Machine Learning Under A Modern Optimization Lens

  machine learning under a modern optimization lens: Machine Learning Under a Modern Optimization Lens Dimitris Bertsimas, Jack William Dunn, 2019
  machine learning under a modern optimization lens: Optimization Over Integers Dimitris Bertsimas, Robert Weismantel, 2005
  machine learning under a modern optimization lens: Machine Learning Refined Jeremy Watt, Reza Borhani, Aggelos K. Katsaggelos, 2020-01-09 An intuitive approach to machine learning covering key concepts, real-world applications, and practical Python coding exercises.
  machine learning under a modern optimization lens: Advanced Finite Element Method in Structural Engineering Yu-Qiu Long, Song Cen, Zhi-Fei Long, 2009-09-29 Advanced Finite Element Method in Structural Engineering systematically introduces the research work on the Finite Element Method (FEM), which was completed by Prof. Yu-qiu Long and his research group in the past 25 years. Seven original theoretical achievements - for instance, the Generalized Conforming Element method, to name one - and their applications in the fields of structural engineering and computational mechanics are discussed in detail. The book also shows the new strategies for avoiding five difficulties that exist in traditional FEM (shear-locking problem of thick plate elements; sensitivity problem to mesh distortion; non-convergence problem of non-conforming elements; accuracy loss problem of stress solutions by displacement-based elements; stress singular point problem) by utilizing foregoing achievements.
  machine learning under a modern optimization lens: Data, Models, and Decisions Dimitris Bertsimas, Robert Michael Freund, 2004 Combines topics from two traditionally distinct quantitative subjects, probability/statistics and management science/optimization, in a unified treatment of quantitative methods and models for management. Stresses those fundamental concepts that are most important for the practical analysis of management decisions: modeling and evaluating uncertainty explicitly, understanding the dynamic nature of decision-making, using historical data and limited information effectively, simulating complex systems, and allocating scarce resources optimally.
  machine learning under a modern optimization lens: Probabilistic Machine Learning Kevin P. Murphy, 2022-03-01 A detailed and up-to-date introduction to machine learning, presented through the unifying lens of probabilistic modeling and Bayesian decision theory. This book offers a detailed and up-to-date introduction to machine learning (including deep learning) through the unifying lens of probabilistic modeling and Bayesian decision theory. The book covers mathematical background (including linear algebra and optimization), basic supervised learning (including linear and logistic regression and deep neural networks), as well as more advanced topics (including transfer learning and unsupervised learning). End-of-chapter exercises allow students to apply what they have learned, and an appendix covers notation. Probabilistic Machine Learning grew out of the author’s 2012 book, Machine Learning: A Probabilistic Perspective. More than just a simple update, this is a completely new book that reflects the dramatic developments in the field since 2012, most notably deep learning. In addition, the new book is accompanied by online Python code, using libraries such as scikit-learn, JAX, PyTorch, and Tensorflow, which can be used to reproduce nearly all the figures; this code can be run inside a web browser using cloud-based notebooks, and provides a practical complement to the theoretical topics discussed in the book. This introductory text will be followed by a sequel that covers more advanced topics, taking the same probabilistic approach.
  machine learning under a modern optimization lens: Handbook On Big Data And Machine Learning In The Physical Sciences (In 2 Volumes) , 2020-03-10 This compendium provides a comprehensive collection of the emergent applications of big data, machine learning, and artificial intelligence technologies to present day physical sciences ranging from materials theory and imaging to predictive synthesis and automated research. This area of research is among the most rapidly developing in the last several years in areas spanning materials science, chemistry, and condensed matter physics.Written by world renowned researchers, the compilation of two authoritative volumes provides a distinct summary of the modern advances in instrument — driven data generation and analytics, establishing the links between the big data and predictive theories, and outlining the emerging field of data and physics-driven predictive and autonomous systems.
  machine learning under a modern optimization lens: The Lion Way Roberto Battiti, Mauro Brunato, 2014-02-21 Learning and Intelligent Optimization (LION) is the combination of learning from data and optimization applied to solve complex and dynamic problems. The LION way is about increasing the automation level and connecting data directly to decisions and actions. More power is directly in the hands of decision makers in a self-service manner, without resorting to intermediate layers of data scientists. LION is a complex array of mechanisms, like the engine in an automobile, but the user (driver) does not need to know the inner workings of the engine in order to realize its tremendous benefits. LION's adoption will create a prairie fire of innovation which will reach most businesses in the next decades. Businesses, like plants in wildfire-prone ecosystems, will survive and prosper by adapting and embracing LION techniques, or they risk being transformed from giant trees to ashes by the spreading competition.
  machine learning under a modern optimization lens: The Analytics Edge Dimitris Bertsimas, Allison K. O'Hair, William R. Pulleyblank, 2016 Provides a unified, insightful, modern, and entertaining treatment of analytics. The book covers the science of using data to build models, improve decisions, and ultimately add value to institutions and individuals--Back cover.
  machine learning under a modern optimization lens: Rollout, Policy Iteration, and Distributed Reinforcement Learning Dimitri Bertsekas, 2021-08-20 The purpose of this book is to develop in greater depth some of the methods from the author's Reinforcement Learning and Optimal Control recently published textbook (Athena Scientific, 2019). In particular, we present new research, relating to systems involving multiple agents, partitioned architectures, and distributed asynchronous computation. We pay special attention to the contexts of dynamic programming/policy iteration and control theory/model predictive control. We also discuss in some detail the application of the methodology to challenging discrete/combinatorial optimization problems, such as routing, scheduling, assignment, and mixed integer programming, including the use of neural network approximations within these contexts. The book focuses on the fundamental idea of policy iteration, i.e., start from some policy, and successively generate one or more improved policies. If just one improved policy is generated, this is called rollout, which, based on broad and consistent computational experience, appears to be one of the most versatile and reliable of all reinforcement learning methods. In this book, rollout algorithms are developed for both discrete deterministic and stochastic DP problems, and the development of distributed implementations in both multiagent and multiprocessor settings, aiming to take advantage of parallelism. Approximate policy iteration is more ambitious than rollout, but it is a strictly off-line method, and it is generally far more computationally intensive. This motivates the use of parallel and distributed computation. One of the purposes of the monograph is to discuss distributed (possibly asynchronous) methods that relate to rollout and policy iteration, both in the context of an exact and an approximate implementation involving neural networks or other approximation architectures. Much of the new research is inspired by the remarkable AlphaZero chess program, where policy iteration, value and policy networks, approximate lookahead minimization, and parallel computation all play an important role.
  machine learning under a modern optimization lens: Numerical Algorithms Justin Solomon, 2015-06-24 Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig
