As an alternative approach to MCMC, VI approximates the posterior distribution using an optimisation approach. Specically, given a family of probability distributions, VI aims to find a member which is most similar to the posterior distribution. VI is known to be more computationally efficient than MCMC, at the cost of loss in accuracy. The aims and tentative timeline of the project are as follows:
• Review and derive VI algorithm for Bayesian inference of NMF. (1.5 weeks)
• Implement the algorithm. (1.5 week)
• Compare the performance of VI and MCMC methods  by using simulated datasets
and real single-cell RNA-seq data. (1.5 weeks)
• Create an R package implementing the VI for Bayesian inference of NMF. (1.5 week)
The University of Melbourne
Gyu Hwan Park is a third-year Bachelor of Science student at the University of Melbourne, majoring in Mathematics & Statistics. He is intrigued by the intersection of modern applied Statistics and Computing in Statistical Machine Learning, Deep Learning and Bayesian Inference, particularly for their ever-increasing impacts in today’s world. With such interests, Gyu Hwan desires to develop further expertise and contribute to meaningful research in the future.