Machine Learning in the Presence of an Adversary

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ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (746 download)

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Book Synopsis Machine Learning in the Presence of an Adversary by : Udam Saini

Download or read book Machine Learning in the Presence of an Adversary written by Udam Saini and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Prediction Games

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Publisher : Universitätsverlag Potsdam
ISBN 13 : 386956203X
Total Pages : 138 pages
Book Rating : 4.8/5 (695 download)

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Book Synopsis Prediction Games by : Michael Brückner

Download or read book Prediction Games written by Michael Brückner and published by Universitätsverlag Potsdam. This book was released on 2012 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many applications one is faced with the problem of inferring some functional relation between input and output variables from given data. Consider, for instance, the task of email spam filtering where one seeks to find a model which automatically assigns new, previously unseen emails to class spam or non-spam. Building such a predictive model based on observed training inputs (e.g., emails) with corresponding outputs (e.g., spam labels) is a major goal of machine learning. Many learning methods assume that these training data are governed by the same distribution as the test data which the predictive model will be exposed to at application time. That assumption is violated when the test data are generated in response to the presence of a predictive model. This becomes apparent, for instance, in the above example of email spam filtering. Here, email service providers employ spam filters and spam senders engineer campaign templates such as to achieve a high rate of successful deliveries despite any filters. Most of the existing work casts such situations as learning robust models which are unsusceptible against small changes of the data generation process. The models are constructed under the worst-case assumption that these changes are performed such to produce the highest possible adverse effect on the performance of the predictive model. However, this approach is not capable to realistically model the true dependency between the model-building process and the process of generating future data. We therefore establish the concept of prediction games: We model the interaction between a learner, who builds the predictive model, and a data generator, who controls the process of data generation, as an one-shot game. The game-theoretic framework enables us to explicitly model the players' interests, their possible actions, their level of knowledge about each other, and the order at which they decide for an action. We model the players' interests as minimizing their own cost function which both depend on both players' actions. The learner's action is to choose the model parameters and the data generator's action is to perturbate the training data which reflects the modification of the data generation process with respect to the past data. We extensively study three instances of prediction games which differ regarding the order in which the players decide for their action. We first assume that both player choose their actions simultaneously, that is, without the knowledge of their opponent's decision. We identify conditions under which this Nash prediction game has a meaningful solution, that is, a unique Nash equilibrium, and derive algorithms that find the equilibrial prediction model. As a second case, we consider a data generator who is potentially fully informed about the move of the learner. This setting establishes a Stackelberg competition. We derive a relaxed optimization criterion to determine the solution of this game and show that this Stackelberg prediction game generalizes existing prediction models. Finally, we study the setting where the learner observes the data generator's action, that is, the (unlabeled) test data, before building the predictive model. As the test data and the training data may be governed by differing probability distributions, this scenario reduces to learning under covariate shift. We derive a new integrated as well as a two-stage method to account for this data set shift. In case studies on email spam filtering we empirically explore properties of all derived models as well as several existing baseline methods. We show that spam filters resulting from the Nash prediction game as well as the Stackelberg prediction game in the majority of cases outperform other existing baseline methods.

Adversarial Machine Learning

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Publisher : Cambridge University Press
ISBN 13 : 1107043468
Total Pages : 341 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Adversarial Machine Learning by : Anthony D. Joseph

Download or read book Adversarial Machine Learning written by Anthony D. Joseph and published by Cambridge University Press. This book was released on 2019-02-21 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study allows readers to get to grips with the conceptual tools and practical techniques for building robust machine learning in the face of adversaries.

