Universal Probability and Applications in Data Science

Alankrita Bhatt (Caltech)

In modern statistical and data science applications, the probability distribution generating the data in question is unknown (or even absent) and decisions must be taken in a purely data-driven manner. In this talk, the information-theoretic approach of universal probability is revisited and expanded upon. This approach gives us general principles and guidelines for assigning sequential probabilities to data (based on which a decision can then be made), and has been used successfully over the years to problems in compression, prediction and estimation among others. The utility of this approach is then demonstrated through the example of universal portfolio selection with side information.