  machine learning under a modern optimization lens: A Gentle Introduction to Optimization B. Guenin, J. Könemann, L. Tunçel, 2014-07-31 Optimization is an essential technique for solving problems in areas as diverse as accounting, computer science and engineering. Assuming only basic linear algebra and with a clear focus on the fundamental concepts, this textbook is the perfect starting point for first- and second-year undergraduate students from a wide range of backgrounds and with varying levels of ability. Modern, real-world examples motivate the theory throughout. The authors keep the text as concise and focused as possible, with more advanced material treated separately or in starred exercises. Chapters are self-contained so that instructors and students can adapt the material to suit their own needs and a wide selection of over 140 exercises gives readers the opportunity to try out the skills they gain in each section. Solutions are available for instructors. The book also provides suggestions for further reading to help students take the next step to more advanced material.
  machine learning under a modern optimization lens: Automated Machine Learning Frank Hutter, Lars Kotthoff, Joaquin Vanschoren, 2019-05-17 This open access book presents the first comprehensive overview of general methods in Automated Machine Learning (AutoML), collects descriptions of existing systems based on these methods, and discusses the first series of international challenges of AutoML systems. The recent success of commercial ML applications and the rapid growth of the field has created a high demand for off-the-shelf ML methods that can be used easily and without expert knowledge. However, many of the recent machine learning successes crucially rely on human experts, who manually select appropriate ML architectures (deep learning architectures or more traditional ML workflows) and their hyperparameters. To overcome this problem, the field of AutoML targets a progressive automation of machine learning, based on principles from optimization and machine learning itself. This book serves as a point of entry into this quickly-developing field for researchers and advanced students alike, as well as providing a reference for practitioners aiming to use AutoML in their work.
  machine learning under a modern optimization lens: Machine Learning in Asset Pricing Stefan Nagel, 2021-05-11 A groundbreaking, authoritative introduction to how machine learning can be applied to asset pricing Investors in financial markets are faced with an abundance of potentially value-relevant information from a wide variety of different sources. In such data-rich, high-dimensional environments, techniques from the rapidly advancing field of machine learning (ML) are well-suited for solving prediction problems. Accordingly, ML methods are quickly becoming part of the toolkit in asset pricing research and quantitative investing. In this book, Stefan Nagel examines the promises and challenges of ML applications in asset pricing. Asset pricing problems are substantially different from the settings for which ML tools were developed originally. To realize the potential of ML methods, they must be adapted for the specific conditions in asset pricing applications. Economic considerations, such as portfolio optimization, absence of near arbitrage, and investor learning can guide the selection and modification of ML tools. Beginning with a brief survey of basic supervised ML methods, Nagel then discusses the application of these techniques in empirical research in asset pricing and shows how they promise to advance the theoretical modeling of financial markets. Machine Learning in Asset Pricing presents the exciting possibilities of using cutting-edge methods in research on financial asset valuation.
  machine learning under a modern optimization lens: Machine Learning for Audio, Image and Video Analysis Francesco Camastra, Alessandro Vinciarelli, 2015-07-21 This second edition focuses on audio, image and video data, the three main types of input that machines deal with when interacting with the real world. A set of appendices provides the reader with self-contained introductions to the mathematical background necessary to read the book. Divided into three main parts, From Perception to Computation introduces methodologies aimed at representing the data in forms suitable for computer processing, especially when it comes to audio and images. Whilst the second part, Machine Learning includes an extensive overview of statistical techniques aimed at addressing three main problems, namely classification (automatically assigning a data sample to one of the classes belonging to a predefined set), clustering (automatically grouping data samples according to the similarity of their properties) and sequence analysis (automatically mapping a sequence of observations into a sequence of human-understandable symbols). The third part Applications shows how the abstract problems defined in the second part underlie technologies capable to perform complex tasks such as the recognition of hand gestures or the transcription of handwritten data. Machine Learning for Audio, Image and Video Analysis is suitable for students to acquire a solid background in machine learning as well as for practitioners to deepen their knowledge of the state-of-the-art. All application chapters are based on publicly available data and free software packages, thus allowing readers to replicate the experiments.
  machine learning under a modern optimization lens: Handbook of Research on Applied Intelligence for Health and Clinical Informatics Thakare, Anuradha Dheeraj, Wagh, Sanjeev J., Bhende, Manisha Sunil, Anter, Ahmed M., Gao, Xiao-Zhi, 2021-10-22 Currently, informatics within the field of public health is a developing and growing industry. Clinical informatics are used in direct patient care by supplying medical practitioners with information that can be used to develop a care plan. Intelligent applications in clinical informatics facilitates with the technology-based solutions to analyze data or medical images and help clinicians to retrieve that information. Decision models aid with making complex decisions especially in uncertain situations. The Handbook of Research on Applied Intelligence for Health and Clinical Informatics is a comprehensive reference book that focuses on the study of resources and methods for the management of healthcare infrastructure and information. This book provides insights on how applied intelligence with deep learning, experiential learning, and more will impact healthcare and clinical information processing. The content explores the representation, processing, and communication of clinical information in natural and engineered systems. This book covers a range of topics including applied intelligence, medical imaging, telehealth, and decision support systems, and also looks at technologies and tools used in the detection and diagnosis of medical conditions such as cancers, diabetes, heart disease, lung disease, and prenatal syndromes. It is an essential reference source for diagnosticians, medical professionals, imaging specialists, data specialists, IT consultants, medical technologists, academicians, researchers, industrial experts, scientists, and students.
  machine learning under a modern optimization lens: Nonlinear Programming Dimitri P. Bertsekas, 1999
  machine learning under a modern optimization lens: Deep Learning Architectures Ovidiu Calin, 2020-02-13 This book describes how neural networks operate from the mathematical point of view. As a result, neural networks can be interpreted both as function universal approximators and information processors. The book bridges the gap between ideas and concepts of neural networks, which are used nowadays at an intuitive level, and the precise modern mathematical language, presenting the best practices of the former and enjoying the robustness and elegance of the latter. This book can be used in a graduate course in deep learning, with the first few parts being accessible to senior undergraduates. In addition, the book will be of wide interest to machine learning researchers who are interested in a theoretical understanding of the subject.
