Bayesian Multinomial Logistic Normal Models through Marginally Latent Matrix-T Processes

Area of Science:

• Statistics
• Computational Biology
• Bioinformatics

Background:

• Bayesian multinomial logistic-normal (MLN) models are widely used for multivariate count data analysis, such as microbiome and gene expression data.
• Current MLN model implementations face scalability issues with large datasets due to computational limitations.

Purpose of the Study:

• To develop efficient inference methods for Bayesian MLN models applicable to large-scale datasets.
• To introduce a new class of models, Marginally Latent Matrix-T Process (Marginally LTP) models, that encompass existing MLN models.
• To accelerate inference for MLN models within the Marginally LTP framework.

Main Methods:

• Introduced the Marginally Latent Matrix-T Process (Marginally LTP) model class.
• Developed an efficient inference scheme tailored for Marginally LTP models.
• Applied specific accelerations to the inference scheme for the Bayesian multinomial logistic-normal (MLN) model subclass.

Main Results:

• Demonstrated that various MLN models with latent structures are special cases of the Marginally LTP class.
• The proposed inference scheme achieves high accuracy for MLN models.
• Achieved significant speedups, often 4-5 orders of magnitude faster than traditional Markov Chain Monte Carlo (MCMC) methods.

Conclusions:

• The Marginally LTP models provide a flexible framework for analyzing complex count data.
• The developed efficient inference scheme overcomes scalability limitations of existing MLN models.
• This advancement enables accurate and rapid analysis of large microbiome and gene expression datasets.