Robustness Verification with Non-Uniform Randomized Smoothing PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Robustness Verification with Non-Uniform Randomized Smoothing PDF full book. Access full book title Robustness Verification with Non-Uniform Randomized Smoothing by Lucas Matthew Tecot. Download full books in PDF and EPUB format.
Author: Lucas Matthew Tecot
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
Get Book Here
Book Description
Formal verification via randomized smoothing has become an effective method for verifying the robustness of machine learning models to adversarial attacks. In this work, I extend randomized smoothing by allowing noises with independent variances on each input element of a smoothed classifier, enabling the flexibility of using non-uniform perturbations rather than the standard l-p norm perturbations. Furthermore, I provide practical optimization methods to find the optimal variance matrix through gradient descent. I evaluate my method on MNIST, Fashion-MNIST, CIFAR-10, ImageNet, and KITTI datasets and show that my optimized non-uniform smoothing noises can certify a region with guaranteed robustness magnitudes larger in volume than previous works. Additionally, my method can be used to evaluate the sensitivity of input features and identify non-robust and robust features.
Author: Lucas Matthew Tecot
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
Get Book Here
Book Description
Formal verification via randomized smoothing has become an effective method for verifying the robustness of machine learning models to adversarial attacks. In this work, I extend randomized smoothing by allowing noises with independent variances on each input element of a smoothed classifier, enabling the flexibility of using non-uniform perturbations rather than the standard l-p norm perturbations. Furthermore, I provide practical optimization methods to find the optimal variance matrix through gradient descent. I evaluate my method on MNIST, Fashion-MNIST, CIFAR-10, ImageNet, and KITTI datasets and show that my optimized non-uniform smoothing noises can certify a region with guaranteed robustness magnitudes larger in volume than previous works. Additionally, my method can be used to evaluate the sensitivity of input features and identify non-robust and robust features.
Author: Roman Vershynin
Publisher: Cambridge University Press
ISBN: 1108415199
Category : Business & Economics
Languages : en
Pages : 299
Get Book Here
Book Description
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author: Bruce Hajek
Publisher: Cambridge University Press
ISBN: 1316241246
Category : Technology & Engineering
Languages : en
Pages : 429
Get Book Here
Book Description
This engaging introduction to random processes provides students with the critical tools needed to design and evaluate engineering systems that must operate reliably in uncertain environments. A brief review of probability theory and real analysis of deterministic functions sets the stage for understanding random processes, whilst the underlying measure theoretic notions are explained in an intuitive, straightforward style. Students will learn to manage the complexity of randomness through the use of simple classes of random processes, statistical means and correlations, asymptotic analysis, sampling, and effective algorithms. Key topics covered include: • Calculus of random processes in linear systems • Kalman and Wiener filtering • Hidden Markov models for statistical inference • The estimation maximization (EM) algorithm • An introduction to martingales and concentration inequalities. Understanding of the key concepts is reinforced through over 100 worked examples and 300 thoroughly tested homework problems (half of which are solved in detail at the end of the book).
Author: Helmut Seidl
Publisher: Springer Science & Business Media
ISBN: 3642288685
Category : Computers
Languages : en
Pages : 614
Get Book Here
Book Description
This book constitutes the refereed proceedings of the 21st European Symposium on Programming, ESOP 2012, held in Tallinn, Estonia, as part of ETAPS 2012, in March/April 2012. The 28 full papers, presented together with one full length invited talk, were carefully reviewed and selected from 92 submissions. Papers were invited on all aspects of programming language research, including: programming paradigms and styles, methods and tools to write and specify programs and languages, methods and tools for reasoning about programs, methods and tools for implementation, and concurrency and distribution.
Author: Tor Lattimore
Publisher: Cambridge University Press
ISBN: 1108486827
Category : Business & Economics
Languages : en
Pages : 537
Get Book Here
Book Description
A comprehensive and rigorous introduction for graduate students and researchers, with applications in sequential decision-making problems.
Author: Tilman M. Davies
Publisher: No Starch Press
ISBN: 1593276516
Category : Computers
Languages : en
Pages : 833
Get Book Here
Book Description
The Book of R is a comprehensive, beginner-friendly guide to R, the world’s most popular programming language for statistical analysis. Even if you have no programming experience and little more than a grounding in the basics of mathematics, you’ll find everything you need to begin using R effectively for statistical analysis. You’ll start with the basics, like how to handle data and write simple programs, before moving on to more advanced topics, like producing statistical summaries of your data and performing statistical tests and modeling. You’ll even learn how to create impressive data visualizations with R’s basic graphics tools and contributed packages, like ggplot2 and ggvis, as well as interactive 3D visualizations using the rgl package. Dozens of hands-on exercises (with downloadable solutions) take you from theory to practice, as you learn: –The fundamentals of programming in R, including how to write data frames, create functions, and use variables, statements, and loops –Statistical concepts like exploratory data analysis, probabilities, hypothesis tests, and regression modeling, and how to execute them in R –How to access R’s thousands of functions, libraries, and data sets –How to draw valid and useful conclusions from your data –How to create publication-quality graphics of your results Combining detailed explanations with real-world examples and exercises, this book will provide you with a solid understanding of both statistics and the depth of R’s functionality. Make The Book of R your doorway into the growing world of data analysis.
Author: Raphaël Cerf
Publisher: Springer
ISBN: 3540348069
Category : Mathematics
Languages : en
Pages : 267
Get Book Here
Book Description
This volume is a synopsis of recent works aiming at a mathematically rigorous justification of the phase coexistence phenomenon, starting from a microscopic model. It is intended to be self-contained. Those proofs that can be found only in research papers have been included, whereas results for which the proofs can be found in classical textbooks are only quoted.
Author: Jayakrishnan Nair
Publisher: Cambridge University Press
ISBN: 1009062964
Category : Mathematics
Languages : en
Pages : 266
Get Book Here
Book Description
Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this engaging package.
Author: Steven M. LaValle
Publisher: Cambridge University Press
ISBN: 9780521862059
Category : Computers
Languages : en
Pages : 844
Get Book Here
Book Description
Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. Written for computer scientists and engineers with interests in artificial intelligence, robotics, or control theory, this is the only book on this topic that tightly integrates a vast body of literature from several fields into a coherent source for teaching and reference in a wide variety of applications. Difficult mathematical material is explained through hundreds of examples and illustrations.
Author: Jonas Peters
Publisher: MIT Press
ISBN: 0262037319
Category : Computers
Languages : en
Pages : 289
Get Book Here
Book Description
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.