  machine learning under a modern optimization lens: Optimization of Power System Operation Jizhong Zhu, 2016-12-08 Optimization of Power System Operation, 2nd Edition, offers a practical, hands-on guide to theoretical developments and to the application of advanced optimization methods to realistic electric power engineering problems. The book includes: New chapter on Application of Renewable Energy, and a new chapter on Operation of Smart Grid New topics include wheeling model, multi-area wheeling, and the total transfer capability computation in multiple areas Continues to provide engineers and academics with a complete picture of the optimization of techniques used in modern power system operation
  machine learning under a modern optimization lens: Optimization in Machine Learning and Applications Anand J. Kulkarni, Suresh Chandra Satapathy, 2019-11-29 This book discusses one of the major applications of artificial intelligence: the use of machine learning to extract useful information from multimodal data. It discusses the optimization methods that help minimize the error in developing patterns and classifications, which further helps improve prediction and decision-making. The book also presents formulations of real-world machine learning problems, and discusses AI solution methodologies as standalone or hybrid approaches. Lastly, it proposes novel metaheuristic methods to solve complex machine learning problems. Featuring valuable insights, the book helps readers explore new avenues leading toward multidisciplinary research discussions.
  machine learning under a modern optimization lens: Optimal Control Brian D. O. Anderson, John B. Moore, 2007-02-27 Numerous examples highlight this treatment of the use of linear quadratic Gaussian methods for control system design. It explores linear optimal control theory from an engineering viewpoint, with illustrations of practical applications. Key topics include loop-recovery techniques, frequency shaping, and controller reduction. Numerous examples and complete solutions. 1990 edition.
  machine learning under a modern optimization lens: Genetic Algorithms in Search, Optimization, and Machine Learning David Edward Goldberg, 1989 A gentle introduction to genetic algorithms. Genetic algorithms revisited: mathematical foundations. Computer implementation of a genetic algorithm. Some applications of genetic algorithms. Advanced operators and techniques in genetic search. Introduction to genetics-based machine learning. Applications of genetics-based machine learning. A look back, a glance ahead. A review of combinatorics and elementary probability. Pascal with random number generation for fortran, basic, and cobol programmers. A simple genetic algorithm (SGA) in pascal. A simple classifier system(SCS) in pascal. Partition coefficient transforms for problem-coding analysis.
  machine learning under a modern optimization lens: Galileo Unbound David D. Nolte, 2018-07-12 Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
  machine learning under a modern optimization lens: Optimization for Machine Learning Suvrit Sra, Sebastian Nowozin, Stephen J. Wright, 2012 An up-to-date account of the interplay between optimization and machine learning, accessible to students and researchers in both communities. The interplay between optimization and machine learning is one of the most important developments in modern computational science. Optimization formulations and methods are proving to be vital in designing algorithms to extract essential knowledge from huge volumes of data. Machine learning, however, is not simply a consumer of optimization technology but a rapidly evolving field that is itself generating new optimization ideas. This book captures the state of the art of the interaction between optimization and machine learning in a way that is accessible to researchers in both fields. Optimization approaches have enjoyed prominence in machine learning because of their wide applicability and attractive theoretical properties. The increasing complexity, size, and variety of today's machine learning models call for the reassessment of existing assumptions. This book starts the process of reassessment. It describes the resurgence in novel contexts of established frameworks such as first-order methods, stochastic approximations, convex relaxations, interior-point methods, and proximal methods. It also devotes attention to newer themes such as regularized optimization, robust optimization, gradient and subgradient methods, splitting techniques, and second-order methods. Many of these techniques draw inspiration from other fields, including operations research, theoretical computer science, and subfields of optimization. The book will enrich the ongoing cross-fertilization between the machine learning community and these other fields, and within the broader optimization community.
  machine learning under a modern optimization lens: Practical Machine Learning with Rust Joydeep Bhattacharjee, 2019-12-10 Explore machine learning in Rust and learn about the intricacies of creating machine learning applications. This book begins by covering the important concepts of machine learning such as supervised, unsupervised, and reinforcement learning, and the basics of Rust. Further, you’ll dive into the more specific fields of machine learning, such as computer vision and natural language processing, and look at the Rust libraries that help create applications for those domains. We will also look at how to deploy these applications either on site or over the cloud. After reading Practical Machine Learning with Rust, you will have a solid understanding of creating high computation libraries using Rust. Armed with the knowledge of this amazing language, you will be able to create applications that are more performant, memory safe, and less resource heavy. What You Will Learn Write machine learning algorithms in RustUse Rust libraries for different tasks in machine learningCreate concise Rust packages for your machine learning applicationsImplement NLP and computer vision in RustDeploy your code in the cloud and on bare metal servers Who This Book Is For Machine learning engineers and software engineers interested in building machine learning applications in Rust.
  machine learning under a modern optimization lens: Perturbations, Optimization, and Statistics Tamir Hazan, George Papandreou, Daniel Tarlow, 2017-09-22 A description of perturbation-based methods developed in machine learning to augment novel optimization methods with strong statistical guarantees. In nearly all machine learning, decisions must be made given current knowledge. Surprisingly, making what is believed to be the best decision is not always the best strategy, even when learning in a supervised learning setting. An emerging body of work on learning under different rules applies perturbations to decision and learning procedures. These methods provide simple and highly efficient learning rules with improved theoretical guarantees. This book describes perturbation-based methods developed in machine learning to augment novel optimization methods with strong statistical guarantees, offering readers a state-of-the-art overview. Chapters address recent modeling ideas that have arisen within the perturbations framework, including Perturb & MAP, herding, and the use of neural networks to map generic noise to distribution over highly structured data. They describe new learning procedures for perturbation models, including an improved EM algorithm and a learning algorithm that aims to match moments of model samples to moments of data. They discuss understanding the relation of perturbation models to their traditional counterparts, with one chapter showing that the perturbations viewpoint can lead to new algorithms in the traditional setting. And they consider perturbation-based regularization in neural networks, offering a more complete understanding of dropout and studying perturbations in the context of deep neural networks.
  machine learning under a modern optimization lens: Deep Learning Ian Goodfellow, Yoshua Bengio, Aaron Courville, 2016-11-10 An introduction to a broad range of topics in deep learning, covering mathematical and conceptual background, deep learning techniques used in industry, and research perspectives. “Written by three experts in the field, Deep Learning is the only comprehensive book on the subject.” —Elon Musk, cochair of OpenAI; cofounder and CEO of Tesla and SpaceX Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.
