STOCHASTIC MODELS

Some of the main stochastic models used in engineering and operations research applications: discrete-time Markov chains, Poisson processes, birth and death processes and other continuous Markov chains, renewal reward processes. Applications: queueing, reliability, inventory, and finance.

• Instructor: Karl Sigman
  CULPA: 15 Info
• 3 points

ANALYSIS OF ALGORITHMS I

Prerequisites: (COMS W3134 or COMS W3136COMS W3137) and (COMS W3203) Introduction to the design and analysis of efficient algorithms. Topics include models of computation, efficient sorting and searching, algorithms for algebraic problems, graph algorithms, dynamic programming, probabilistic methods, approximation algorithms, and NP-completeness.

• Instructor: Nakul Verma
  CULPA: 10 h-index: 16 Info
• 3 points

SIMULATION

Generation of random numbers from given distributions; variance reduction; statistical output analysis; introduction to simulation languages; application to financial, telecommunications, computer, and production systems. Graduate students must register for 3 points. Undergraduate students must register for 4 points. Note: Students who have taken IEOR E4703 Monte Carlo simulation may not register for this course for credit. Recitation section required.

• Instructor: Karl Sigman
  CULPA: 15 Info
• 3 points

ARTIFICIAL INTELLIGENCE

Prior knowledge of Python is recommended. Provides a broad understanding of the basic techniques for building intelligent computer systems. Topics include state-space problem representations, problem reduction and and-or graphs, game playing and heuristic search, predicate calculus, and resolution theorem proving, AI systems and languages for knowledge representation, machine learning and concept formation and other topics such as natural language processing may be included as time permits.

• Instructor: Tony B Dear
  CULPA: 17 Info
• 3 points

NATURAL LANGUAGE PROCESSING

Computational approaches to natural language generation and understanding. Recommended preparation: some previous or concurrent exposure to AI or Machine Learning. Topics include information extraction, summarization, machine translation, dialogue systems, and emotional speech. Particular attention is given to robust techniques that can handle understanding and generation for the large amounts of text on the Web or in other large corpora. Programming exercises in several of these areas.

• Instructor: Daniel Bauer
  CULPA: 17 h-index: 13 Info
• 3 points

TOPICS IN QUANT FINANCE

AI Applications in Finance

Selected topics of interest in the area of quantitative finance. Offerings vary each year; some topics include energy derivatives, experimental finance, foreign exchange and related derivative instruments, inflation derivatives, hedge fund management, modeling equity derivatives in Java, mortgage-backed securities, numerical solutions of partial differential equations, quantitative portfolio management, risk management, trade and technology in financial markets.

• Instructor: Ali Hirsa
  h-index: 8 Info
• 3 points

TOPICS IN QUANT FINANCE

FINANCIAL CORRELATIONS

Stochastic control has broad applications in almost every walk of life, including finance, revenue management, energy, health care and robotics. Classical, model-based stochastic control theory assumes that the system dynamics and reward functions are known and given, whereas modern, model-free stochastic control problems call for reinforcement learning to learn optimal policies in an unknown environment. This course covers model-based stochastic control and model-free reinforcement learning, both in continuous time with continuous state space and possibly continuous control (action) space. It includes the following topics: Shortest path problem, calculus of variations and optimal control; formulation of stochastic control; maximum principle and backward stochastic differential equations; dynamic programming and Hamilton-Jacobi-Bellman (HJB) equation; linear-quadratic control and Riccati equations; applications in high-frequency trading; exploration versus exploitation in reinforcement learning; policy evaluation and martingale characterization; policy gradient; q-learning; applications in diffusion models for generative AI.

• Instructor: Gunter Meissner
  Info
• 3 points

MACHINE LEARNING

Topics from generative and discriminative machine learning including least squares methods, support vector machines, kernel methods, neural networks, Gaussian distributions, linear classification, linear regression, maximum likelihood, exponential family distributions, Bayesian networks, Bayesian inference, mixture models, the EM algorithm, graphical models and hidden Markov models. Algorithms implemented in MATLAB.

• Instructor: Nakul Verma
  CULPA: 10 h-index: 16 Info
• 3 points

SMALL-SCALE MECH BEHAVIOR

SMALL SCALE MECHANICAL BE

Mechanics of small-scale materials and structures require nonlinear kinematics and/or nonlinear stress vs. strain constitutive relations to predict mechanical behavior. Topics include variational calculus, deformation and vibration of beam, strings, plates, and membranes; fracture, delamination, bulging, buckling of thin films, among others. Thermodynamics of solids will be reviewed to provide the basis for a detailed discussion of nonlinear elastic behavior as well as the study of the equilibrium and stability of surfaces.

• Instructor: Jeffrey W Kysar
  CULPA: 9 h-index: 37 Info
• 3 points