February 15, 2024

Bayesian Inference for Deep Learning

Convolutional neural networks [CNN] have been used widely for image classification. However, CNN usually needs large amounts of data. Small amounts make CNNs prone to over fitting [Blei D. M., Kucukelbir A., and McAuliffe J. D. (2018)]. This makes it unable to properly weigh what inputs properly correspond to the outputs of a data analysis. 

Bayesian Inference studies has been a popular topic in machine learning, where it helps to reduce the problem network overfitting associated with neural networks. We have seen several integrations of Bayesian ideas into several types of neural networks [Yu, H., et al. (2021)][Rodrigo, H. and Tsokos, C. (2020)]. By incorporating Bayesian analysis in to CNN, we could possibly make them more efficient, even with a small amount of data. 

In this project, we will introduce three different Bayesian Inference methods, particularly the evidence approach [MacKay, D. J. C. (1992)], Hybrid Monte Carlo, and the combination of both [Rodrigo, H. and Tsokos, C. (2020)]. Specifically the Hybrid Monte Carlo has with the intention increasing the efficacy of the convolutional neural networks with the Bayesian approaches with the image analysis.

About the speaker

When Ricardo Reyna started going to school, he noticed there was something about math that was so appealing. He decided to participate in math competitions in his school district from 7th grade till 10th grade. He applied and got accepted to attend his local university, University of Texas Pan American, to take College Algebra and Elementary Statistics classes. This was eye opening for him, it made him see that math is fun. So he applied to universities with pharmacy as his mindset and started to attend University of Texas Rio Grande Valley. But after a Calculus class and a very insightful conversation with professors, he applied and was accepted into the Pathways Program for Mathematics. Through this program he worked closely with a mentor and other resources that brought him to a specific math field he likes, statistics. University has only deepened Ricardo's respect for math and given him a better perspective of how math, more specifically statistics and health can be intertwined. In his Bachelor’s Degree and Master’s Degree, both had a concentration in Statistics. He has been accepted into a PhD program for Mathematics at UTRGV and plans to accomplish the things he sets his heart to do.