Recurrent DNA copy number alterations (CNA) measured with array comparative genomic 
hybridization (aCGH) reveal 
important molecular features of human genetics and 
disease. Studying aCGH profiles from a phenotypic group of individuals can 
determine important recurrent CNA patterns that suggest a strong correlation to the 
phenotype. Computational approaches to detecting recurrent CNAs from a set of aCGH 
experiments have typically relied on discretizing the noisy log ratios and 
subsequently inferring patterns. We demonstrate that this can have the effect of 
filtering out important signals present in the raw data. In this article we develop 
statistical models that jointly infer CNA patterns and the discrete labels by 
borrowing statistical strength across samples. 

We propose extending single 
sample aCGH HMMs to the multiple sample case in order to infer shared CNAs. We 
model recurrent CNAs as a profile encoded by a master sequence of states that 
generates the samples. We show how to improve on two basic models by performing 
joint inference of the discrete labels and providing sparsity in the output. We 
demonstrate on synthetic ground truth data and real data from lung cancer cell 
lines how these two important features of our model improve results over baseline 
models. We include standard quantitative metrics and a qualitative assessment on 
which to base our conclusions.