CSE675: Stochastic Simulation and Inference
Instructor: Wen Dong (UBIT: wendong)
Abstract
An emerging application for the stochastic process is analyzing complex natural
and social systems using data collected from sensor networks and the World Wide
Web that tracks the temporal evolution of those systems. By applying the
stochastic process to data, we can improve commuter traffic, tune
organizational efficiency, and control the spread of epidemics. In this course,
we will learn how to construct and simulate the Markov processes that are the
common abstractions of many dynamic systems, and learn the mathematical
properties of these processes. Overall, this hands-on course trains students to
apply stochastic-process thinking to the temporal dynamics of complex systems,
as captured by data.
Course Outline
The stochastic process is a language for studying the statistics of how systems
with randomness evolve over time. This process has found application in
statistical mechanics, systems biology, finance, and artificial intelligence –
to name only a few examples. However, an emerging application for the
stochastic process is analyzing complex natural and social systems using the
data collected from sensor networks and the World Wide Web. By applying the
stochastic process to data, we can do things from improving commuter traffic
and tuning organizational efficiency to controlling the spread of epidemics.
This hands-on course trains students to apply stochastic-process thinking to
the temporal dynamics of complex systems, and emphasizes the value of this kind
of thinking. The stochastic process is a wide topic that has developed for more
than a century in math and applied fields, so we will confine our math to the
undergraduate non-math-major level but keep our simulation and inference
algorithms parallel to the corresponding proofs that our mathematics colleagues
are familiar with. We will learn how to construct and simulate the Markov
processes that are the common abstractions of many dynamic systems, and learn
the mathematical properties of these processes. We will also sample some of the
most significant breakthroughs in the field in order to inspire students to
build useful and innovative applications for complex systems and data.
Ultimately, this course will explore the novel applications of stochastic
processes for studying the dynamics of our social systems – as captured by
textual and sensor data through Markov chain Monte Carlo, mean field
approximation, and Gaussian process approximation.
Goals
By the end of this course, students should be able to do the following:
* Simulate Markov processes and understand their
properties
* Use Markov processes to study the dynamics of
complex systems
* Make inferences about complex systems from data
that tracks the temporal evolution of those systems with Markov processes.
Lecture Schedule
Part A: Simulation of Markov Processes
01 Introduction: examples, why we care, what we can do, review of probability
theory
02 Simulating random variables from different probability distributions
03 Simulating Markov processes
Part B: Bayesian Inference of Markov Processes
04 Exact Inference: message passing and expectation maximization
05 MCMC: Gibbs sampler, Metropolis-Hastings algorithm, and hybrid MCMC schemes
06 Legendre-Fenchel transform, mean field
approximation, Gaussian process approximation
Part C: Complex Systems as Markov Processes
07 The dynamics of network formation
08 Diffusion in social networks: voting process and contact process
09 Urban dynamics
10 Non-equilibrium statistical mechanics
Part D: Properties of Markov Processes
11 Markov chain: absorbing, regular and ergodic Markov chains, stopping time,
strong Markov property
12 Random walks: first passage time distribution, stopping time and strong
Markov property, Wald’s identity, strong law of large numbers
13 Queuing process
14-15 Research paper presentations: poster or talk
Assessment Overview
Assessment will be based on four problem sets (15% each) plus your final
research paper (30%). Late submissions are worth only half credit. Each student
is supposed to share with the class detailed notes of 1-2 lectures (10%).