Knowledge Distillation of Uncertainty using Deep Latent Factor Model

Deep ensembles deliver state-of-the-art, reliable uncertainty quantification, but their heavy computational and memory requirements hinder their practical deployments to real applications such as on-device AI. Knowledge distillation compresses an ensemble into small student models, but existing techniques struggle to preserve uncertainty partly because reducing the size of DNNs typically results in variation reduction. To resolve this limitation, we introduce a new method of distribution distillation (i.e. compressing a teacher ensemble into a student distribution instead of a student ensemble) called Gaussian distillation, which estimates the distribution of a teacher ensemble through a special Gaussian process called the deep latent factor model (DLF) by treating each member of the teacher ensemble as a realization of a certain stochastic process. The mean and covariance functions in the DLF model are estimated stably by using the expectation-maximization (EM) algorithm. By using multiple benchmark datasets, we demonstrate that the proposed Gaussian distillation outperforms existing baselines. In addition, we illustrate that Gaussian distillation works well for fine-tuning of language models and distribution shift problems.

Bayesian Neural Networks for Functional ANOVA model

With the increasing demand for interpretability in machine learning, functional ANOVA decomposition has gained renewed attention as a principled tool for breaking down high-dimensional function into low-dimensional components that reveal the contributions of different variable groups. Recently, Tensor Product Neural Network (TPNN) has been developed and applied as basis functions in the functional ANOVA model, referred to as ANOVA-TPNN. A disadvantage of ANOVA-TPNN, however, is that the components to be estimated must be specified in advance, which makes it difficult to incorporate higher-order TPNNs into the functional ANOVA model due to computational and memory constraints. In this work, we propose Bayesian-TPNN, a Bayesian inference procedure for the functional ANOVA model with TPNN basis functions, enabling the detection of higher-order components with reduced computational cost compared to ANOVA-TPNN. We develop an efficient MCMC algorithm and demonstrate that Bayesian-TPNN performs well by analyzing multiple benchmark datasets. Theoretically, we prove that the posterior of Bayesian-TPNN is consistent.