  machine learning under a modern optimization lens: Machine Learning for Developers Rodolfo Bonnin, 2017-10-26 Your one-stop guide to becoming a Machine Learning expert. About This Book Learn to develop efficient and intelligent applications by leveraging the power of Machine Learning A highly practical guide explaining the concepts of problem solving in the easiest possible manner Implement Machine Learning in the most practical way Who This Book Is For This book will appeal to any developer who wants to know what Machine Learning is and is keen to use Machine Learning to make their day-to-day apps fast, high performing, and accurate. Any developer who wants to enter the field of Machine Learning can effectively use this book as an entry point. What You Will Learn Learn the math and mechanics of Machine Learning via a developer-friendly approach Get to grips with widely used Machine Learning algorithms/techniques and how to use them to solve real problems Get a feel for advanced concepts, using popular programming frameworks. Prepare yourself and other developers for working in the new ubiquitous field of Machine Learning Get an overview of the most well known and powerful tools, to solve computing problems using Machine Learning. Get an intuitive and down-to-earth introduction to current Machine Learning areas, and apply these concepts on interesting and cutting-edge problems. In Detail Most of us have heard about the term Machine Learning, but surprisingly the question frequently asked by developers across the globe is, “How do I get started in Machine Learning?”. One reason could be attributed to the vastness of the subject area because people often get overwhelmed by the abstractness of ML and terms such as regression, supervised learning, probability density function, and so on. This book is a systematic guide teaching you how to implement various Machine Learning techniques and their day-to-day application and development. You will start with the very basics of data and mathematical models in easy-to-follow language that you are familiar with; you will feel at home while implementing the examples. The book will introduce you to various libraries and frameworks used in the world of Machine Learning, and then, without wasting any time, you will get to the point and implement Regression, Clustering, classification, Neural networks, and more with fun examples. As you get to grips with the techniques, you'll learn to implement those concepts to solve real-world scenarios for ML applications such as image analysis, Natural Language processing, and anomaly detections of time series data. By the end of the book, you will have learned various ML techniques to develop more efficient and intelligent applications. Style and approach This book gives you a glimpse of Machine Learning Models and the application of models at scale using clustering, classification, regression and reinforcement learning with fun examples. Hands-on examples will be presented to understand the power of problem solving with Machine Learning and Advanced architectures, software installation, and configuration.
  machine learning under a modern optimization lens: Utilizing Educational Data Mining Techniques for Improved Learning: Emerging Research and Opportunities Bhatt, Chintan, Sajja, Priti Srinivas, Liyanage, Sidath, 2019-08-02 Modern education has increased its reach through ICT tools and techniques. To manage educational data with the help of modern artificial intelligence, data and web mining techniques on dedicated cloud or grid platforms for educational institutes can be used. By utilizing data science techniques to manage educational data, the safekeeping, delivery, and use of knowledge can be increased for better quality education. Utilizing Educational Data Mining Techniques for Improved Learning: Emerging Research and Opportunities is a critical scholarly resource that explores data mining and management techniques that promote the improvement and optimization of educational data systems. The book intends to provide new models, platforms, tools, and protocols in data science for educational data analysis and introduces innovative hybrid system models dedicated to data science. Including topics such as automatic assessment, educational analytics, and machine learning, this book is essential for IT specialists, data analysts, computer engineers, education professionals, administrators, policymakers, researchers, academicians, and technology experts.
  machine learning under a modern optimization lens: Computer Vision Simon J. D. Prince, 2012-06-18 A modern treatment focusing on learning and inference, with minimal prerequisites, real-world examples and implementable algorithms.
  machine learning under a modern optimization lens: Practical Methods of Optimization R. Fletcher, 2013-06-06 Fully describes optimization methods that are currently most valuable in solving real-life problems. Since optimization has applications in almost every branch of science and technology, the text emphasizes their practical aspects in conjunction with the heuristics useful in making them perform more reliably and efficiently. To this end, it presents comparative numerical studies to give readers a feel for possibile applications and to illustrate the problems in assessing evidence. Also provides theoretical background which provides insights into how methods are derived. This edition offers revised coverage of basic theory and standard techniques, with updated discussions of line search methods, Newton and quasi-Newton methods, and conjugate direction methods, as well as a comprehensive treatment of restricted step or trust region methods not commonly found in the literature. Also includes recent developments in hybrid methods for nonlinear least squares; an extended discussion of linear programming, with new methods for stable updating of LU factors; and a completely new section on network programming. Chapters include computer subroutines, worked examples, and study questions.
  machine learning under a modern optimization lens: TinyML Pete Warden, Daniel Situnayake, 2019-12-16 Deep learning networks are getting smaller. Much smaller. The Google Assistant team can detect words with a model just 14 kilobytes in size—small enough to run on a microcontroller. With this practical book you’ll enter the field of TinyML, where deep learning and embedded systems combine to make astounding things possible with tiny devices. Pete Warden and Daniel Situnayake explain how you can train models small enough to fit into any environment. Ideal for software and hardware developers who want to build embedded systems using machine learning, this guide walks you through creating a series of TinyML projects, step-by-step. No machine learning or microcontroller experience is necessary. Build a speech recognizer, a camera that detects people, and a magic wand that responds to gestures Work with Arduino and ultra-low-power microcontrollers Learn the essentials of ML and how to train your own models Train models to understand audio, image, and accelerometer data Explore TensorFlow Lite for Microcontrollers, Google’s toolkit for TinyML Debug applications and provide safeguards for privacy and security Optimize latency, energy usage, and model and binary size
  machine learning under a modern optimization lens: Machine Learning Kevin P. Murphy, 2012-08-24 A comprehensive introduction to machine learning that uses probabilistic models and inference as a unifying approach. Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package—PMTK (probabilistic modeling toolkit)—that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.
