181 - 190 of 236 results for: MS

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.

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.

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.

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.

Advanced Topics in Applied Data Science

Theoretical foundations of modern techniques at the intersection of causal inference and machine learning. Topics may include: semi-parametric inference and semi-parametric efficiency, modern statistical learning theory, Neyman orthogonality and double/debiased machine learning, theoretical foundations of high-dimensional linear regression, theoretical foundations of non-linear regression models, such as random forests and neural networks, adaptive non-parametric estimation of conditional moment models, estimation and inference on heterogeneous treatment effects, causal inference and reinforcement learning, off-policy evaluation, adaptive experimentation and inference.

This course examines the principles and methods required to make artificial intelligence (AI) systems reliable and scientifically sound. Topics include evaluation and benchmarking, notions of validity, distribution shift, causality, predictive inference, AI-assisted statistical inference, data attribution, and beyond. Problem sets will involve both mathematical components and coding projects to see the practical effects of the methods we develop.

Artificial intelligence is expanding the frontier of algorithm design, enabling new ways to reason about and solve complex optimization problems. This course explores how AI methods - ranging from graph neural networks and diffusion models to large language models - can be integrated into the algorithm design pipeline. We will study how to use machine learning to design new algorithms, enhance classical algorithms with data-driven components, and optimize algorithm performance in specific application domains. Topics will span both practical approaches, such as differentiable optimization and generative AI for combinatorial problems, to theoretical perspectives, including approximation guarantees and the limits of learned algorithms.

Risk management of large scale computing and networking systems with respect to security, data integrity, performance collapse, and service disruption. Qualitative and analytical basis for assessment, modeling, control, and mitigation of network risks. Stochastic risk models. Contact process. Random fields on networks. Virus and worm propagation dynamics and containment. Denial of service attacks. Intruder detection technologies. Distributed network attacks and countermeasures. Disaster recovery networks. Network protection services and resource placement. Autonomic self-defending networks. Economics of risk management. Emphasis is on analytics and quantitative methods.