Machine Learning in the Presence of an Adversary

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Publisher :
ISBN 13 :
Total Pages : 92 pages
Book Rating : 4.:/5 (746 download)

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Book Synopsis Machine Learning in the Presence of an Adversary by : Udam Saini

Download or read book Machine Learning in the Presence of an Adversary written by Udam Saini and published by . This book was released on 2008 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Robust Machine Learning Algorithms and Systems for Detection and Mitigation of Adversarial Attacks and Anomalies

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Publisher : National Academies Press
ISBN 13 : 0309496098
Total Pages : 83 pages
Book Rating : 4.3/5 (94 download)

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Book Synopsis Robust Machine Learning Algorithms and Systems for Detection and Mitigation of Adversarial Attacks and Anomalies by : National Academies of Sciences, Engineering, and Medicine

Download or read book Robust Machine Learning Algorithms and Systems for Detection and Mitigation of Adversarial Attacks and Anomalies written by National Academies of Sciences, Engineering, and Medicine and published by National Academies Press. This book was released on 2019-08-22 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Intelligence Community Studies Board (ICSB) of the National Academies of Sciences, Engineering, and Medicine convened a workshop on December 11â€"12, 2018, in Berkeley, California, to discuss robust machine learning algorithms and systems for the detection and mitigation of adversarial attacks and anomalies. This publication summarizes the presentations and discussions from the workshop.

Adversarial Machine Learning

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Publisher : Springer Nature
ISBN 13 : 3031015800
Total Pages : 152 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Adversarial Machine Learning by : Yevgeniy Tu

Download or read book Adversarial Machine Learning written by Yevgeniy Tu and published by Springer Nature. This book was released on 2022-05-31 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The increasing abundance of large high-quality datasets, combined with significant technical advances over the last several decades have made machine learning into a major tool employed across a broad array of tasks including vision, language, finance, and security. However, success has been accompanied with important new challenges: many applications of machine learning are adversarial in nature. Some are adversarial because they are safety critical, such as autonomous driving. An adversary in these applications can be a malicious party aimed at causing congestion or accidents, or may even model unusual situations that expose vulnerabilities in the prediction engine. Other applications are adversarial because their task and/or the data they use are. For example, an important class of problems in security involves detection, such as malware, spam, and intrusion detection. The use of machine learning for detecting malicious entities creates an incentive among adversaries to evade detection by changing their behavior or the content of malicius objects they develop. The field of adversarial machine learning has emerged to study vulnerabilities of machine learning approaches in adversarial settings and to develop techniques to make learning robust to adversarial manipulation. This book provides a technical overview of this field. After reviewing machine learning concepts and approaches, as well as common use cases of these in adversarial settings, we present a general categorization of attacks on machine learning. We then address two major categories of attacks and associated defenses: decision-time attacks, in which an adversary changes the nature of instances seen by a learned model at the time of prediction in order to cause errors, and poisoning or training time attacks, in which the actual training dataset is maliciously modified. In our final chapter devoted to technical content, we discuss recent techniques for attacks on deep learning, as well as approaches for improving robustness of deep neural networks. We conclude with a discussion of several important issues in the area of adversarial learning that in our view warrant further research. Given the increasing interest in the area of adversarial machine learning, we hope this book provides readers with the tools necessary to successfully engage in research and practice of machine learning in adversarial settings.

Adversarial Machine Learning

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Publisher : Springer Nature
ISBN 13 : 3030997723
Total Pages : 316 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Adversarial Machine Learning by : Aneesh Sreevallabh Chivukula

Download or read book Adversarial Machine Learning written by Aneesh Sreevallabh Chivukula and published by Springer Nature. This book was released on 2023-03-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: A critical challenge in deep learning is the vulnerability of deep learning networks to security attacks from intelligent cyber adversaries. Even innocuous perturbations to the training data can be used to manipulate the behaviour of deep networks in unintended ways. In this book, we review the latest developments in adversarial attack technologies in computer vision; natural language processing; and cybersecurity with regard to multidimensional, textual and image data, sequence data, and temporal data. In turn, we assess the robustness properties of deep learning networks to produce a taxonomy of adversarial examples that characterises the security of learning systems using game theoretical adversarial deep learning algorithms. The state-of-the-art in adversarial perturbation-based privacy protection mechanisms is also reviewed. We propose new adversary types for game theoretical objectives in non-stationary computational learning environments. Proper quantification of the hypothesis set in the decision problems of our research leads to various functional problems, oracular problems, sampling tasks, and optimization problems. We also address the defence mechanisms currently available for deep learning models deployed in real-world environments. The learning theories used in these defence mechanisms concern data representations, feature manipulations, misclassifications costs, sensitivity landscapes, distributional robustness, and complexity classes of the adversarial deep learning algorithms and their applications. In closing, we propose future research directions in adversarial deep learning applications for resilient learning system design and review formalized learning assumptions concerning the attack surfaces and robustness characteristics of artificial intelligence applications so as to deconstruct the contemporary adversarial deep learning designs. Given its scope, the book will be of interest to Adversarial Machine Learning practitioners and Adversarial Artificial Intelligence researchers whose work involves the design and application of Adversarial Deep Learning.

