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Mitigating the Effects of Non-Identifiability on Inference for Bayesian Neural Networks with Latent Variables
Yaniv Yacoby · Weiwei Pan · Finale Doshi-Velez

Tue Jul 25 05:00 PM -- 06:30 PM (PDT) @ Exhibit Hall 1 #114

Bayesian Neural Networks with Latent Variables (BNN+LVs) capture predictive uncertainty by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable). In this work, we first show that BNN+LV suffers from a serious form of non-identifiability: explanatory power can be transferred between the model parameters and latent variables while fitting the data equally well. We demonstrate that as a result, in the limit of infinite data, the posterior mode over the network weights and latent variables is asymptotically biased away from the ground-truth. Due to this asymptotic bias, traditional inference methods may in practice yield parameters that generalize poorly and misestimate uncertainty. Next, we develop a novel inference procedure that explicitly mitigates the effects of likelihood non-identifiability during training and yields high-quality predictions as well as uncertainty estimates. We demonstrate that our inference method improves upon benchmark methods across a range of synthetic and real data-sets.

Author Information

Yaniv Yacoby (Harvard University)
Weiwei Pan (Harvard University)
Finale Doshi-Velez (Harvard University)
Finale Doshi-Velez

Finale Doshi-Velez is a Gordon McKay Professor in Computer Science at the Harvard Paulson School of Engineering and Applied Sciences. She completed her MSc from the University of Cambridge as a Marshall Scholar, her PhD from MIT, and her postdoc at Harvard Medical School. Her interests lie at the intersection of machine learning, healthcare, and interpretability. Selected Additional Shinies: BECA recipient, AFOSR YIP and NSF CAREER recipient; Sloan Fellow; IEEE AI Top 10 to Watch

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