🧮 Math Derivation of a Top-Ranked scRNA-seq Imputation Method (SAVER)
Mathematical models used in SAVER, a tool of scRNAseq imputation, could well depict the structure inherent to the scRNAseq datasets as suggested by its superior performance. Here we derive SAVER's Poisson–gamma mixture model (also known as negative binomial model) and its Bayesian framework that leverage conjugate priors to estimate the posterior distribution of gene expression levels.
May 27, 2025
🎓 Math Rationale for ELBO/KL in Bayesian Inference and VAEs
Marginal likelihood is often intractable in Bayesian Inference. Thus ELBO is used as a lower bound to the log marginal likelihood. I derives the ELBO and KL divergence in Bayesian inference, and shows how they are used in Variational Autoencoders (VAEs).
May 27, 2025