If more than one good linear approximation is available, then it is natural to try to exploit all of them simultaneously. This is called multiple linear cryptanalysis. The first part of this chapter discusses multiple linear cryptanalysis in general. The second part focuses on the special case with a set of masks that forms a vector space, which is called multidimensional linear cryptanalysis.

Finding linear trails with high absolute correlation quickly becomes tedious work, especially for ciphers with a more complicated structure than the example that we have worked with so far. Since the total number of trails is finite, finding linear trails with a maximal absolute correlation is an example of a combinatorial optimization problem. This chapter discusses three commonly used optimization methods: Matsui’s branch and bound method, mixed-integer linear programming, and satisfiability or satisfiability modulo theories. At the same time, the chapter introduces two additional example ciphers that follow a different design strategy.

In this chapter we present some of the most popular approaches to clustering, and discuss general techniques for evaluating and validating the quality of a data partition.

In this chapter we explore several aspects in portfolio allocation that go beyond the classical single-period mean/variance model discussed in Chapter 11.

This chapter introduces the basic formalism of representing text, and looks at widely used techniques in the analysis of textual data such as topic modeling, language modeling, and classification.

This chapter introduce a basic statistical models for static and dynamic data generation, and discusses classical Bayesian approach for the estimation of the parameters of the model.

This chapter introduces linear regression, the workhorse of statistics and (supervised) learning, which relates an input vector to an output response by means of linear combination.

This chapter introduces the basic terminology and formalism on graph theory. Next, we introduce various types of networks that are of interest in finance.

This chapter introduces the representation and organization of data. We illustrate standard preliminary data manipulation and visualization techniques.

In this chapter, we introduce principal component analysis (PCA), a common practice to reduce its dimensionality, and discuss the link between PCA and low-rank approximations.

This chatper first introduces the kernel trick, which allows us to operate in the original lower-dimensional domain. We then discuss decision tree and ensemble methods for reducing data over-fitting.

This chapter introduces the numerical convex optimization problem that minimize a certain objective function subject to some constraints. We also introduce an efficient algorithm for solving such problems.

This chapter introduces the classical mean/variance portfolio design approach, and discusses extensions of the basic model, including transaction costs, market impact, and risk beyond the variance.

This chapter provides an overview of the topics covered in this, the book’s structure, the scope and presentation of the books, and the target audience for the book.