Assistant Professor |

2145 Sheridan Road, Evanston, IL 60208-3109

Email: chang-han.rhee@northwestern.edu

http://chrhee.github.io/

Rare Event Analysis, Large Deviations, Heavy Tails

Simulation and Statistical Inference of Stochastic Processes

Markov chain Monte Carlo, Exact Estimation

Sensitivity Analysis, Gradient Estimation

Experimental Design

Although rare, rare events matter.
For example, rare catastrophic events — such as large scale black out, market crash, and earthquake — have major impacts on society.
Moreover, the need for understanding and controling (less dramatic) rare events frequently arises in many problems in statistics, science, and engineering.
The theory of large deviations has a long and successful history in providing systematic tools for understanding rare events.
(Varadhan won Abel Prize in 2007 for his contributions to the large deviations theory!)
However, the classical large deviations theory often falls short when the underlying uncertainties are heavy-tailed.
This is a serious problem, since heavy tails are observed in many man-made systems (e.g., degree distribution in social network, financial loss, CPU requirement and file size in computer systems, size of power outage) as well as natural phenomena (e.g., earthquake, flood).
Moreover, in many applications it has been observed that there is a structural difference in the way system-wide rare events arise when the underlying uncertainties are heavy-tailed.
Roughly speaking, in light-tailed settings, the system-wide rare events arise because **everything goes wrong a little bit** (conspiracy principle), whereas in heavy-tailed settings, the system-wide rare events arise because **only a few things go wrong, but they go terribly wrong** (catastrophe principle).
Due to such a fundamental difference, as well as the ubiquitous presence of the heavy-tailed distributions in modern engineering systems, a comprehensive theory of large deviations for heavy-tailed rare events has long been called for.
While the extreme value theory community has made impressive progress in understanding the catastrophe principle over the last couple of decades, most of the literature has been focused on model-specific results or results pertaining to rare events that are caused by a single extreme behavior.
My recent papers [1, 2, 3] establish heavy-tailed large deviations theory and rigorously characterize the catastrophe principle for fundamental stochastic processes such as Levy processes and random walks with heavy-tailed increments;
in particualr, our theory fully characterizes the heavy-tailed rare events that require more than one single extreme behavior.
The new theory facilitates understanding of a wide range of rare events that arise in applications.
In particular, we were able to solve long standing open problems in simulation and queueing theory — i.e., designing the universal and strongly efficient rare-event simulation algorithm [3] and identifying the queue length asymptotics of multiple server queue with heavy-tailed service times [2].

Ph.D., Computational and Mathematical Engineering, Stanford University

M.S., Computational and Mathematical Engineering, Stanford University

B.S., Mathematics and Computer Science, Seoul National University

INFORMS Simulation Society Outstanding Simulation Publication Award, 2016

George Nicholson Student Paper Competition Finalist, 2013

Best Student Paper Award (MS/OR focused), Winter Simulation Conference, 2012

Samsung Fellowship, 2008–2012

Bohan Chen (PhD at CWI Stochastics): co-supervised with Bert Zwart; defended in December 2019

Mihail Bazhba (PhD at CWI Stochastics): co-supervised with Bert Zwart; scheduled to defend in May 2021

Zhe Su (PhD at Northwestern IEMS)

Xingyu Wang (PhD at Northwetern IEMS)

Jingyi Zhao (MS at Northwestern ESAM): graduated in March 2020

- Eliminating sharp minima from SGD with truncated heavy tails
*with X. Wang and S. Oh*

arXiv:2102.04297

- Sample-path large deviations for a class of heavy-tailed Markov additive processes
*with B. Chen and B. Zwart*

arXiv:2010.10751

- Sample-path large deviations for unbounded additive functionals of the reflected random walk
*with M. Bazhba, J. Blanchet, B. Zwart*

arXiv:2003.14381

- Rare-event simulation for multiple jump events in heavy-tailed Levy processes with infinite activities
*with X. Wang*

*2020 Winter Simulation Conference,*(2020)

- Sample-path large deviations for Levy processes and random walks with Weibull increments
*with M. Bazhba, J. Blanchet, and B. Zwart*

*Annals of Applied Probability*, 30(6): 2695–2739, (2020)

- Sample-path large deviations for Levy processes and random walks with regularly varying increments
*with J. Blanchet and B. Zwart*

*Annals of Probability*, 47(6): 3551-3605, (2019)

- Efficient rare-event simulation for multiple jump events in regularly varying random walks and compound Poisson processes
*with B. Chen, J. Blanchet, and B. Zwart*

*Mathematics of Operations Research*, 44(3): 919-942, (2019)

- Queue length asymptotics for the multiple server queue with heavy-tailed Weibull service times
*with M. Bazhba, J. Blanchet, and B. Zwart*

*Queueing Systems*, 93(3–4): 195-226, (2019)

- Importance sampling of heavy-tailed iterated random functions
*with B. Chen and B. Zwart*

*Advances in Applied Probability*, 50(3): 805-832. (2018)

- Lyapunov conditions for differentiability of Markov chain expectations: the absolutely continuous case
*with P. Glynn*

arXiv:1707.03870

- Space filling design for non-linear models
*with E. Zhou and P. Qiu.*

Under minor revision for*Stochastic Systems*, arXiv:1710.11616

- Unbiased estimation with square root convergence for SDE models
*with P. Glynn*

*Operations Research,*63(5): 1026–1043. (2015)

**2016 INFORMS Simulation Society Outstanding Simulation Publication Award.**

- Exact estimation for equilibrium of Markov chains
*with P. Glynn*

*Journal of Applied Probability (Special Jubilee Issue),*51A:377-389, (2014)

- An iterative algorithm for sampling from manifolds
*with E. Zhou and P. Qiu*

*2014 Winter Simulation Conference,*(2014)

- A new approach to unbiased estimation for SDE's
*with P. Glynn*

*2012 Winter Simulation Conference,*(2012)

**Best Student Paper Award (MS/OR focused)**

- Strongly efficient rare-event simulation for multiple jump events in regularly varying Levy processes with infinite activities
*with X. Wang*

- Sample-path large deviations for Levy driven stochastic differential equations
*with X. Wang and Z. Su*

- Queue length asymptotics for the queueing networks with heavy-tailed Weibull input
*with M. Bazhba and B. Zwart*

- Rare event simulation for electric power distribution networks with high variability
*with N. Vasmel, and B. Zwart*

- On heavy-tailed estimators
*with Z. Su, B. Chen, and B. Zwart*.

- Quasi-variational problems in heavy-tailed large deviations theory
*with B. Zwart and J. Blanchet*

- Lyapunov conditions for differentiability of Markov chain expectations: the contracting case
*with P. Glynn*