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Evaluating Bayesian Models with Posterior Dispersion Indices
Alp Kucukelbir · Yixin Wang · David Blei

Sun Aug 06 06:06 PM -- 06:24 PM (PDT) @ C4.9& C4.10

Probabilistic modeling is cyclical: we specify a model, infer its posterior, and evaluate its performance. Evaluation drives the cycle, as we revise our model based on how it performs. This requires a metric. Traditionally, predictive accuracy prevails. Yet, predictive accuracy does not tell the whole story. We propose to evaluate a model through posterior dispersion. The idea is to analyze how each datapoint fares in relation to posterior uncertainty around the hidden structure. This highlights datapoints the model struggles to explain and provides complimentary insight to datapoints with low predictive accuracy. We present a family of posterior dispersion indices (PDI) that capture this idea. We show how a PDI identifies patterns of model mismatch in three real data examples: voting preferences, supermarket shopping, and population genetics.

Author Information

Alp Kucukelbir (Columbia University)
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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