Abstract:
Ever since the advent of correlation and simple linear regression at the turn of the 20th century, Statistics has been known as a data driven discipline within the spectrum of mathematical sciences. Subsequently, the flow of statistical approaches typically has encompassed several stages, including data collection, model fitting, and parameter interpretation. While earlier statistical attempts were mostly devoted to the establishment of a theoretical framework for inference, the growth and popularity of computational techniques in recent years have significantly shifted modern statistical methodologies from theory to applications, and thus have made them far more computationally driven. In particular, robust computational techniques such as Hamiltonian Markov Chain Monte Carlo techniques have emboldened the applications of Bayesian modeling for scientific problem solving. In this talk, I will discuss some areas in which there is a considerable overlap between statistical modeling of Big Data and Machine Learning. For example, I will draw upon the role of mixture models, Dirichlet process priors, Gaussian processes, and dimensionality reduction methods in Statistics to demonstrate their dual functionality in the current approaches for classification and prediction, as practiced in Machine Learning. I will then suggest a potentially unifying infrastructure for both disciplines, where the two cultures can further collaborate to offer more robust solutions for solving scientific inquiries.