Date of Award


Document Type

Open Access Dissertation


Computer Science and Engineering

First Advisor

Gabriel Terejanu


Normal neural networks trained with gradient descent and back-propagation have received great success in various applications. On one hand, point estimation of the network weights is prone to over-fitting problems and lacks important uncertainty information associated with the estimation. On the other hand, exact Bayesian neural network methods are intractable and non-applicable for real-world applications. To date, approximate methods have been actively under development for Bayesian neural networks, including but not limited to: stochastic variational methods, Monte Carlo dropouts, and expectation propagation. Though these methods are applicable for current large networks, there are limits to these approaches with either underestimation or over-estimation of uncertainty. Extended Kalman filters (EKFs) and unscented Kalman filters (UKFs), which are widely used in data assimilation community, adopt a different perspective of inferring the parameters. Nevertheless, EKFs are incapable of dealing with highly non-linearity, while UKFs are inapplicable for large network architectures. Ensemble Kalman filters (EnKFs) serve as great methodology in atmosphere and oceanology disciplines targeting extremely high-dimensional, non-Gaussian, and nonlinear state-space models. So far, there is little work that applies EnKFs to estimate the parameters of deep neural networks. By considering neural network as a nonlinear function, we augment the network prediction with parameters as new states and adapt the state-space model to update the parameters. In the first work, we describe the ensemble Kalman filter, two proposed training schemes for training both fully-connected and Long Short-term Memory (LSTM) networks, and experiment iv with 10 UCI datasets and a natural language dataset for different regression tasks. To further evaluate the effectiveness of the proposed training scheme, we trained a deep LSTM network with the proposed algorithm, and applied it on five realworld sub-event detection tasks. With a formalization of the sub-event detection task, we develop an outlier detection framework and take advantage of the Bayesian Long Short-term Memory (LSTM) network to capture the important and interesting moments within an event. In the last work, we propose a framework for student knowledge estimation using Bayesian network. By constructing student models with Bayesian network, we can infer the new state of knowledge on each concept given a student. With a novel parameter estimate algorithm, the model can also indicate misconception on each question. Furthermore, we develop a predictive validation metric with expected data likelihood of the student model to evaluate the design of questions.