Title: Bayesian Combinatorial Lottery Ticket Machine: Bayes Meets Extremal Combinatorics
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: Extremal combinatorics, Lottery Ticket hypothesis, Bayesian nonparametrics

Abstract: Inspired by the lottery ticket hypothesis (LTH) suggesting that the redundancy of neural networks (NNs) is useful for regression tasks, this paper demonstrates that the redundancy suggested by \emph{extremal combinatorics} is useful for Bayesian machine learning (BML), including ranking, classification, hierarchical clustering,  phylogenetic analysis, and relational data analysis.
In general, BML offers the advantage of quantifying uncertainty across all possible models (hypotheses) that explain data (observable phenomena in nature and society), making it particularly useful in applications that require transparency in data analysis, such as biomedical health and finance. However, its practical use is hindered by challenges in (1) model construction (often involving measure theory), (2) inference algorithm design (such as Markov chain Monte Carlo (MCMC) tailored to individual case studies), and (3) theoretical analysis (such as the mixing time of MCMC).
Inspired by how deep learning --- which has achieved great success in recent years --- effectively circumvents these challenges faced by BML, we import insights from extremal combinatorics, which can be regarded as analogous to the LTH phenomenon of NNs, into BML.
Our contributions include (1) a unified model construction method that expresses random target objects (e.g., a permutation representing the order of visits to cities in the \emph{traveling salesman problem}) by randomly selecting a substructure from universal objects (e.g., the \emph{superpermutation}), (2) a simple MCMC algorithm for Bayesian inference that is naturally derived from this model representation, and (3) a theoretical upper bound on the MCMC mixing time.