Sparse latent factor models with interactions: analysis of gene expression data. (English) Zbl 1288.62164

Mayrink, Vinicius Diniz; Lucas, Joseph Edward

Ann. Appl. Stat. 7, No. 2, 799-822 (2013).

Summary: Sparse latent multi-factor models have been used in many exploratory and predictive problems with high-dimensional multivariate observations. Because of concerns with identifiability, the latent factors are almost always assumed to be linearly related to the measured feature variables. We explore the analysis of multi-factor models with different structures of interactions between latent factors, including multiplicative effects as well as a more general framework for nonlinear interactions introduced via a Gaussian process. We utilize sparsity priors to test whether the factors and interaction terms have significant effects. The performance of the models is evaluated through simulated and real data applications in genomics. Variation in the number of copies of regions of the genome is a well-known and important feature of most cancers. We examine interactions between factors directly associated with different chromosomal regions detected with copy number alteration in breast cancer data. In this context, significant interaction effects for specific genes suggest synergies between duplications and deletions in different regions of the chromosome.

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
92C40	Biochemistry, molecular biology
65C60	Computational problems in statistics (MSC2010)
92C50	Medical applications (general)

Software:

BioHMM

References:

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