Monte Carlo Methods

I purchased this book based on the previous reviews and based on the table of contents. Some of the topics (Langevin / Hamiltonian MCMC, energy based models) are ones that I want to understand better.The authors unapologetically launch into some pretty heavy material. In large part, I am writing this review so that potential readers are aware of the required background to understand this book. The authors take for granted the following background:Stochastic differential equations / stochastic calculusMultivariate calculus and calculus used by physicistsDifferential geometryLinear algebraProbability theory, including Bayesian statisticsCurrent notational conventions and operations in the above fieldsIt is almost as though in order to learn from this book, you have to already understand this book! Be an expert in the field before you get your hands on this one!Unfortunately, since I have a background in neither stochastic differential equations nor differential geometry, I was unable to follow the material on the topics that most interested me. Is this a comment about the quality of the book (hence my two star rating)? I believe it is. It reflects a choice on the part of the authors to provide little background about the methods themselves, but rather devote most of the book to application. The sections of the text that describe the methods are very condensed, the coverage is incomplete, and the exposition is patchy - not at all systematic. The exposition is non-existent in parts. For example, Fig. 2.10 is supposed to illustrate the Conditional Density Propagation algorithm with a series of pictures, but the explanations of what the pictures represent are missing. In other places the authors state they avoid details for space and refer the reader to the original publications. So, this book provides some of the "what" but very little of the "why". You will not get a good intuition about why the methods work from this text. I felt that this book is not written as a text to teach. It is written to show off rather than to show. Oddly, there are exercises following each chapter, so I suppose the authors intended it to be a text book?!The authors also take it for granted that notational conventions are already understood by the readership. This is problematic because they are inconsistent in their notation. (For example, in some places, variables are bold, and the same variable is not bold in other places (e.g., the r path variable in example 1.3)). Further, there are multiple other errors throughout the book. Typos are commonplace: words are misspelled, grammar needs work, and some equations are incorrect or unclear (e.g., p. 4 the book states omega_lattice(h) is a subset of omega_lattice(h). What is that supposed to mean?), word choice is very confusing in places, and some words (e.g., definite / indefinite articles) are missing. The book jumps from topic to topic with no synthetic unification of the ideas. For example, Langevin dynamics are introduced quite early on, but the more thorough discussion is presented in a much later chapter. Overall, the book felt rushed and unpolished.I found it particularly disturbing that multiple different people seemed to have contributed to the writing of the book, but they are not credited in any substantial form. It appears that a graduate student wrote the last three chapters. In a book with 11 chapters, shouldn't someone who wrote three of them be included as a co-author? When you look at the last three chapters, this person is not mentioned anywhere! It is disturbing to me when senior researchers take advantage of junior researchers like this. Thank you, Mitchell Hill, for contributing some of the most well written chapters of the book. Photos of men are spaced throughout the book, and occasionally the text makes no reference to the photo whatsoever. I guess we assume the photos represent the creators of the methods? Or, perhaps they are the people who wrote the sections of the text? Who knows?Negatives aside, this book has some real strengths. It introduces many very fascinating applications and highlights, however briefly, many powerful techniques. I will use the book to provide a listing of a lot of cool techniques. I learned about (I didn't learn) many new techniques from this book. I will need to go to the original references to understand the techniques themselves. (For example, Green's original article about reversible jump MCMC explains the why and the how of MCMC jump processes through spaces of different dimensionality; this book does not. It simply states Green's results in compact form - perhaps useful if you already know the theory, but not useful if you want to understand the theory.)Although it is not as up-to-date, I found the Kroese, Taimre, and Botev a much better treatment of this subject for those readers interested in the how and why of Monte Carlo methods. It provides a more systematic, clearer exposition.

If you are a researcher, practitioner or student in AI/machine learning/statistics, and want to gain a deeper understanding beyond trendy research topics in the last 5 years, you will enjoy reading this book. The book provides a systematic view of Monte Carlo algorithms for performing various tasks in statistical models: simulation, sampling, estimating a quantity, as well as learning and inference. Despite a long history, Monte Carlo methods are still actively being used in many recent applications, including DeepMind's AlphaGo (Monte Carlo Tree Search, page 44 - 46), photo-realistic image generation (Langevin Monte Carlo and generator networks, page 355 - 364), unsupervised leaning (page 413 - 417) and many more. This book connects the dots with many different applications and is a great reference book of algorithms old and new.Trendy research topics come and go, but the underlying theory and algorithms are long lasting. I am glad that I bought this book, learned about so many hidden gems in statistical machine learning.

I bought this book for the revision of some concepts that might be used in my research. To my surprise, this book adds a lot of more new materials than the time we took the class and the new material really opened my mind, especially the parts related to energy-based models. This book has been used for the Monte Carlo course at UCLA for more than ten years, and I took the class a few years ago.  When people design AI algorithms, they seldom relate to the physical world and physical theory with AI algorithms, this book paves a new path for the computer vision field. There's a saying "Vast ocean embraces streams to its tide; Norms received promise one far and wide (Chinese: 海纳百川，取则行远)", and it's up to you to accept or not ...

Finding a good book on Monte Carlo Methods is more or less like doing Monte Carlo "search". This book is an excellent one. From the perspective of a learner, this book covers all the fundamentals of MC methods with enjoyable rigor using many classic and state-of-the-art illustrative examples. It gives me many "aha" and "wow" moments when reading through the book. It is accessible to graduate students in ECE, Applied Math and CS, or to people who have similar backgrounds. From the perspective of an instructor, this book is also written in a way favoring smooth teaching and learning. I plan to use it for one of my current courses. I think the students will love it too. Overall, this book did a wonderful job!

This book is perfectly designed for readers in both Statistics and Computer Science background. It covers a board range of Monte Carlo methods with further examples and real-life applications that are also fresh and up-to-date. Each chapter is rigorously written, accompanied by illustrative figures and exercises to help with the understandings. Most importantly, I found this book could be read multiple times like research papers and each time will give me some new ideas to dig deeper. The aftertaste of this book is like a bottle of well-aged wine, and you can also put it on your shelf as a reference book, which becomes handy and useful whenever you need it!Strongly recommended.

This book is a very special and good resource for someone who is interested in MCMC techniques. Especially, it seeks to bridge the gap between statistics and computer science (such as computer vision, machine learning, and artificial intelligence). Different from other traditional MCMC books, this one provides not only a comprehensive overview of the MCMC algorithms with interesting computer vision examples, but also up-to-date developments of MCMC-based learning schemes for deep statistical generative models. We can also learn about how computer vision scientists develop MCMC algorithms to solve different types of computer vision problems, such as image parsing, image synthesis, and image embedding, etc.

The Monte Carlo is a class of charming methods for solving statistical problems. However, the book is merely a summary of concepts with little insightful or rigorous interpretations. Typos are everywhere, to a degree of misleading. The examples of the applications are lack of sufficient background introduction, and thus far from self contained. Be cautious before buying! This is more of a reading note of the authors prepared in a rush.