Data injection attacks serve as the hallmark example of the security concerns posed by the incorporation of advanced sensing and communication capabilities in power systems. Data injection attacks arise when one or several malicious attackers compromise a subset of the meters used by the state estimation procedure with the aim of manipulating the estimate obtained by the network operator. This chapter surveys the main data injection attacks that are formulated under the assumption that the state variables do not posses a probabilistic description and, therefore, the network operator implements unbiased state estimation procedures. Data injection attacks without this assumption are also studied. In particular, when the network operator perform minimum mean square error (MMSE) estimation, a fundamental trade-off is established between the distortion induced by the attacker and the achievable probability of attack detection. Within this setting, optimal attack strategies are described. The chapter also describes stealth attack constructions that simultaneously minimize the amount of information obtained by the network operator and the probability of attack detection.

Machine-learning algorithms can be viewed as stochastic transformations that map training data to hypotheses. Following Bousquet and Elisseeff, we say such an algorithm is stable if its output does not depend too much on any individual training example. Since stability is closely connected to generalization capabilities of learning algorithms, it is of interest to obtain sharp quantitative estimates on the generalization bias of machine-learning algorithms in terms of their stability properties. We describe several information-theoretic measures of algorithmic stability and illustrate their use for upper-bounding the generalization bias of learning algorithms. Specifically, we relate the expected generalization error of a learning algorithm to several information-theoretic quantities that capture the statistical dependence between the training data and the hypothesis. These include mutual information and erasure mutual information, and their counterparts induced by the total variation distance. We illustrate the general theory through examples, including the Gibbs algorithm and differentially private algorithms, and discuss strategies for controlling the generalization error.

A grand challenge in representation learning is the development of computational algorithms that learn the explanatory factors of variation behind high-dimensional data. Representation models (encoders) are often determined for optimizing performance on training data when the real objective is to generalize well to other (unseen) data. This chapter provides an overview of fundamental concepts in statistical learning theory and the information-bottleneck principle. This serves as a mathematical basis for the technical results, in which an upper bound to the generalization gap corresponding to the cross-entropy risk is given. When this penalty term times a suitable multiplier and the cross-entropy empirical risk are minimized jointly, the problem is equivalent to optimizing the information-bottleneck objective with respect to the empirical data distribution. This result provides an interesting connection between mutual information and generalization, and helps to explain why noise injection during the training phase can improve the generalization ability of encoder models and enforce invariances in the resulting representations.

The ability to understand and solve high-dimensional inference problems is essential for modern data science. This chapter examines high-dimensional inference problems through the lens of information theory and focuses on the standard linear model as a canonical example that is both rich enough to be practically useful and simple enough to be studied rigorously. In particular, this model can exhibit phase transitions where an arbitrarily small change in the model parameters can induce large changes in the quality of estimates. For this model, the performance of optimal inference can be studied using the replica method from statistical physics but, until recently, it was not known whether the resulting formulas were actually correct. In this chapter, we present a tutorial description of the standard linear model and its connection to information theory. We also describe the replica prediction for this model and outline the authors’ recent proof that it is exact.

Graph Signal Processing (GSP) is a general theory, whose goal is to bring about tools for graph signals analysis that are a direct generalization of Digital Signal Processing (DSP). The goal of this chapter is understanding the graph-spectral properties of the signals, which are typically explained through the linear generative model using graph filters. Are PMU a graph signal that obeys the linear generative model prevalent in the literature? If so, what kind of graph-filter structure and excitation justifies the properties discussed already? Can we derive new strategies to sense and process these data based on GSP? By putting the link between PMU data and GSP on the right footing, we can determine to what extent GSP tools are useful, and specify how we can use the basic equations for gaining theoretical insight that support the observations.

This chapter focuses on critical infrastructures in the power grid, which often rely on Industrial Control Systems (ICS) to operate and are exposed to vulnerabilities ranging from physical damage to injection of information that appears to be consistent with industrial control protocols. This way, infiltration of firewalls protecting the control perimeter of the control network becomes a significant tread. The goal of this chapter is to review identification and intrusion detection algorithms for protecting the power grid, based on the knowledge of the expected behavior of the system.

Processing, storing, and communicating information that originates as an analog phenomenon involve conversion of the information to bits. This conversion can be described by the combined effect of sampling and quantization. The digital representation in this procedure is achieved by first sampling the analog signal so as to represent it by a set of discrete-time samples and then quantizing these samples to a finite number of bits. Traditionally, these two operations are considered separately. The sampler is designed to minimize information loss due to sampling based on prior assumptions about the continuous-time input. The quantizer is designed to represent the samples as accurately as possible, subject to the constraint on the number of bits that can be used in the representation. The goal of this chapter is to revisit this paradigm by considering the joint effect of these two operations and to illuminate the dependence between them.