Machine Learning on Graphs in the Presence of Noise and Adversaries

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (124 download)

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Book Synopsis Machine Learning on Graphs in the Presence of Noise and Adversaries by : Aleksandar Bojchevski

Download or read book Machine Learning on Graphs in the Presence of Noise and Adversaries written by Aleksandar Bojchevski and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Adversary-Aware Learning Techniques and Trends in Cybersecurity

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Publisher : Springer Nature
ISBN 13 : 3030556921
Total Pages : 229 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Adversary-Aware Learning Techniques and Trends in Cybersecurity by : Prithviraj Dasgupta

Download or read book Adversary-Aware Learning Techniques and Trends in Cybersecurity written by Prithviraj Dasgupta and published by Springer Nature. This book was released on 2021-01-22 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to give researchers and practitioners in the cross-cutting fields of artificial intelligence, machine learning (AI/ML) and cyber security up-to-date and in-depth knowledge of recent techniques for improving the vulnerabilities of AI/ML systems against attacks from malicious adversaries. The ten chapters in this book, written by eminent researchers in AI/ML and cyber-security, span diverse, yet inter-related topics including game playing AI and game theory as defenses against attacks on AI/ML systems, methods for effectively addressing vulnerabilities of AI/ML operating in large, distributed environments like Internet of Things (IoT) with diverse data modalities, and, techniques to enable AI/ML systems to intelligently interact with humans that could be malicious adversaries and/or benign teammates. Readers of this book will be equipped with definitive information on recent developments suitable for countering adversarial threats in AI/ML systems towards making them operate in a safe, reliable and seamless manner.

The Role of Data Geometry in Adversarial Machine Learning

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Publisher :
ISBN 13 :
Total Pages : 175 pages
Book Rating : 4.5/5 (57 download)

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Book Synopsis The Role of Data Geometry in Adversarial Machine Learning by : Arjun Nitin Bhagoji

Download or read book The Role of Data Geometry in Adversarial Machine Learning written by Arjun Nitin Bhagoji and published by . This book was released on 2020 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: As machine learning (ML) systems become ubiquitous, it is critically important to ensure that they are secure against adversaries. This is the focus of the recently developing sub-field of adversarial machine learning, which aims to analyze and defend ML systems. In this thesis, we uncover the crucial role that data geometry plays in adversarial ML. We show that it helps craft effective attacks against real-world ML systems, develop defenses that are robust to adaptive attacks and is instrumental in deriving fundamental bounds on the robustness of ML systems. Our focus is mainly on evasion attacks carried out using adversarial examples, which are maliciously modified inputs that cause catastrophic failures of ML systems at test time. The \\emph{first part of the thesis} deals with black-box attacks on ML systems. These are attacks carried out by adversaries with only query access to the systems under attack. Nevertheless, we show that these are as pernicious as attacks with full knowledge of the system, demonstrating that adversarial examples do indeed represent a serious threat to deployed ML systems. We use data geometry to increase the query efficiency of these attacks and leverage this to carry out the first effective attack on a commercially deployed ML system in an ethical manner. The \\emph{second part of the thesis} considers the use of dimensionality reduction to defend against evasion attacks. These defenses are effective against a variety of attacks, crucially including those with full knowledge of the defense. We use Principal Component Analysis to carry out this dimensionality reduction and also propose a variant of it known as anti-whitening, both of which improve the security-utility trade-off for ML systems. The \\emph{third part of the thesis} steps away from the attack-defense arms race to develop fundamental limits on learning in the presence of evasion attacks. Our first result uses the underlying geometry of the data and the theory of optimal transport to find an upper bound on classifier performance in the presence of an adversary. We provide exact results for the case of Gaussian distributions and completely characterize adversarial learning in this case. We further use our results to demonstrate the gap from optimality that exists for current defenses. The second result looks at how such classifiers can be learned. We extend the theory of PAC-learning to account for an adversary and demonstrate sample complexity bounds in the case of learning with an evasion attack by defining the Adversarial VC-dimension. We characterize learning with linear classifiers exactly and provide examples to show how Adversarial VC-dimension differs from the standard VC-dimension. In the \\emph{final part of the thesis}, we relax two critical assumptions about adversaries that we make throughout to expand the scope of attacks that are possible. First, we introduce out-of-distribution adversarial examples, which relax the assumption that adversarial examples have to be generated from the same data distribution used during training. This allows us to analyze the security properties of open-world ML systems. Second, we consider the impact of training-time adversaries on practical distributed learning systems. Since these aggregate models from multiple clients during the learning process, they are particularly vulnerable to an adversary controlling malicious clients. We show that with the use of model poisoning attacks, the learned model can be induced to misclassify points chosen by the adversary. In summary, we have shown how data geometry can be leveraged to find, analyze and mitigate the vulnerability of ML systems to evasion attacks. Nevertheless, as the scope of possible attacks increases, new theoretical insights and defenses have to be developed to engineer truly robust ML systems. We hope this thesis points the way forward for fundamental and actionable research in this domain.

