MS&E 212: Graph and Combinatorial Optimization (MS&E 112)
Optimization problems dealing with graph structure. Topics: introduction to graph theory; combinatorial optimization problems on networks including network flows, matching, and assignment problems; NP-completeness and approximation algorithms; applications in the study of social networks, market design, and bioinformatics. Prerequisites: basic concepts in linear algebra, probability theory, and programming methodology.
Last offered: Winter 2024
| 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.
Last offered: Autumn 2020
| Units: 3
MS&E 215: Beyond Worst-Case Analysis (CS 264)
This course is motivated by problems for which the traditional worst-case analysis of algorithms fails to differentiate meaningfully between different solutions, or recommends an intuitively "wrong" solution over the "right" one. This course studies systematically alternatives to traditional worst-case analysis that nevertheless enable rigorous and robust guarantees on the performance of an algorithm. Topics include: instance optimality; smoothed analysis; parameterized analysis and condition numbers; models of data (pseudorandomness, locality, diffuse adversaries, etc.); average-case analysis; robust distributional analysis; resource augmentation; planted and semi-random graph models. Motivating problems will be drawn from online algorithms, online learning, constraint satisfaction problems, graph partitioning, scheduling, linear programming, hashing, machine learning, and auction theory. Prerequisites:
CS161 (required). CS261 is recommended but not required.
Last offered: Spring 2025
| Units: 3
MS&E 218: Applied Data Science (CME 218)
This is a multidisciplinary graduate level course designed to give students hands-on experience working in teams through real-world project-based research and experiential classroom activities. Students work in dynamic teams with the support of course faculty and mentors, researching preselected topics. Students apply a computational and data analytics lens and use design thinking methodology. The course exposes students to important techniques in applied data science as well as to the soft skills necessary for success in applied data science, such as ethics, unintended consequences and team building. Enrollment by application only. Graduate students only. The course application closes Sept 25, 2023. Application and more information:
https://forms.gle/gzGXkJmGMVYuJabK7
Last offered: Autumn 2023
| Units: 3
| Repeatable
2 times
(up to 6 units total)
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
| Units: 3
MS&E 221: Stochastic Modeling
Focus is on time-dependent random phenomena. Topics: discrete time Markov chains, Markov jump processes, queueing theory, and applications. Emphasis on model-building, computation, and related calibration and statistical issues.
Terms: Spr
| Units: 3
MS&E 223: Stochastic Simulation and Monte Carlo Methods
Modeling and simulation of stochastic systems for uncertainty quantification and decision making. Topics include generation of univariate and multivariate random variables (inversion, acceptance-rejection, Gaussian models, copulas), simulation of Brownian motion and stochastic differential equations, statistical output analysis (confidence intervals and stopping rules), variance reduction (control variates, stratification, conditional Monte Carlo), bias analysis and removal, randomized multilevel Monte Carlo, and steady-state estimation via regenerative methods. Emphasis is placed on modular simulation architectures that integrate modeling, sampling, variance reduction, debiasing, and statistical certification. Applications arise in engineering, finance, operations research, and machine learning. Prerequisites: Calculus-based probability and basic statistics. Students are expected to implement and validate simulation algorithms using modern computational tools.
Terms: Spr
| Units: 3
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: multivariable calculus; probability; experience with R.
Terms: Aut
| Units: 3
Instructors:
Johari, R. (PI)
;
Elfarsdottir, A. (TA)
;
Sojitra, R. (TA)
;
Thapa, I. (TA)
;
Xing, W. (TA)
MS&E 228: Applied Causal Inference with Machine Learning and AI (CS 288)
Fundamentals of modern applied causal inference. The course introduces the basic principles of causal inference and machine learning and shows how the two combine in practice to deliver causal insights and policy implications in real-world datasets, allowing for high-dimensionality and flexible estimation. Lectures provide the foundations of these new methodologies and proofs of their properties, and course assignments involve real-world data (from the social sciences and tech industry) as well as synthetic data analysis based on these methodologies. Prerequisites include mathematical maturity in probability, statistics, optimization, linear algebra, and calculus. Recommended: 226 or equivalent.
Terms: Win
| Units: 3
MS&E 229: Bayesian Linear Regression
Using data (and judgment if desired), Bayesian Linear Regression generates joint and marginal probability distributions over quantities of interest and applies those probability distributions to prediction. To ensure proper application and interpretation of linear regression, whether Bayesian or classical, the course develops Bayesian linear regression in depth, omitting no steps. In addition to assessing underlying data, the Bayesian linear conjugate system developed enables analytical answers that are straightforward, perceptive, blazingly quick, simple to implement, and produce results. They are an archetype for more intricate Bayesian systems, presaging what to anticipate. We pay attention to "big data" and "small data," the latter more characteristic of real world Decision Analysis. Serial data gathering is illustrated, and classical is shown to be a special case of Bayes. All course examples are solved using R or Excel; there is little emphasis on simulation. Students work examples, do projects, and explain findings. Matrix algebra and continuous probability are highly recommended.
Terms: Win
| Units: 3
Instructors:
Nesbitt, D. (PI)