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In this work, we empirically explore the question: how can we assess thequality of samples from some target distribution? We assume that the samplesare provided by some valid Monte Carlo procedure, so we are guaranteed that thecollection of samples will asymptotically approximate the true distribution.Most current evaluation approaches focus on two questions: (1) Has the chainmixed, that is, is it sampling from the distribution? and (2) How independentare the samples (as MCMC procedures produce correlated samples)? Focusing onthe case of Bayesian nonnegative matrix factorization, we empirically evaluatestandard metrics of sampler quality as well as propose new metrics to captureaspects that these measures fail to expose. The aspect of sampling that is ofparticular interest to us is the ability (or inability) of sampling methods tomove between multiple optima in NMF problems. As a proxy, we propose and studya number of metrics that might quantify the diversity of a set of NMFfactorizations obtained by a sampler through quantifying the coverage of theposterior distribution. We compare the performance of a number of standardsampling methods for NMF in terms of these new metrics.

An Empirical Comparison of Sampling Quality Metrics: A Case Study for Bayesian Nonnegative Matrix Factorization