  machine learning under a modern optimization lens: Financial Signal Processing and Machine Learning Ali N. Akansu, Sanjeev R. Kulkarni, Dmitry M. Malioutov, 2016-04-21 The modern financial industry has been required to deal with large and diverse portfolios in a variety of asset classes often with limited market data available. Financial Signal Processing and Machine Learning unifies a number of recent advances made in signal processing and machine learning for the design and management of investment portfolios and financial engineering. This book bridges the gap between these disciplines, offering the latest information on key topics including characterizing statistical dependence and correlation in high dimensions, constructing effective and robust risk measures, and their use in portfolio optimization and rebalancing. The book focuses on signal processing approaches to model return, momentum, and mean reversion, addressing theoretical and implementation aspects. It highlights the connections between portfolio theory, sparse learning and compressed sensing, sparse eigen-portfolios, robust optimization, non-Gaussian data-driven risk measures, graphical models, causal analysis through temporal-causal modeling, and large-scale copula-based approaches. Key features: Highlights signal processing and machine learning as key approaches to quantitative finance. Offers advanced mathematical tools for high-dimensional portfolio construction, monitoring, and post-trade analysis problems. Presents portfolio theory, sparse learning and compressed sensing, sparsity methods for investment portfolios. including eigen-portfolios, model return, momentum, mean reversion and non-Gaussian data-driven risk measures with real-world applications of these techniques. Includes contributions from leading researchers and practitioners in both the signal and information processing communities, and the quantitative finance community.
  machine learning under a modern optimization lens: Algorithmic Aspects of Machine Learning Ankur Moitra, 2018-09-27 Introduces cutting-edge research on machine learning theory and practice, providing an accessible, modern algorithmic toolkit.
  machine learning under a modern optimization lens: Reinforcement Learning and Stochastic Optimization Warren B. Powell, 2022-03-15 REINFORCEMENT LEARNING AND STOCHASTIC OPTIMIZATION Clearing the jungle of stochastic optimization Sequential decision problems, which consist of “decision, information, decision, information,” are ubiquitous, spanning virtually every human activity ranging from business applications, health (personal and public health, and medical decision making), energy, the sciences, all fields of engineering, finance, and e-commerce. The diversity of applications attracted the attention of at least 15 distinct fields of research, using eight distinct notational systems which produced a vast array of analytical tools. A byproduct is that powerful tools developed in one community may be unknown to other communities. Reinforcement Learning and Stochastic Optimization offers a single canonical framework that can model any sequential decision problem using five core components: state variables, decision variables, exogenous information variables, transition function, and objective function. This book highlights twelve types of uncertainty that might enter any model and pulls together the diverse set of methods for making decisions, known as policies, into four fundamental classes that span every method suggested in the academic literature or used in practice. Reinforcement Learning and Stochastic Optimization is the first book to provide a balanced treatment of the different methods for modeling and solving sequential decision problems, following the style used by most books on machine learning, optimization, and simulation. The presentation is designed for readers with a course in probability and statistics, and an interest in modeling and applications. Linear programming is occasionally used for specific problem classes. The book is designed for readers who are new to the field, as well as those with some background in optimization under uncertainty. Throughout this book, readers will find references to over 100 different applications, spanning pure learning problems, dynamic resource allocation problems, general state-dependent problems, and hybrid learning/resource allocation problems such as those that arose in the COVID pandemic. There are 370 exercises, organized into seven groups, ranging from review questions, modeling, computation, problem solving, theory, programming exercises and a “diary problem” that a reader chooses at the beginning of the book, and which is used as a basis for questions throughout the rest of the book.
  machine learning under a modern optimization lens: Machine Learning with R Brett Lantz, 2013-10-25 Written as a tutorial to explore and understand the power of R for machine learning. This practical guide that covers all of the need to know topics in a very systematic way. For each machine learning approach, each step in the process is detailed, from preparing the data for analysis to evaluating the results. These steps will build the knowledge you need to apply them to your own data science tasks.Intended for those who want to learn how to use R's machine learning capabilities and gain insight from your data. Perhaps you already know a bit about machine learning, but have never used R; or perhaps you know a little R but are new to machine learning. In either case, this book will get you up and running quickly. It would be helpful to have a bit of familiarity with basic programming concepts, but no prior experience is required.
  machine learning under a modern optimization lens: Machine Learning Design Patterns Valliappa Lakshmanan, Sara Robinson, Michael Munn, 2020-10-15 The design patterns in this book capture best practices and solutions to recurring problems in machine learning. The authors, three Google engineers, catalog proven methods to help data scientists tackle common problems throughout the ML process. These design patterns codify the experience of hundreds of experts into straightforward, approachable advice. In this book, you will find detailed explanations of 30 patterns for data and problem representation, operationalization, repeatability, reproducibility, flexibility, explainability, and fairness. Each pattern includes a description of the problem, a variety of potential solutions, and recommendations for choosing the best technique for your situation. You'll learn how to: Identify and mitigate common challenges when training, evaluating, and deploying ML models Represent data for different ML model types, including embeddings, feature crosses, and more Choose the right model type for specific problems Build a robust training loop that uses checkpoints, distribution strategy, and hyperparameter tuning Deploy scalable ML systems that you can retrain and update to reflect new data Interpret model predictions for stakeholders and ensure models are treating users fairly
  machine learning under a modern optimization lens: Reinforcement Learning and Optimal Control Dimitri P. Bertsekas, 2020
  machine learning under a modern optimization lens: The Great Mental Models, Volume 1 Shane Parrish, Rhiannon Beaubien, 2024-10-15 Discover the essential thinking tools you’ve been missing with The Great Mental Models series by Shane Parrish, New York Times bestselling author and the mind behind the acclaimed Farnam Street blog and “The Knowledge Project” podcast. This first book in the series is your guide to learning the crucial thinking tools nobody ever taught you. Time and time again, great thinkers such as Charlie Munger and Warren Buffett have credited their success to mental models–representations of how something works that can scale onto other fields. Mastering a small number of mental models enables you to rapidly grasp new information, identify patterns others miss, and avoid the common mistakes that hold people back. The Great Mental Models: Volume 1, General Thinking Concepts shows you how making a few tiny changes in the way you think can deliver big results. Drawing on examples from history, business, art, and science, this book details nine of the most versatile, all-purpose mental models you can use right away to improve your decision making and productivity. This book will teach you how to: Avoid blind spots when looking at problems. Find non-obvious solutions. Anticipate and achieve desired outcomes. Play to your strengths, avoid your weaknesses, … and more. The Great Mental Models series demystifies once elusive concepts and illuminates rich knowledge that traditional education overlooks. This series is the most comprehensive and accessible guide on using mental models to better understand our world, solve problems, and gain an advantage.
Inventory Management in the Era of Big Data - MIT
machine learning techniques employed do not address optimal decision-making under uncertainty that is appropriate for operations management prob-lems and, in particular, for inventory management. We study how these data, leveraged appropriately, can correctly and successfully inform inventory man-agement decisions and provide a competitive edge.

