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131 - 140 of 204 results for: MS

MS&E 313: Almost Linear Time Graph Algorithms (CS 269G)

Over the past decade there has been an explosion in activity in designing new provably efficient fast graph algorithms. Leveraging techniques from disparate areas of computer science and optimization researchers have made great strides on improving upon the best known running times for fundamental optimization problems on graphs, in many cases breaking long-standing barriers to efficient algorithm design. In this course we will survey these results and cover the key algorithmic tools they leverage to achieve these breakthroughs. Possible topics include but are not limited to, spectral graph theory, sparsification, oblivious routing, local partitioning, Laplacian system solving, and maximum flow. Prerequisites: calculus and linear algebra.
Last offered: Autumn 2018

MS&E 315: Advanced Optimization Theory

Advanced optimization methods, algorithmic techniques, and proof strategies for obtaining provably efficient methods for minimizing high dimensional continuous functions. Focus on solving broad canonical optimization and obtaining start-of-the-art running times for both general oracle-based optimization problems as well as structured problems. Topics vary year to year based on interest. Possible topics include (but are not limited to) critical point computation of non-convex functions, linear system solving, eigenvector computation, finite sum optimization, linear system solving, principle component analysis, interior point methods, linear programming, semi-definite programming, and cutting-plane methods. Prerequisite: MS&E 213 or equivalent.
Last offered: Spring 2020

MS&E 316: Discrete Mathematics and Algorithms (CME 305)

Topics: Basic Algebraic Graph Theory, Matroids and Minimum Spanning Trees, Submodularity and Maximum Flow, NP-Hardness, Approximation Algorithms, Randomized Algorithms, The Probabilistic Method, and Spectral Sparsification using Effective Resistances. Topics will be illustrated with applications from Distributed Computing, Machine Learning, and large-scale Optimization. Prerequisites: CS 261 is highly recommended, although not required.
Terms: Win | Units: 3

MS&E 319: Approximation Algorithms

The theory of matching with its roots in the work of mathematical giants like Euler and Kirchhoff has played a central and catalytic role in combinatorial optimization for decades. More recently, the growth of online marketplaces for allocating advertisements, rides, or other goods and services has led to new interest and progress in this area. The course starts with classic results characterizing matchings in bipartite and general graphs and explores connections with algebraic graph theory, permanent, Pfaffian and counting and sampling matchings. Those results are complemented with models and algorithms developed for modern applications in market design, online advertising, and ride sharing. May be repeated for credit. Prerequisite: 212, CS 261, or equivalent.
Terms: Win | Units: 3 | Repeatable for credit
Instructors: Saberi, A. (PI)

MS&E 321: Stochastic Systems

Topics in stochastic processes, emphasizing applications. Markov chains in discrete and continuous time; Markov processes in general state space; Lyapunov functions; regenerative process theory; renewal theory; martingales, Brownian motion, and diffusion processes. Application to queueing theory, storage theory, reliability, and finance. Prerequisites: 221 or STATS 217; MATH 113, 115. (Glynn)
Terms: Spr | Units: 3

MS&E 322: Stochastic Calculus and Control

Ito integral, existence and uniqueness of solutions of stochastic differential equations (SDEs), diffusion approximations, numerical solutions of SDEs, controlled diffusions and the Hamilton-Jacobi-Bellman equation, and statistical inference of SDEs. Applications to finance and queueing theory. Prerequisites: 221 or STATS 217: MATH 113, 115.
Last offered: Spring 2019

MS&E 323: Stochastic Simulation

Emphasis is on the theoretical foundations of simulation methodology. Generation of uniform and non-uniform random variables. Discrete-event simulation and generalized semi-Markov processes. Output analysis (autoregressive, regenerative, spectral, and stationary times series methods). Variance reduction techniques (antithetic variables, common random numbers, control variables, discrete-time, conversion, importance sampling). Stochastic optimization (likelihood ratio method, perturbation analysis, stochastic approximation). Simulation in a parallel environment. Prerequisite: MS&E 221 or equivalent.
Terms: Aut | Units: 3

MS&E 324: Stochastic Methods in Engineering (CME 308, MATH 228)

The basic limit theorems of probability theory and their application to maximum likelihood estimation. Basic Monte Carlo methods and importance sampling. Markov chains and processes, random walks, basic ergodic theory and its application to parameter estimation. Discrete time stochastic control and Bayesian filtering. Diffusion approximations, Brownian motion and an introduction to stochastic differential equations. Examples and problems from various applied areas. Prerequisites: exposure to probability and background in analysis.
Terms: Spr | Units: 3
Instructors: Glynn, P. (PI)

MS&E 325: Optimal Transport in Operations Research, Statistics, and Economics

Current stochastic models, motivated by a wide range of applications in engineering, business, and science, as well as the design and analysis of associated computational methods for performance analysis and control of such stochastic systems.
Last offered: Winter 2020

MS&E 326: Advanced Topics in Game Theory with Engineering Applications

Advanced Topics in Game Theory with Engineering Applications
| Repeatable for credit (up to 99 units total)
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