The camera slowly scans Chris Dancy’s face, first focusing on a profile of his bespectacled eyes, then quickly switching to a frontal shot to examine his contemplative expression at close range. Seconds later, the angle shifts again, the panorama now filmed as though from behind Dancy’s shoulder. The foreground looks blurry to start with. But once the lens adjusts, the viewer clearly sees the nearby cityscape at which Dancy longingly gazes.

Chapter 1 presents a brief overview of the book and the basics on inpainting, visual perception and Gestalt laws, together with a presentation of the Fitzwilliam Museum dataset of illuminated manuscripts, selected to represent different types of damage and consequent restoration challenges, which will be used throughout the book.

Recommender systems have become deeply integrated into daily life, shaping decisions in online shopping, news consumption, learning, and entertainment. These systems offer personalized suggestions, enhancing user experiences in various scenarios. Behind this, machine learning engineers drive the constant evolution of recommendation technology. Described as the “growth engine” of the internet, recommender systems play a critical role in the digital ecosystem. This chapter explores the role of these systems, why they are essential, and how they are architected from a technical perspective.

This chapter explores the pivotal role of modeling as a conduit between diverse data representations and applications in real, complex systems. The emphasis is on portraying modeling in terms of multivariate probabilities, laying the foundation for the probabilistic data-driven modeling framework.

The Introduction presents an overview of the use of automated legal guidance by government agencies. It offers examples of chatbots, virtual assistants, and other online tools in use across US federal government agencies and shows how the government is committed to expanding their application. The Introduction sets forth some of the critical features of automated legal guidance, including its tendency to make complex aspects of the law seem simple. The Introduction previews how automated legal guidance promises to increase access to complex statutes and regulations. However, the Introduction cautions that there are underappreciated costs of automated legal guidance, including that its simplification of statutes and regulations is more likely to harm members of the public who lack access to legal counsel than high-income and wealthy individuals. The Introduction provides a roadmap for the remainder of the book.

This chapter delves into the complexities and challenges of data science, emphasizing the potential pitfalls and ethical considerations inherent in decision-making based on data. It explores the intricate nature of data, which can be multifaceted, noisy, temporally and spatially disjointed, and often a result of the interplay among numerous interconnected components. This complexity poses significant difficulties in drawing causal inferences and making informed decisions.

A central theme of the chapter is the compromise of privacy that individuals may face in the quest for data-driven insights, which raises ethical concerns regarding the use of personal data. The discussion extends to the concept of algorithmic fairness, particularly in the context of racial bias, shedding light on the need for mitigating biases in data-driven decision-making processes.

Through a series of examples, the chapter illustrates the challenges and potential pitfalls associated with data science, underscoring the importance of robust methodologies and ethical considerations. It concludes with a thought-provoking examination of income inequality as a controversial example of data science in practice. The example highlights the nuanced interplay between data, decisions, and societal impacts.

This opening chapter provides a historical perspective on the evolution of computing, tracing its journey from early computational methods to the emergence of networking and the advent of data-centric computing. The chapter sets out to inspire readers to develop a holistic understanding of the intricate interactions among hardware, software, and networking. It introduces the principle of hardware and software codesign as a critical approach in constructing efficient data management systems. The goal is to achieve high throughput and low latency in modern data processing, setting the stage for the detailed exploration that follows in subsequent chapters.

Chapter 1 discusses the motivation for the book and the rationale for its organization into four parts: preliminary considerations, evaluation for classification, evaluation in other settings, and evaluation from a practical perspective. In more detail, the first part provides the statistical tools necessary for evaluation and reviews the main machine learning principles as well as frequently used evaluation practices. The second part discusses the most common setting in which machine learning evaluation has been applied: classification. The third part extends the discussion to other paradigms such as multi-label classification, regression analysis, data stream mining, and unsupervised learning. The fourth part broadens the conversation by moving it from the laboratory setting to the practical setting, specifically discussing issues of robustness and responsible deployment.

Network science has exploded in popularity since the late 1990s. But it flows from a long and rich tradition of mathematical and scientific understanding of complex systems. We can no longer imagine the world without evoking networks. And network data is at the heart of it. In this chapter, we set the stage by highlighting network sciences ancestry and the exciting scientific approaches that networks have enabled, followed by a tour of the basic concepts and properties of networks.

