@article{zhang_zhou_zhou_sun_2017, title={Regression models for multivariate count data}, volume={26}, DOI={10.1080/10618600.2016.1154063}, abstractNote={ABSTRACT Data with multivariate count responses frequently occur in modern applications. The commonly used multinomial-logit model is limiting due to its restrictive mean-variance structure. For instance, analyzing count data from the recent RNA-seq technology by the multinomial-logit model leads to serious errors in hypothesis testing. The ubiquity of overdispersion and complicated correlation structures among multivariate counts calls for more flexible regression models. In this article, we study some generalized linear models that incorporate various correlation structures among the counts. Current literature lacks a treatment of these models, partly because they do not belong to the natural exponential family. We study the estimation, testing, and variable selection for these models in a unifying framework. The regression models are compared on both synthetic and real RNA-seq data. Supplementary materials for this article are available online.}, number={1}, journal={Journal of Computational and Graphical Statistics}, author={Zhang, Y. W. and Zhou, H. and Zhou, J. and Sun, W.}, year={2017}, pages={1–13} }
 @article{zhou_zhang_2012, title={EM vs MM: A case study}, volume={56}, ISSN={["1872-7352"]}, DOI={10.1016/j.csda.2012.05.018}, abstractNote={The celebrated expectation–maximization (EM) algorithm is one of the most widely used optimization methods in statistics. In recent years it has been realized that EM algorithm is a special case of the more general minorization–maximization (MM) principle. Both algorithms create a surrogate function in the first (E or M) step that is maximized in the second M step. This two step process always drives the objective function uphill and is iterated until the parameters converge. The two algorithms differ in the way the surrogate function is constructed. The expectation step of the EM algorithm relies on calculating conditional expectations, while the minorization step of the MM algorithm builds on crafty use of inequalities. For many problems, EM and MM derivations yield the same algorithm. This expository note walks through the construction of both algorithms for estimating the parameters of the Dirichlet-Multinomial distribution. This particular case is of interest because EM and MM derivations lead to two different algorithms with completely distinct operating characteristics. The EM algorithm converges quickly but involves solving a nontrivial maximization problem in the M step. In contrast the MM updates are extremely simple but converge slowly. An EM–MM hybrid algorithm is derived which shows faster convergence than the MM algorithm in certain parameter regimes. The local convergence rates of the three algorithms are studied theoretically from the unifying MM point of view and also compared on numerical examples.}, number={12}, journal={COMPUTATIONAL STATISTICS & DATA ANALYSIS}, author={Zhou, Hua and Zhang, Yiwen}, year={2012}, month={Dec}, pages={3909–3920} }