With rapid development in hardware storage, precision instrument manufacturing, and economic globalization etc., data in various forms have become ubiquitous in human life. This enormous amount of data can be a double-edged sword. While it provides the possibility of modeling the world with a higher fidelity and greater flexibility, improper modeling choices can lead to false discoveries, misleading conclusions, and poor predictions. Typical data-mining, machine-learning, and statistical-inference procedures learn from and make predictions on data by fitting parametric or non-parametric models. However, there exists no model that is universally suitable for all datasets and goals. Therefore, a crucial step in data analysis is to consider a set of postulated candidate models and learning methods (the model class) and select the most appropriate one. We provide integrated discussions on the fundamental limits of inference and prediction based on model-selection principles from modern data analysis. In particular, we introduce two recent advances of model-selection approaches, one concerning a new information criterion and the other concerning modeling procedure selection.

The purpose of this chapter is to set the stage for the book and for the upcoming chapters. We first overview classical information-theoretic problems and solutions. We then discuss emerging applications of information-theoretic methods in various data-science problems and, where applicable, refer the reader to related chapters in the book. Throughout this chapter, we highlight the perspectives, tools, and methods that play important roles in classic information-theoretic paradigms and in emerging areas of data science. Table 1.1 provides a summary of the different topics covered in this chapter and highlights the different chapters that can be read as a follow-up to these topics.

The electric power system is evolving toward a massively distributed infrastructure with millions of controllable nodes. Its future operational landscape will be markedly different from existing operations, in which power generation is concentrated at a few large fossil-fuel power plants, use of renewable generation and storage is relatively rare, and loads typically operate in open-loop fashion. This chapter provides an overview of the technical developments that aim to leverage advances in optimization and control to develop distributed control frameworks for next-generation power systems that ensure stability, preserve reliability, and meet economic objectives and customer preferences.

Approximate computation methods with provable performance guarantees are becoming important and relevant tools in practice. In this chapter we focus on sketching methods designed to reduce data dimensionality in computationally intensive tasks. Sketching can often provide better space, time, and communication complexity trade-offs by sacrificing minimal accuracy. This chapter discusses the role of information theory in sketching methods for solving large-scale statistical estimation and optimization problems. We investigate fundamental lower bounds on the performance of sketching. By exploring these lower bounds, we obtain interesting trade-offs in computation and accuracy. We employ Fano’s inequality and metric entropy to understand fundamental lower bounds on the accuracy of sketching, which is parallel to the information-theoretic techniques used in statistical minimax theory.

Studies of prosumer decision making in the smart grid have focused on a single decision within the framework of expected utility theory (EUT) and behavioral theories such as Prospect Theory. This chapter studies prosumer decision making in a more natural market situation in which a prosumer has to decide whether to make a sale of solar energy units generated at her home every day or hold (store) the energy units in anticipation of a future sale at a better price. Specifically, it proposes a new behavioral model that extends EUT to take into account bounded horizons (in terms of the number of days) that prosumers implicitly impose on their decision making in arriving at “hold” or “sell” decisions of energy units. The new behavioral model assumes that humans make decisions that will affect their lives within a bounded horizon regardless of how far into the future their units may be sold. Modeling the utility of the prosumer using parameters such as the offered price on a day, the available energy units on a day, and the probabilities of the forecast prices, both traditional EUT and the proposed behavioral model with bounded horizons are fit to prosumer data.

Fast and accurate unveiling of power-line outages is of paramount importance not only for preventing faults that may lead to blackouts but also for routine monitoring and control tasks of the smart grid. This chapter presents a sparse overcomplete model to represent the effects of (potentially multiple) power line outages on synchronized bus voltage angle measurements. Based on this model, efficient compressive sensing algorithms can be adopted to identify outaged lines at linear complexity of the total number of lines. Furthermore, the effects of uncertainty in synchronized measurements will be analyzed, along with the optimal placement of measurement units.

This chapter studies the impact of the deployment of electric vehicles (EVs) at a large scale on the existing and future energy networks. The impact on the grid is assessed in terms of residential distribution network (DN) costs. Essentially, the main goal to optimize the battery charging schedules of EVs to minimize a cost that takes into account residential distribution transformer aging and the distribution energy losses. Within this context, the underlying mathematical tool is a static noncooperative game that describes the interaction between all EVs and the DN operator. An equilibrium analysis is conducted for this game in both its atomic and nonatomic versions.

This chapter describes methods to detect and identify power system transmission line outages in near real time. These methods exploit statistical properties of the small random fluctuations in electricity generation as well as energy demand to which a power system is subject to as time evolves. To detect and identify transmission line outages, a linearized incremental small-signal power system model is used in conjunction with high-speed synchronized voltage phase angle measurements obtained from phasor measurement units. By monitoring the statistical properties of voltage phase angle time-series, line outages are detected and identified using techniques borrowed from the theory of quickest change detection. Several case studies are considered for the cases of detecting and identifying single- and double-line outages in an accurate and timely fashion.