Unraveling a geometric conspiracy
Hamiltonian Monte Carlo is a powerful approach for efficiently exploring complex probability distributions not just in theory but also in practice. That power, however, relies on a delicate conspiracy on differential geometric properties. In this talk I will first discuss the properties necessary for the scalable performance of Hamiltonian Monte Carlo. I will then present recent work that introduces a general theory of measure-informed geometry that can be used to fully generalize these properties, providing a foundation for the generalization of Hamiltonian Monte Carlo without any compromise to its performance.