Recent advancements in the study of cyber-physical systems (CPS) have addressed the combination of computation, networking, physical processes, and human involvement as an overall system to improve adaptability, autonomy, efficiency, functionality, reliability, safety, and usability. Among other lines of CPS research, machine learning (ML) has emerged as an indispensable component for state estimation, prediction, diagnosis, structure identification, operation specification, event detection, etc. This work particularly discusses three learning tasks that are commonly encountered in CPS sensing and operation applications. The primary motivations underlying this dissertation are (1) to incorporate the unique characteristics of the data generated from system measurement, and (2) to facilitate the integration of ML into other components of CPS, such as sensing and control subsystems.

More specifically, we first consider learning interaction structures for sparse sensing. With the generic directed information maximization as the learning objective, we discuss two subset selection problems and provide performance guarantees for greedy algorithms by extending the notion of submodularity. Practically, the proposed learning framework can be applied broadly to streaming feature selection, causality mining, sensor placement, as well as the construction of causal graphs. The second learning task discussed in this work is focused on the detection of outliers or novelties from multiple correlated time series data generated from CPS measurement. The key issue being addressed is the utilization of the correlation information in the smoothing process of multiple sequences. Two methods, one based on a multi-task extension of non-parametric time series modeling and the other based on merging hidden Markov model with matrix factorization, are established and analyzed. Lastly, we discuss the task of learning system requirement for agile operation and optimal control. The classical ML paradigm is modified with "shape constraints" to facilitate its usage for optimal control or to capture class imbalance for event detection. While developing new learning formulations, we also propose a novel global optimization procedure, namely parametric dual maximization, that is able to solve a class of modified machine learning problems having non-convex objectives.