On Neural Networks as Infinite Tree-Structured Probabilistic Graphical Models

Deep neural networks (DNNs) lack the precise semantics and definitive probabilistic interpretation of probabilistic graphical models (PGMs). In this paper, we propose an innovative solution by constructing infinite tree-structured PGMs that correspond exactly to neural networks. Our research reveals that DNNs, during forward propagation, indeed perform approximations of PGM inference that are precise in this alternative PGM structure. Not only does our research complement existing studies that describe neural networks as kernel machines or infinite-sized Gaussian processes, it also elucidates a more direct approximation that DNNs make to exact inference in PGMs. Potential benefits include improved pedagogy and interpretation of DNNs, and algorithms that can merge the strengths of PGMs and DNNs

Scalable Data Augmentation for Deep Learning

Scalable Data Augmentation (SDA) provides a framework for training deep learning models using auxiliary hidden layers. Scalable MCMC is available for network training and inference. SDA provides a number of computational advantages over traditional algorithms, such as avoiding backtracking, local modes and can perform optimization with stochastic gradient descent (SGD) in TensorFlow. Standard deep neural networks with logit, ReLU and SVM activation functions are straightforward to implement. To illustrate our architectures and methodology, we use P\'{o}lya-Gamma logit data augmentation for a number of standard datasets. Finally, we conclude with directions for future research