Jonas Peters

Jonas Peters is Professor of Statistics at the University of Copenhagen.

  • The Raven's Hat

    Fallen Pictures, Rising Sequences, and Other Mathematical Games

    Jonas Peters and Nicolai Meinshausen

    Games that show how mathematics can solve the apparently unsolvable.

    This book presents a series of engaging games that seem unsolvable—but can be solved when they are translated into mathematical terms. How can players find their ID cards when the cards are distributed randomly among twenty boxes? By applying the theory of permutations. How can a player guess the color of her own hat when she can only see other players' hats? Hamming codes, which are used in communication technologies. Like magic, mathematics solves the apparently unsolvable. The games allow readers, including university students or anyone with high school–level math, to experience the joy of mathematical discovery.

    The authors set up each game, specifying the number of players and props needed, and show readers how mathematical language reveals the problem's underlying structure. They explain the mathematical concepts with many examples, describe the history of the problem, and offer practical advice. Colorful and clever illustrations, featuring a flock of mathematically inclined ravens, help clarify things. All of the games can be presented to an audience; each one runs from sixty to ninety minutes, suitable for seminar presentations or lectures. The authors aim at maintaining mathematical precision while avoiding overly complex notation. Appendixes go into more detail, reviewing frequently used mathematical symbols, providing further information on a range of mathematical concepts, and offering chapter-specific mathematical explanations.

    • Paperback $24.95
  • Elements of Causal Inference

    Elements of Causal Inference

    Foundations and Learning Algorithms

    Jonas Peters, Dominik Janzing, and Bernhard Schölkopf

    A concise and self-contained introduction to causal inference, increasingly important in data science and machine learning.

    The mathematization of causality is a relatively recent development, and has become increasingly important in data science and machine learning. This book offers a self-contained and concise introduction to causal models and how to learn them from data. After explaining the need for causal models and discussing some of the principles underlying causal inference, the book teaches readers how to use causal models: how to compute intervention distributions, how to infer causal models from observational and interventional data, and how causal ideas could be exploited for classical machine learning problems. All of these topics are discussed first in terms of two variables and then in the more general multivariate case. The bivariate case turns out to be a particularly hard problem for causal learning because there are no conditional independences as used by classical methods for solving multivariate cases. The authors consider analyzing statistical asymmetries between cause and effect to be highly instructive, and they report on their decade of intensive research into this problem.

    The book is accessible to readers with a background in machine learning or statistics, and can be used in graduate courses or as a reference for researchers. The text includes code snippets that can be copied and pasted, exercises, and an appendix with a summary of the most important technical concepts.

    • Hardcover $45.00