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Title: Noise injection regularization in large models with applications to neural networks and graphical models Authors:  Fang Liu - University of Notre Dame (United States) [presenting]
Abstract: The noise injection regularization technique (NIRT) is an approach to mitigate over-fitting in large models. We will demonstrate the applications of the NIRT in two scenarios of learning large models: Neural Networks (NN) and Graphical Models (GM). For NNs, we develop a NIRT called whiteout that injects adaptive Gaussian noises during the training of NNs. We show that the optimization objective function associated with whiteout in generalized linear models has a closed-form penalty term that has connections with a wide range of regularizations and includes the bridge, lasso, ridge, and elastic net penalization as special cases; it can also be extended to offer regularizations similar to the adaptive lasso and group lasso. For GMs, we develop an AdaPtive Noisy Data Augmentation regularization (PANDA) approach to promote sparsity in estimating individual graphical models and similarity among multiple graphs through training of generalized linear models. On the algorithmic level, PANDA can be implemented in a straightforward manner by iteratively solving for MLEs without constrained optimizations. For both the NN and PANDA approaches, we use simulated and real-life data to demonstrate their applications and show their superiority or comparability with existing methods.