Street-lights LED Lens Design Optimization using Machine Learning
keywords: lens optimization, machine learning, deep learning, neural network, multi-output, regression. i. Contents Contents ... LED lenses are an important aspect of modern lighting technology, as they can help re-duce energy consumption and contribute to a more sustainable environment. In order to

Toward Predictive Digital Twins
• Use machine learning to train an interpretable, explainable reactive model asset state noisy sensor data ... Bertsimas, D., and Dunn, J., "Machine Learning under a Modern Optimization Lens." Dynamic Ideas (2018). Title: Toward predictive digital twins via component-based reduced-order models and interpretable machine learning

Baichuan Mo - MIT
Relevant classes: Machine Learning •Machine Learning Under Modern Optimization Lens •Deep Learning • Reinforcement Learning •Linear Optimization (A+) •Non-linear Optimization •Integer and Combinatorial Optimization •Robust Optimization •Fundamentals of Probability •Modern Discrete Probability •Applied Probability

KIMBERLY VILLALOBOS CARBALLO - GitHub Pages
Thesis: Integrating Optimization and Machine Learning: Theory, Computation and Healthcare Applications Massachusetts Institute of Technology Cambridge, MA, USA Bachelor of Science in Mathematics. GPA: 5.0/5.0 2015 - 2019 ... Machine Learning Under a Modern Optimization Lens (MIT 15.095) Guest Lecture 2023 ...

Develop More Accurate Machine Learning Models with MIP
The book provides an original treatment of machine learning (ML) using convex, robust and mixed integer optimization that leads to solutions to central ML problems at large scale that can be found in seconds/minutes, can be certi ed to be optimal in minutes/hours, and outperform classical heuristic approaches in out-of-sample experiments.

Best subset selection via a modern optimization lens
In this paper, we address problem (1.1) using modern optimization methods, specifically mixed integer optimization (MIO) and a discrete extension of first-order continuous optimization methods. Using a wide variety of synthetic and real datasets, we demonstrate that our approach solves problems with n in the 1000s

Baichuan Mo - MIT
Relevant classes: Machine Learning •Machine Learning Under Modern Optimization Lens •Deep Learning • Reinforcement Learning •Linear Optimization (A+) •Non-linear Optimization •Integer and Combinatorial Optimization •Robust Optimization •Fundamentals of Probability •Modern Discrete Probability •Applied Probability

Modern Machine Learning: Applications and Methods - Springer
Modern Machine Learning: Applications and Methods 21 2 How Can We Teach a Machine to Learn? When we talk about ML we are referring to the process through which a computer learns how to solve a problem. This learning can be classified in two main different types of learning: supervised and unsupervised (Géron, 2019). 2.1 Supervised Learning

Understanding modern machine learning models through the lens …
Theory for Neural Networks. The empirical success of deep learning has inspired many fun-damental research questions in statistical machine learning. Firstly, large neural networks are often trained in the overparameterized regime, i.e., the number of …

Understanding modern machine learning models through the lens …
RidgeRegressioninHighDimensions ProblemSetting&Assumptions • DataGeneration: y i = x⊤β ∗ + ε i,1≤i ≤n. x i ∈Rd. i.i.d.labelnoisesatisfiesE[ε] = 0,Var ...

Optimal classification trees Dimitris Bertsimas & Jack Dunn
Machine Learning ISSN 0885-6125 Volume 106 Number 7 Mach Learn (2017) 106:1039-1082 DOI 10.1007/s10994-017-5633-9 Optimal classification trees ... examination of statistics under a modern optimization lens by using MIO to formulate and solve the decision tree training problem, and provide empirical evidence of the success of ...