We begin by illustrating the interplay between questions of scientific interest and the use of data in seeking answers. Graphs provide a window through which meaning can often be extracted from data. Numeric summary statistics and probability distributions provide a form of quantitative scaffolding for models of random as well as nonrandom variation. Simple regression models foreshadow the issues that arise in the more complex models considered later in the book. Frequentist and Bayesian approaches to statistical inference are contrasted, the latter primarily using the Bayes Factor to complement the limited perspective that p-values offer. Akaike Information Criterion (AIC) and related "information" statistics provide a further perspective. Resampling methods, where the one available dataset is used to provide an empirical substitute for a theoretical distribution, are introduced. Remaining topics are of a more general nature. RStudio is one of several tools that can help in organizing and managing work. The checks provided by independent replication at another time and place are an indispensable complement to statistical analysis. Questions of data quality, of relevance to the questions asked, of the processes that generated the data, and of generalization, remain just as important for machine learning and other new analysis approaches as for more classical methods.

This chapter frames the book. It explains the focus of women as a historically highly relevant category while acknowledging the multiplicities of (gender) identities and relations that the rise of queer theory has opened. It also draws attention to the different experiences that women have at work in relation to technology, which are mediated in complex ways by ethnic and class backgrounds as well as issues of sexuality. The chapter outlines the different disciplinary orientations the book draws upon – including feminist theory, science, technology, and society studies, sociology of work, political economy, organizational studies, labour history, as well as CSCW, HCI, and participatory design – to then introduce the key concepts and theories used in the book: the distinction between sex and gender, intersectionality, the problematic notion of race, the view of engineers/designers making ethical-political choices, the concept of technology. It forwards the notion of practice-based research and the importance of involving users in design decisions as key to achieving gender equality in design. These concepts will be elaborated as well as made ‘practical’ in the course of the book.

In this chapter we draw motivation from real-world networks and formulate random graph models for them. We focus on some of the models that have received the most attention in the literature, namely, Erdos–Rényi random graphs, inhomogeneous random graphs, configuration models, and preferential attachment models. We follow Volume 1, both for the motivation as well as for the introduction of the random graph models involved. Furthermore, we add some convenient additional results, such as degree-truncation for configuration models and switching techniques for uniform random graphs with prescribed degrees. We also discuss preliminaries used in the book, for example concerning power-law distributions.

In this chapter, we describe a few discrete probability models to which we will come back repeatedly throughout the book. While there exists a vast array of well-studied random combinatorial structures (permutations, partitions, urn models, Boolean functions, polytopes, etc.), our focus is primarily on a limited number of graph-based processes, namely percolation, random graphs, Ising models, and random walks on networks. We will not attempt to derive the theory of these models exhaustively here. Instead we will employ them to illustrate some essential techniques from discrete probability. Note that the toolkit developed in this book is meant to apply to other probabilistic models of interest as well, and in fact many more will be encountered along the way. After a brief review of graph basics and Markov chains theory, we formally introduce our main models. We also formulate various key questions about these models that will be answered (at least partially) later on. We assume that the reader is familiar with the measure-theoretic foundations of probability. A refresher of all required concepts and results is provided in the appendix.

We provide a short, self-contained introduction to deep neural networks that is aimed at mathematically inclined readers. We promote the use of a vect--matrix formalism that is well suited to the compositional structure of these networks and that facilitates the derivation/description of the backpropagation algorithm. We present a detailed analysis of supervised learning for the two most common scenarios, (i) multivariate regression and (ii) classification, which rely on the minimization of least squares and cross-entropy criteria, respectively.

How certain can we be about projections of future climate change from computer models? In 1979, President Jimmy Carter asked the US National Academy of Science to address this question, and the quest for an answer laid the foundation for a new way of comparing and assessing computational models of climate change. My own work on climate models began with a similar question, and led me to investigate how climate scientists build and test their models. My research took me to climate modelling labs in five different countries, where I interviewed dozens of scientists. In this chapter, we will examine the motivating questions for that work, and explore the original benchmark experiment for climate models – known as Charney sensitivity – developed in response to President Carter’s question.

Introduction to the book material.

Optimization on Riemannian manifolds–the result of smooth geometry and optimization merging into one elegant modern framework–spans many areas of science and engineering, including machine learning, computer vision, signal processing, dynamical systems and scientific computing.

This text introduces the differential geometry and Riemannian geometry concepts that will help students and researchers in applied mathematics, computer science and engineering gain a firm mathematical grounding to use these tools confidently in their research. Its charts-last approach will prove more intuitive from an optimizer's viewpoint, and all definitions and theorems are motivated to build time-tested optimization algorithms. Starting from first principles, the text goes on to cover current research on topics including worst-case complexity and geodesic convexity. Readers will appreciate the tricks of the trade sprinkled throughout the book for conducting research in this area and for writing effective numerical implementations.