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81 - 90 of 206 results for: MS

MS&E 211X: Introduction to Optimization (Accelerated) (ENGR 62X, MS&E 111X)

Optimization theory and modeling. The role of prices, duality, optimality conditions, and algorithms in finding and recognizing solutions. Perspectives: problem formulation, analytical theory, computational methods, and recent applications in engineering, finance, and economics. Theories: finite dimensional derivatives, convexity, optimality, duality, and sensitivity. Methods: simplex and interior-point, gradient, Newton, and barrier. Prerequisite: CME 100 or MATH 51 or equivalent.
Terms: Aut | Units: 3-4

MS&E 212: Mathematical Programming and Combinatorial Optimization (MS&E 112)

Combinatorial and mathematical programming (integer and non-linear) techniques for optimization. Topics: linear program duality and LP solvers; integer programming; combinatorial optimization problems on networks including minimum spanning trees, shortest paths, and network flows; matching and assignment problems; dynamic programming; linear approximations to convex programs; NP-completeness. Hands-on exercises. Prerequisites: basic concepts in linear algebra, probability theory, CS 106A or X.
Terms: Aut | Units: 3

MS&E 213: Introduction to Optimization Theory (CS 269O)

Introduction of core algorithmic techniques and proof strategies that underlie the best known provable guarantees for minimizing high dimensional convex functions. Focus on broad canonical optimization problems and survey results for efficiently solving them, ultimately providing the theoretical foundation for further study in optimization. In particular, focus will be on first-order methods for both smooth and non-smooth convex function minimization as well as methods for structured convex function minimization, discussing algorithms such as gradient descent, accelerated gradient descent, mirror descent, Newton's method, interior point methods, and more. Prerequisite: multivariable calculus and linear algebra.
Terms: Aut | Units: 3

MS&E 220: Probabilistic Analysis

Concepts and tools for the analysis of problems under uncertainty, focusing on structuring, model building, and analysis. Examples from legal, social, medical, and physical problems. Topics include axioms of probability, probability trees, random variables, distributions, conditioning, expectation, change of variables, and limit theorems. Prerequisite: multivariable calculus and some linear algebra.
Terms: Aut, Sum | Units: 3-4

MS&E 221: Stochastic Modeling

Focus is on time-dependent random phenomena. Topics: discrete and continuous time Markov chains, renewal processes, queueing theory, and applications. Emphasis is on building a framework to formulate and analyze probabilistic systems. Prerequisite: 220 or equivalent, or consent of instructor.
Terms: Spr | Units: 3
Instructors: Glynn, P. (PI)

MS&E 223: Simulation

Discrete-event systems, generation of uniform and non-uniform random numbers, Monte Carlo methods, programming techniques for simulation, statistical analysis of simulation output, efficiency-improvement techniques, decision making using simulation, applications to systems in computer science, engineering, finance, and operations research. Prerequisites: working knowledge of a programming language such as C, C++, Java, Python, or FORTRAN; calculus-base probability; and basic statistical methods.
Last offered: Spring 2020

MS&E 226: Fundamentals of Data Science: Prediction, Inference, Causality

This course is about understanding "small data": these are datasets that allow interaction, visualization, exploration, and analysis on a local machine. The material provides an introduction to applied data analysis, with an emphasis on providing a conceptual framework for thinking about data from both statistical and machine learning perspectives. Topics will be drawn from the following list, depending on time constraints and class interest: approaches to data analysis: statistics (frequentist, Bayesian) and machine learning; binary classification; regression; bootstrapping; causal inference and experimental design; multiple hypothesis testing. Class lectures will be supplemented by data-driven problem sets and a project. Prerequisites: CME 100 or MATH 51; 120, 220 or STATS 116; experience with R at the level of CME/ STATS 195 or equivalent.
Terms: Aut | Units: 3

MS&E 230: Incentives and Algorithms

Many policies and algorithms interact with many self-interested agents. Provides students methodology and vocabulary to analyze and design such problems. Provides foundations of basic economics and game theoretic concepts and will apply them to a variety of real world applications. Topics: equilibrium analysis, auction design, matching markets, social choice, externalities and network design. Applications: matching marketplaces (NRMP, Upwork, college admissions), dynamic pricing in ride-sharing, advertising mechanisms, reputation systems, platform design, kidney exchange and organ allocations, food banks. Relation to MS&E 232: while 232 provides an extensive introduction to game theory, this course focuses on designing the "rules of the game" to achieve good economic outcomes and will cover only a few basic topics from MS&E 232, including more on application and algorithmic design. Prerequisites: basic mathematical maturity at the level of Math 51, and probability at the level of MS&E 120, 220 or EE 178.
Terms: Spr | Units: 3
Instructors: Ashlagi, I. (PI)

MS&E 231: Introduction to Computational Social Science (SOC 278)

With a vast amount of data now collected on our online and offline actions -- from what we buy, to where we travel, to who we interact with -- we have an unprecedented opportunity to study complex social systems. This opportunity, however, comes with scientific, engineering, and ethical challenges. In this hands-on course, we develop ideas from computer science and statistics to address problems in sociology, economics, political science, and beyond. We cover techniques for collecting and parsing data, methods for large-scale machine learning, and principles for effectively communicating results. To see how these techniques are applied in practice, we discuss recent research findings in a variety of areas. Prerequisites: introductory course in applied statistics, and experience coding in R, Python, or another high-level language.
Last offered: Autumn 2019

MS&E 232: Introduction to Game Theory

Examines foundations of strategic environments with a focus on game theoretic analysis. Provides a solid background to game theory as well as topics in behavioral game theory and the design of marketplaces. Introduction to analytic tools to model and analyze strategic interactions as well as engineer the incentives and rules in marketplaces to obtain desired outcomes. Technical material includes non-cooperative and cooperative games, behavioral game theory, equilibrium analysis, repeated games, social choice, mechanism and auction design, and matching markets. Exposure to a wide range of applications. Lectures, presentations, and discussion. Prerequisites: basic mathematical maturity at the level of Math 51, and probability at the level of MS&E 120 or EE 178.
Terms: Spr | Units: 3
Instructors: Johari, R. (PI)
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