Best subset selection via a modern optimization lens
In this paper, we address problem (1.1) using modern optimization methods, specifically mixed integer optimization (MIO) and a discrete extension of first-order continuous optimization methods. Using a wide variety of synthetic and real datasets, we demonstrate that our approach solves problems with n in the 1000s

Operations Research Center - Massachusetts Institute of Technology
Conducting research at the intersection of machine learning and optimization, with application to ... for Machine Learning Under a Modern Optimization Lens (15.095) ... Teaching assistant for a class which provides MIT graduate students with a modern treatment of machine learning using the lenses of convex, robust, and mixed-integer ...

Machine Learning Under A Modern Optimization Lens (PDF)
Machine Learning Under A Modern Optimization Lens Machine Learning Under a Modern Optimization Lens Dimitris Bertsimas,Jack William Dunn,2019 MACHINE LEARNING Chandra S.S., Vinod,Hareendran S., Anand,2021-01-01 The present book is primarily intended for

Learning Interpretable Decision Rule Sets: A Submodular Optimization …
Interpretability is becoming one of the key considerations when deploying machine learning models to high-stake decision-making scenarios. Black box models, such as random forests and deep neural ... the rule set learning problem was revisited under modern optimization lens and several new algorithms were developed [22, 49, 28, 35, 48, 51 ...

Optimization for Machine Learning - Massachusetts Institute of …
Optimization for Machine Learning April 27, 2021 Lecture 17: Geometric Optimization — I 6.881: MIT ... Under the exponential map, this subspace is mapped to a two dimensional submanifold of U ⇢ M. The sectional curvature (x, U ) is defined as the Gauss curvature of U at x. As we will mainly analyze manifold trigonometry, for worst-case ...

Operations Research - MIT
2. Mixed Integer Optimization Background In this section, we present a brief overview of mixed inte-ger optimization (MIO), including the simply astonishing advances it has enjoyed in the last 25 years. The general form of an MIQO problem is as follows: min 8`T Q`C`T a9 s0t0 A`¶b † i 2801191 8i2' † j 2 C1 8j y'1

Cynthia Zeng - GitHub Pages
MIT Machine Learning Under a Modern Optimization Lens Cambridge, US Teaching Assistant Fall, 2022 ·Master of Business Analytics core course; 100+ students. ·Provided Master and Ph.D. students with a unified, insightful, and modern treatment of machine learning using the lenses of convex, robust, and mixed-integer optimization.

Large area optimization of meta-lens via data-free machine learning
ARTICLE Large area optimization of meta-lens via data-free machine learning Maksym Zhelyeznyakov 1 , Johannes Fröch1,2, Anna Wirth-Singh2, Jaebum Noh3, Junsuk Rho 3,4,5, Steve Brunton 6 & Arka ...

A Machine Learning-based Framework for Optimizing the …
in traffic and network state. Advances in machine learning and parallel computing underpin new powerful tools that have the potential to tackle these complex challenges. In this paper, we develop a general machine learning-based framework that leverages artificial intelligence to forecast future traffic demands and characterize traffic ...

Predictive and Prescriptive Methods in Operations Research and Machine …
focus on ML problems from a modern optimization perspective. For sparse shape-constrained regression problems, we propose modern optimization based algorithms that are scalable, and recover the true support with high accuracy and low false positive rates. Thesis Supervisor: Dimitris J. Bertsimas Title: Boeing Leaders for Global Operations Professor

Learning Interpretable Decision Rule Sets: A Submodular Optimization …
Interpretability is becoming one of the key considerations when deploying machine learning models to high-stake decision-making scenarios. Black box models, such as random forests and deep neural ... the rule set learning problem was revisited under modern optimization lens and several new algorithms were developed [22, 49, 28, 35, 48, 51 ...

Vassilis Digalakis Jr - MIT
Machine Learning Under a Modern Optimization Lens (15.095) { Instructor in charge: Dimitris Bertsimas. { Teaching assistant for a class which provides MIT graduate students with a modern treatment of machine learning using the lenses of convex, robust, and mixed-integer optimization.

Operations Research Center
2019 15.095 Machine Learning Under a Modern Optimization Lens TA(MBaN/MSc/PhD level) (Fall) Instructor: Dimitris Bertsimas. Syllabus. Teaching Assistant for a course which provides masters/PhD students with a modern treatment of Machine Learning using the lenses of convex, robust and mixed-integer optimization. Duties: preparing and leading ...

Optimization Over Integers Bertsimas Dynamic Ideas - Medair
Problems Patrick Jaillet: Routing Optimization Under Uncertainty Linear Programming (LP) Optimization with Excel Solver 6. Monte Carlo Simulation 11. Introduction to Machine Learning Introduction To Optimization: Objective Functions and …

Machine Learning for Yield Learning and Optimization
Recent advance in machine learning has brought a lot of new opportunities in improving the performance and efficiency of IC yield learning and optimization. This paper surveys some recent results of using various machine learning/deep learning techniques for such purpose, including performance modeling under uncertainty, lithography modeling

Graph Machine Learning through the Lens of Bilevel Optimization …
Zheng, He, Qiu, Wang, Wipf Definition3Wesaythatamessagefunctionf M sat- isfiesagradientrepresentationcriteriaif f M(h u,r,h v) = ∂ζ(h u,h v;r) ∂h v f M(h v,r − ...

Anil Kumar Pandey and M. P. Singh - JESTR
optimization of microstrip antenna parameters using ANN for X band (8-12 GHz) and Ku band (12-18 GHz) applications. An advanced Machine-learning-assisted optimization method has been reported for antenna optimization with maximum gain 7.4 dBi in [45]. Research paper [46] proposed a new design of isotropic antenna by using machine learning

Develop More Accurate Machine Learning Models with MIP
The book provides an original treatment of machine learning (ML) using convex, robust ... Machine Learning under a Modern Optimization Lens MACHINE LEARNING UNDER A MODERN OPTIMIZATION LENS DIMITRIS BERTSIMAS JACK DUNN Dimitris Bertsimas and Daisy Zhuo Interpretable AI September 2020 10 / 38.

