  Deep neural networks (DNNs) have received tremendous attention and achieved
great success in various applications, such as image and video analysis,
natural language processing, recommendation systems, and drug discovery.
However, inherent uncertainties derived from different root causes have been
realized as serious hurdles for DNNs to find robust and trustworthy solutions
for real-world problems. A lack of consideration of such uncertainties may lead
to unnecessary risk. For example, a self-driving autonomous car can misdetect a
human on the road. A deep learning-based medical assistant may misdiagnose
cancer as a benign tumor.
  In this work, we study how to measure different uncertainty causes for DNNs
and use them to solve diverse decision-making problems more effectively. In the
first part of this thesis, we develop a general learning framework to quantify
multiple types of uncertainties caused by different root causes, such as
vacuity (i.e., uncertainty due to a lack of evidence) and dissonance (i.e.,
uncertainty due to conflicting evidence), for graph neural networks. We provide
a theoretical analysis of the relationships between different uncertainty
types. We further demonstrate that dissonance is most effective for
misclassification detection and vacuity is most effective for
Out-of-Distribution (OOD) detection. In the second part of the thesis, we study
the significant impact of OOD objects on semi-supervised learning (SSL) for
DNNs and develop a novel framework to improve the robustness of existing SSL
algorithms against OODs. In the last part of the thesis, we create a general
learning framework to quantity multiple uncertainty types for multi-label
temporal neural networks. We further develop novel uncertainty fusion operators
to quantify the fused uncertainty of a subsequence for early event detection.
