chandler; Chen, Kailei; Hewitt, Kyle J.; Bresnick, Emery H.; Keleş, Sündüz. A hierarchical framework for state-space matrix inference and clustering. Ann. Appl. Stat. 10 (2016), no. 3, 1348--1372. doi:10.1214/16-AOAS938.

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Supplemental materials

  • Supplement to “A hierarchical framework for state-space matrix inference and clustering”. Supplementary methods, simulation studies, tables, and figures.