STATISTICS
popular sparse learning algorithms. Our exact algorithm is based on a stan-dalone branch-and-bound (BnB) framework, which can solve the associated ... Machine Learning Under a Modern Optimization Lens. Dynamic Ideas LLC, Charlestown, MA. [9] BERTSIMAS,D.,KING,A.andMAZUMDER, R. (2016). Best subset selection via a modern …

Operations Research Center - Massachusetts Institute of Technology
15.095 Machine Learning Under a Modern Optimization Lens or by taking another suitable statistics subject such as 6.7910J/9.520J, 6.7900, 14.382, 15.680 plus four additional graduate level subjects approved by the SM advisor. Students may substitute approved graduate level courses for the three basic courses, but must take ...

Toward Predictive Digital Twins - University of Texas at Austin
• Use machine learning to train an interpretable, explainable reactive model asset state noisy sensor data ... Bertsimas, D., and Dunn, J., "Machine Learning under a Modern Optimization Lens." Dynamic Ideas (2018). Title: Toward predictive digital twins via component-based reduced-order models and interpretable machine learning

Best Subset Selection via a Modern Optimization Lens
methods in convex optimization [45] and mixed integer optimization (MIO), see [4]. We do not guarantee polynomial time solution times as these do not exist for the best subset problem unless P=NP.

Learning Interpretable Decision Rule Sets: A Submodular Optimization …
Interpretability is becoming one of the key considerations when deploying machine learning models to high-stake decision-making scenarios. Black box models, such as random forests and deep neural ... the rule set learning problem was revisited under modern optimization lens and several new algorithms were developed [22, 49, 28, 35, 48, 51 ...

Machine Learning Under A Modern Optimization Lens (2024)
Machine Learning Under A Modern Optimization Lens: Machine Learning Under a Modern Optimization Lens Dimitris Bertsimas,Jack William Dunn,2019 Rollout, Policy Iteration, and Distributed Reinforcement Learning Dimitri Bertsekas,2021-08-20 The purpose of this book is to develop in greater depth some of the methods from the author s Reinforcement ...

Develop More Accurate Machine Learning Models with MIP
The book provides an original treatment of machine learning (ML) using convex, robust ... Machine Learning under a Modern Optimization Lens MACHINE LEARNING UNDER A MODERN OPTIMIZATION LENS DIMITRIS BERTSIMAS JACK DUNN Dimitris Bertsimas and Daisy Zhuo Interpretable AI September 2020 10 / 38.

Category Theory in Machine Learning - University of Cambridge
While these issues are in general not exclusive to machine learning, the subfield of deep learning is notoriously ad-hoc (Olah, 2015). In his NeurIPS Test of Time award speech (Rahimi, 2018), Ali Rahimi has compared modern machine learning to alchemy1, citing examples of machine learning models performance dropping drastically after

Optimization for Machine Learning - Lagout.org
Since its earliest days as a discipline, machine learning has made use of optimization formulations and algorithms. Likewise, machine learning has contributed to optimization, driving the development of new optimization approaches that address the …

Best Subset Selection from a Modern Optimization Lens by …
Following \Best Subset Selection from a Modern Optimization Lens" by Bertsimas, King, and Mazumder (2016) Trevor Hastie Robert Tibshirani Ryan J. Tibshirani ... in statistics, machine learning, and optimization dedicated to e cient algorithms for this problem. On the other hand, the best subset selection problem (1) is nonconvex and is known to ...

Machine Learning Under A Modern Optimization Lens (book)
Machine Learning Under A Modern Optimization Lens: Machine Learning Under a Modern Optimization Lens Dimitris Bertsimas,Jack William Dunn,2019 Rollout, Policy Iteration, and Distributed Reinforcement Learning Dimitri Bertsekas,2021-08-20 The purpose of this book is to develop in greater depth some of the methods from the author s Reinforcement ...

Agni Orfanoudaki - MIT
Machine Learning Provides Evidence that Stroke Risk is Not Linear: The Non-Linear Framingham Stroke Risk Score (with A. Mark, D. Bertsimas, C. Cadisch, E. Chesley, A. Nouh, and B. Stein) ... Machine Learning Under a Modern Optimization Lens, Graduate, Guest Lecture Fall, 2020 Introduction to Operations Management, MBA, Teaching Assistant Spring ...

Machine Learning Under A Modern Optimization Lens (PDF)
Machine Learning Under A Modern Optimization Lens: Machine Learning Under a Modern Optimization Lens Dimitris Bertsimas,Jack William Dunn,2019 MACHINE LEARNING Chandra S.S., Vinod,Hareendran S., Anand,2021-01-01 The present book is primarily intended for undergraduate and postgraduate students of computer science and engineering information ...

Develop More Accurate Machine Learning Models with MIP
The book provides an original treatment of machine learning (ML) using convex, robust and mixed integer optimization that leads to solutions to central ML problems at large scale that can be found in seconds/minutes, can be certi ed to be optimal in minutes/hours, and outperform classical heuristic approaches in out-of-sample experiments.

Machine Learning Under A Modern Optimization Lens [PDF]
Machine Learning Under A Modern Optimization Lens Machine Learning Under a Modern Optimization Lens Dimitris Bertsimas,Jack William Dunn,2019 MACHINE LEARNING Chandra S.S., Vinod,Hareendran S., Anand,2021-01-01 The present book is primarily intended for

Practical Bayesian Optimization of Machine Learning Algorithms
2 Bayesian Optimization with Gaussian Process Priors As in other kinds of optimization, in Bayesian optimization we are interested in finding the mini-mum of a function f(x) on some bounded set X, which we will take to be a subset of RD. What makes Bayesian optimization different from other procedures is that it constructs a probabilistic

Optimization and Machine Learning Algorithms for Intelligent
Optimization and Machine Learning Algorithms for Intelligent Microwave Sensing: AReview Akram Sheikhi, Maryam Bazgir, ... This method relies on a resonator structure perturbed by a sample-under-test (SUT), with the properties of the SUT being estimated based on alterations ... microwave lens, the intensity and direction of the microwave vector ...