BNP 14 - Keynote Speaker: Sara Wade

Описание: Sara Wade

Understanding Uncertainty in Bayesian Cluster Analysis

The Bayesian approach to clustering is often appreciated for its ability to provide
uncertainty in the partition structure. However, summarizing the posterior distribution
over the clustering structure can be challenging, due the discrete, unordered nature and
massive dimension of the space. While recent advancements provide a single clustering
estimate to represent the posterior, this ignores uncertainty and may even be
unrepresentative in instances where the posterior is multimodal. To enhance our
understanding of uncertainty, we propose to summarize the posterior samples with not
one, but multiple clustering estimates, each corresponding to a different part of the space
of partitions that receives substantial posterior mass. In this work, we propose to find such
clustering estimates by approximating the posterior distribution in a Wasserstein distance
sense, equipped with a suitable metric on the partition space. An interesting byproduct is
that a locally optimal solution to this problem can be found using the k-medoids algorithm
on the partition space to divide the posterior samples into different groups, each
represented by one of the clustering estimates. Using both synthetic and real datasets, we
show that our proposal helps to improve the understanding of uncertainty, particularly
when the data clusters are not well separated, or when the employed model is misspecified.

Keywords: clustering, uncertainty, variation of information, Wasserstein distance

Co-authors: Cecilia Balocchi