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Perturbations, optimization, and statistics
Hazan T., Papandreou G., Tarlow D., The MIT Press, Cambridge, MA, 2016. 412 pp. Type: Book (978-0-262035-64-4)
Date Reviewed: Oct 19 2017

The latest research in machine learning shows that the injection of perturbations into both learning and inference procedures may result in increased predictive accuracy. In almost every machine learning problem, decisions are made based on current knowledge; surprisingly, even with supervised training methods, it is not always beneficial to go for the right decision. Even when tackling a problem with deep learning algorithms, we may be confronted with problematic behaviors, such as misclassification of high-quality images or identification of perturbations as features. It has been “hypothesized that these behaviors are tied with limitations in the internal representations learned by these architectures, and that these same limitations would inhibit integration of these architectures into heterogeneous multi-component [artificial general intelligence, AGI] architectures” [1]. This book is a collection of papers presented at diverse topic-related workshops and summarizes how injecting adversarial or even random noise into learning and interference can be beneficial.

Machine learning is an ever-evolving field, and this book provides the answers to many emerging research questions about why and when the introduction of perturbations may be useful, and how to sensibly integrate them. It covers the state of the art and can be split into three topic clusters: the development of new perturbation models and learning algorithms, the understanding of perturbation models, and understanding and developing new perturbation-based regularization techniques.

The perturb-and-map method, for example, turns deterministic energy minimization algorithms into efficient probabilistic machines. As it is an application-driven approach, the hands-on reader is prepared to further explore its applications in computer vision or machine learning applications. Also, well-established algorithms, such as randomized optimum models, are reviewed, and new applications, such as the application to the problem of factorizing shortest paths into edge- and driver-specific trait vectors, are introduced. Again, the reader is prepared to explore the application of similar models to novel scenarios, for example, highly structured data such as images and text. The book also introduces alternatives to well-established algorithms, such as the application of the herding algorithm as an alternative to the maximum likelihood estimation for Markov random fields. Herding defines a deterministic dynamical system at the edge of chaos and generates a sequence of model states and parameters by alternating parameter perturbations with state maximizations, where the sequence of states can be interpreted as samples from an associated Markov random field (MRF) model. Thus, it skips the parameter estimation step of the maximum likelihood estimation and converts a set of moments from the training data into a sequence of model parameters accompanied by a sequence of pseudo-samples. The evaluation of the algorithm shows that the performance is competitive with standard algorithms. Further chapters cover the learning of a-posteriori perturbation models, expected values of random maximum a-posteriori perturbations, perturbation techniques in online learning, adversarial perturbations of deep neural networks, but also data augmentation via Lévy processes.

As indicated, the book is a collection of papers that are connected by a common theme--perturbations. Although the focus is on the mathematics of the introduced/discussed algorithms, most of the chapters conclude with open research directions and application scenarios, which allow the reader to dive deeper if needed.

The book is intended for people with expert knowledge in machine learning, and although the authors explain all required mathematical and statistical concepts, the reader should have a solid mathematical background. A website providing exercises accompanies the book. The authors focus on explaining novel algorithms and application scenarios for such, and there is no room left for introducing fundamental machine learning mathematics.

Reviewer:  Florian Neukart Review #: CR145598 (1712-0787)
1) Goertzel, B. Are there deep reasons underlying the pathologies of today's deep learning algorithms?. In Proc. of AGI 2015. Springer, 2015, 70–79.
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