Characterizing the Limits and Defenses of Machine Learning in Adversarial Settings

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Characterizing the Limits and Defenses of Machine Learning in Adversarial Settings by : Nicolas Papernot

Download or read book Characterizing the Limits and Defenses of Machine Learning in Adversarial Settings written by Nicolas Papernot and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in machine learning (ML) in recent years have enabled a dizzying array of applications such as object recognition, autonomous systems, security diagnostics, and playing the game of Go. Machine learning is not only a new paradigm for building software and systems, it is bringing social disruption at scale. There is growing recognition that ML exposes new vulnerabilities in software systems, yet the technical communitys understanding of the nature and extent of these vulnerabilities remains limited. In this thesis, I focus my study on the integrity of ML models. Integrity refers here to the faithfulness of model predictions with respect to an expected outcome. This property is at the core of traditional machine learning evaluation, as demonstrated by the pervasiveness of metrics such as accuracy among practitioners. A large fraction of ML techniques were designed for benign execution environments. Yet, the presence of adversaries may invalidate some of these underlying assumptions by forcing a mismatch between the distributions on which the model is trained and tested. As ML is increasingly applied and being relied on for decision-making in critical applications like transportation or energy, the models produced are becoming a target for adversaries who have a strong incentive to force ML to mispredict. I explore the space of attacks against ML integrity at test time. Given full or limited access to a trained model, I devise strategies that modify the test data to create a worst-case drift between the training and test distributions. The implications of this part of my research is that an adversary with very weak access to a system, and little knowledge about the ML techniques it deploys, can nevertheless mount powerful attacks against such systems as long as she has the capability of interacting with it as an oracle: i.e., send inputs of the adversarys choice and observe the ML prediction. This systematic exposition of the poor generalization of ML models indicates the lack of reliable confidence estimates when the model is making predictions far from its training data. Hence, my efforts to increase the robustness of models to these adversarial manipulations strive to decrease the confidence of predictions made far from the training distribution. Informed by my progress on attacks operating in the black-box threat model, I first identify limitations to two defenses: defensive distillation and adversarial training. I then describe recent defensive efforts addressing these shortcomings. To this end, I introduce the Deep k-Nearest Neighbors classifier, which augments deep neural networks with an integrity check at test time. The approach compares internal representations produced by the deep neural network on test data with the ones learned on its training points. Using the labels of training points whose representations neighbor the test input across the deep neural networks layers, I estimate the nonconformity of the prediction with respect to the models training data. An application of conformal prediction methodology then paves the way for more reliable estimates of the models prediction credibility, i.e., how well the prediction is supported by training data. In turn, we distinguish legitimate test data with high credibility from adversarial data with low credibility. This research calls for future efforts to investigate the robustness of individual layers of deep neural networks rather than treating the model as a black-box. This aligns well with the modular nature of deep neural networks, which orchestrate simple computations to model complex functions. This also allows us to draw connections to other areas like interpretability in ML, which seeks to answer the question of: How can we provide an explanation for the model prediction to a human? Another by-product of this research direction is that I better distinguish vulnerabilities of ML models that are a consequence of the ML algorithms from those that can be explained by artifacts in the data.

