Towards a Theory of Non-Log-Concave Sampling
The task of sampling from a given density is a fundamental computational task with numerous applications in statistics, machine learning and applied mathematics. In the last decade, the iteration complexity of sampling from a smooth and (strongly) log-concave density has been well-studied. However, a general theory of sampling when the above mentioned assumptions are not satisfied is lacking. In this talk, taking motivation from the theory of non-convex optimization, I will discuss a recently proposed framework for establishing the iteration complexity of sampling when the target density satisfies only the relatively milder Holder-smoothness assumption. I will also discuss several extensions and applications of our result; in particular, it yields a new state-of-the-art guarantee for sampling from distributions which satisfy a Poincar\'e inequality.
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