Research

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“Nothing takes place in the world whose meaning is not that of some maximum or minimum” - Leonhard Euler

Comparing 4 Langevin diffusions and momentum method on Ackley function.

Left: Langevin diffusion on the contour lines of Ackley function. Right: Improved Langevin diffusion by Fang et al. (SPA 1997)

Left: Classical SA on a randomly generated 50-node TSP. Right: Discrete ISA on the same 50-node TSP.

Left: Classical SA on a randomly generated 500-node TSP. Right: Discrete ISA on the same 500-node TSP.

Stochastic Gradient Langevin Dynamics (SGLD) on Walker2d: falls over, inches itself forward

Stochastic Gradient Landscape Modified Langevin Dynamics (SGLMLD) on Walker2d: keeps stepping forward

Comparing 4 landscape-modified Metropolis-Hastings of an Ising model on a 50x50 box

Comparing 4 landscape-modified Metropolis-Hastings of a 3-state Potts model on a 50x50 box

Research interests:

Markov chains, Markov processes: theory and applications
Stochastic algorithms: Markov chain Monte Carlo, Metropolis-Hastings, simulated annealing, Langevin dynamics, Hamiltonian Monte Carlo
Statistical physics, applied probability, theoretical computer science, stochastic optimization, Bayesian statistics, information theory

Preprints:

Youjia Wang and Michael C.H. Choi. Information-theoretic classification of the cutoff phenomenon in Markov processes. Submitted. [arXiv]

Michael C.H. Choi, Youjia Wang and Geoffrey Wolfer. A rate-distortion framework for MCMC algorithms: geometry and factorization of multivariate Markov chains. Submitted. [arXiv]

Michael C.H. Choi and Geoffrey Wolfer. Markov chain entropy games and the geometry of their Nash equilibria. Submitted. [arXiv] [ Slides]

Michael C.H. Choi and Youjia Wang. [Improved Langevin Monte Carlo for stochastic optimization via landscape modification] (https://arxiv.org/abs/2302.03973). [arXiv]

Michael C.H. Choi and Jing Zhang. Improved annealing for sampling from multimodal distributions via landscape modification. [arXiv]

Michael C.H. Choi. On the convergence of an improved and adaptive kinetic simulated annealing. [arXiv] [ Slides] [ Youtube]

Michael C.H. Choi. Universality of the Langevin diffusion as scaling limit of a family of Metropolis-Hastings processes I: fixed dimension. Submitted. [arXiv]

Publications:

Michael C.H. Choi and Geoffrey Wolfer. Systematic approaches to generate reversiblizations of Markov chains. IEEE Trans. Inform. Theory (2024), Volume 70, Issue 5, pp. 3145-3161. [arXiv] [doi] [ Slides]

Michael C.H. Choi. Improved Metropolis-Hastings algorithms via landscape modifcation with applications to simulated annealing and the Curie-Weiss model. Adv. in Appl. Probab. (2024), Volume 56, Issue 2, pp. 587-620. [arXiv] [doi]

Michael C.H. Choi, Venkatkrishna Karumanchi. Landscape modification meets surrogate optimization: towards developing an improved stochastic response surface method. Proceedings of Winter Simulation Conference 2022. [ResearchGate]

Michael C.H. Choi, Zhipeng Huang. Generalized Markov chain tree theorem and Kemeny’s constant for a class of non-Markovian matrices. Statist. Probab. Lett. (2023), Volume 193, 109739. [ResearchGate][doi]

Michael C.H. Choi. Hitting, mixing and tunneling asymptotics of Metropolis-Hastings reversiblizations in the low-temperature regime. J. Math. Anal. Appl. (2021), Volume 497, Issue 1, 124853. [ResearchGate] [doi]

Michael C.H. Choi. An improved variant of simulated annealing that converges under fast cooling. Markov Process. Related Fields (2021), Volume 27, Issue 1, pp. 123-154. [Slides] [Handwritten notes] [arXiv] [doi]

Michael C.H. Choi, Pierre Patie. Analysis of non-reversible Markov chains via similarity orbit. Combin. Probab. Comput. (2020), Volume 29, Issue 4, pp. 508-536. [ Slides] [arXiv][doi]

Michael C.H. Choi, Chihoon Lee and Jian Song. Entropy flow and De Bruijn’s identity for a class of stochastic differential equations driven by fractional Brownian motion. Probab. Engrg. Inform. Sci., to appear. [arXiv][doi]

Michael C.H. Choi. Metropolis-Hastings reversiblizations of non-reversible Markov chains. Stochastic Process. Appl. (2020), Volume 130 Issue 2 Page 1041-1073. [ Slides] [arXiv][doi]

Michael C.H. Choi and Lu-Jing Huang. On hitting time, mixing time and geometric interpretations of Metropolis-Hastings reversiblizations. J. Theoret. Probab. (2020), Volume 33 Issue 2 Page 1144-1163. [arXiv][doi]

Michael C.H. Choi, Evelyn Li. A Hoeffding’s inequality for uniformly ergodic diffusion process. Statist. Probab. Lett. (2019), Volume 150 Page 23-28. [arXiv][doi]

Michael C.H. Choi. On resistance distance of Markov chain and its sum rules. Linear Algebra Appl. (2019), Volume 571 Page 14-25. [arXiv][doi]

Michael C.H. Choi, Pierre Patie. Skip-free Markov chains. Trans. Amer. Math. Soc. (2019), Volume 371 Number 10 Page 7301-7342. [arXiv][doi]

Michael C.H. Choi. Velocity formulae between entropy and hitting time for Markov chains. Statist. Probab. Lett. (2018), Volume 141 Page 62-67. [arXiv][doi]

Michael C.H. Choi. Hitting time and mixing time bounds of Stein’s factors. Electron. Commun. Probab. 23 (2018), paper no. 6. [arXiv][doi]

Michael C.H. Choi, Pierre Patie. A sufficient condition for continuous-time finite skip-free Markov chains to have real eigenvalues. Proceedings of AMMCS-CAIMS 2015.

Michael C.H. Choi, Eric C.K. Cheung. On the expected discounted dividends in the Cramer-Lundberg model with more frequent ruin monitoring than dividend decisions. Insurance Math. Econom. (2014) Volume 59 121-132. [doi]