Variational Bayes under Model Misspecification
Yixin Wang · David Blei

Tue Dec 10th 05:30 -- 07:30 PM @ East Exhibition Hall B + C #171

Variational Bayes (VB) is a scalable alternative to Markov chain Monte Carlo (MCMC) for Bayesian posterior inference. Though popular, VB comes with few theoretical guarantees, most of which focus on well-specified models. However, models are rarely well-specified in practice. In this work, we study VB under model misspecification. We prove the VB posterior is asymptotically normal and centers at the value that minimizes the Kullback-Leibler (KL) divergence to the true data-generating distribution. Moreover, the VB posterior mean centers at the same value and is also asymptotically normal. These results generalize the variational Bernstein--von Mises theorem [29] to misspecified models. As a consequence of these results, we find that the model misspecification error dominates the variational approximation error in VB posterior predictive distributions. It explains the widely observed phenomenon that VB achieves comparable predictive accuracy with MCMC even though VB uses an approximating family. As illustrations, we study VB under three forms of model misspecification, ranging from model over-/under-dispersion to latent dimensionality misspecification. We conduct two simulation studies that demonstrate the theoretical results.

Author Information

Yixin Wang (Columbia University)
David Blei (Columbia University)

David Blei is a Professor of Statistics and Computer Science at Columbia University, and a member of the Columbia Data Science Institute. His research is in statistical machine learning, involving probabilistic topic models, Bayesian nonparametric methods, and approximate posterior inference algorithms for massive data. He works on a variety of applications, including text, images, music, social networks, user behavior, and scientific data. David has received several awards for his research, including a Sloan Fellowship (2010), Office of Naval Research Young Investigator Award (2011), Presidential Early Career Award for Scientists and Engineers (2011), Blavatnik Faculty Award (2013), and ACM-Infosys Foundation Award (2013). He is a fellow of the ACM.

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