Machine Learning and Cybernetics

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Publisher : Springer
ISBN 13 : 3662456524
Total Pages : 460 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Machine Learning and Cybernetics by : Xizhao Wang

Download or read book Machine Learning and Cybernetics written by Xizhao Wang and published by Springer. This book was released on 2014-12-04 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th International Conference on Machine Learning and Cybernetics, Lanzhou, China, in July 2014. The 45 revised full papers presented were carefully reviewed and selected from 421 submissions. The papers are organized in topical sections on classification and semi-supervised learning; clustering and kernel; application to recognition; sampling and big data; application to detection; decision tree learning; learning and adaptation; similarity and decision making; learning with uncertainty; improved learning algorithms and applications.

Game Theory and Machine Learning for Cyber Security

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Publisher : John Wiley & Sons
ISBN 13 : 1119723949
Total Pages : 546 pages
Book Rating : 4.1/5 (197 download)

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Book Synopsis Game Theory and Machine Learning for Cyber Security by : Charles A. Kamhoua

Download or read book Game Theory and Machine Learning for Cyber Security written by Charles A. Kamhoua and published by John Wiley & Sons. This book was released on 2021-09-08 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: GAME THEORY AND MACHINE LEARNING FOR CYBER SECURITY Move beyond the foundations of machine learning and game theory in cyber security to the latest research in this cutting-edge field In Game Theory and Machine Learning for Cyber Security, a team of expert security researchers delivers a collection of central research contributions from both machine learning and game theory applicable to cybersecurity. The distinguished editors have included resources that address open research questions in game theory and machine learning applied to cyber security systems and examine the strengths and limitations of current game theoretic models for cyber security. Readers will explore the vulnerabilities of traditional machine learning algorithms and how they can be mitigated in an adversarial machine learning approach. The book offers a comprehensive suite of solutions to a broad range of technical issues in applying game theory and machine learning to solve cyber security challenges. Beginning with an introduction to foundational concepts in game theory, machine learning, cyber security, and cyber deception, the editors provide readers with resources that discuss the latest in hypergames, behavioral game theory, adversarial machine learning, generative adversarial networks, and multi-agent reinforcement learning. Readers will also enjoy: A thorough introduction to game theory for cyber deception, including scalable algorithms for identifying stealthy attackers in a game theoretic framework, honeypot allocation over attack graphs, and behavioral games for cyber deception An exploration of game theory for cyber security, including actionable game-theoretic adversarial intervention detection against advanced persistent threats Practical discussions of adversarial machine learning for cyber security, including adversarial machine learning in 5G security and machine learning-driven fault injection in cyber-physical systems In-depth examinations of generative models for cyber security Perfect for researchers, students, and experts in the fields of computer science and engineering, Game Theory and Machine Learning for Cyber Security is also an indispensable resource for industry professionals, military personnel, researchers, faculty, and students with an interest in cyber security.

Machine Learning Algorithms

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Publisher : Springer Nature
ISBN 13 : 3031163753
Total Pages : 109 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Machine Learning Algorithms by : Fuwei Li

