In the big data era, statistical and stochastic learning for distributed and intelligent systems focuses on enhancing and improving the robustness of learning models that have become pervasive and are being deployed for decision-making in real-life applications including general classification, prediction, and sparse sensing. The growing prospect of statistical learning approaches such as Linear Discriminant Analysis and distributed Learning being used (e.g., community sensing) has raised concerns around the robustness of algorithm design. Recent work on anomalies detection has shown that such Learning models can also succumb to the so-called \u27edge-cases\u27 where the real-life operational situation presents data that are not well-represented in the training data set. Such cases have been the primary reason for quite a few mis-classification bottleneck problems recently. Although initial research has begun to address scenarios with specific Learning models, there remains a significant knowledge gap regarding the detection and adaptation of learning models to \u27edge-cases\u27 and extreme ill-posed settings in the context of distributed and intelligent systems. With this motivation, this dissertation explores the complex in several typical applications and associated algorithms to detect and mitigate the uncertainty which will substantially reduce the risk in using statistical and stochastic learning algorithms for distributed and intelligent systems