Download or read book Machine Learning Algorithms written by Fuwei Li and published by Springer Nature. This book was released on 2022-11-14 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates the optimal adversarial attacks against several important signal processing algorithms. Through presenting the optimal attacks in wireless sensor networks, array signal processing, principal component analysis, etc, the authors reveal the robustness of the signal processing algorithms against adversarial attacks. Since data quality is crucial in signal processing, the adversary that can poison the data will be a significant threat to signal processing. Therefore, it is necessary and urgent to investigate the behavior of machine learning algorithms in signal processing under adversarial attacks. The authors in this book mainly examine the adversarial robustness of three commonly used machine learning algorithms in signal processing respectively: linear regression, LASSO-based feature selection, and principal component analysis (PCA). As to linear regression, the authors derive the optimal poisoning data sample and the optimal feature modifications, and also demonstrate the effectiveness of the attack against a wireless distributed learning system. The authors further extend the linear regression to LASSO-based feature selection and study the best strategy to mislead the learning system to select the wrong features. The authors find the optimal attack strategy by solving a bi-level optimization problem and also illustrate how this attack influences array signal processing and weather data analysis. In the end, the authors consider the adversarial robustness of the subspace learning problem. The authors examine the optimal modification strategy under the energy constraints to delude the PCA-based subspace learning algorithm. This book targets researchers working in machine learning, electronic information, and information theory as well as advanced-level students studying these subjects. R&D engineers who are working in machine learning, adversarial machine learning, robust machine learning, and technical consultants working on the security and robustness of machine learning are likely to purchase this book as a reference guide.

Safe and Trustworthy Machine Learning

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Publisher : Frontiers Media SA
ISBN 13 : 2889714144
Total Pages : 101 pages
Book Rating : 4.8/5 (897 download)

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Book Synopsis Safe and Trustworthy Machine Learning by : Bhavya Kailkhura

Download or read book Safe and Trustworthy Machine Learning written by Bhavya Kailkhura and published by Frontiers Media SA. This book was released on 2021-10-29 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Machine Learning for Data Science Handbook

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Publisher : Springer Nature
ISBN 13 : 3031246284
Total Pages : 975 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Machine Learning for Data Science Handbook by : Lior Rokach

Download or read book Machine Learning for Data Science Handbook written by Lior Rokach and published by Springer Nature. This book was released on 2023-08-17 with total page 975 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book organizes key concepts, theories, standards, methodologies, trends, challenges and applications of data mining and knowledge discovery in databases. It first surveys, then provides comprehensive yet concise algorithmic descriptions of methods, including classic methods plus the extensions and novel methods developed recently. It also gives in-depth descriptions of data mining applications in various interdisciplinary industries.

Adversarial Robustness in Machine Learning

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (138 download)

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Book Synopsis Adversarial Robustness in Machine Learning by : Muni Sreenivas Pydi

Download or read book Adversarial Robustness in Machine Learning written by Muni Sreenivas Pydi and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deep learning based classification algorithms perform poorly on adversarially perturbed data. Adversarial risk quantifies the performance of a classifier in the presence of an adversary. Numerous definitions of adversarial risk---not all mathematically rigorous and differing subtly in the details---have appeared in the literature. Adversarial attacks are designed to increase the adversarial risk of classifiers, and robust classifiers are sought that can resist such attacks. It was hitherto unknown what the theoretical limits on adversarial risk are, and whether there is an equilibrium in the game between the classifier and the adversary. In this thesis, we establish a mathematically rigorous foundation for adversarial robustness, derive algorithm-independent bounds on adversarial risk, and provide alternative characterizations based on distributional robustness and game theory. Key to these results are the numerous connections we discover between adversarial robustness and optimal transport theory. We begin by examining various definitions for adversarial risk, and laying down conditions for their measurability and equivalences. In binary classification with 0-1 loss, we show that the optimal adversarial risk is determined by an optimal transport cost between the probability distributions of the two classes. Using the couplings that achieve this cost, we derive the optimal robust classifiers for several univariate distributions. Using our results, we compute lower bounds on adversarial risk for several real-world datasets. We extend our results to general loss functions under convexity and smoothness assumptions. We close with alternative characterizations for adversarial robustness that lead to the proof of a pure Nash equilibrium in the two-player game between the adversary and the classifier. We show that adversarial risk is identical to the minimax risk in a robust hypothesis testing problem with Wasserstein uncertainty sets. Moreover, the optimal adversarial risk is the Bayes error between a worst-case pair of distributions belonging to these sets. Our theoretical results lead to several algorithmic insights for practitioners and motivate further study on the intersection of adversarial robustness and optimal transport.