Research Interests

Hongmei Chi

Cyber Security
Security/privacy models/Issues for various computing enviornments, especially apply machine learning in cyberceurity applications, such as mobile health apps, deepfake detection, cloud computing, insider threat, digital forensics in mobile device and social networking sites.
HPC and Parallel Computing
Development of random number generators for use on multi-core processors and GPU and Mobile(handheld) Device. SPRNG library.

Parallel Quasirandom Numbers
QMC applications have high degrees of parallelism, can tolerate large latencies, and usually require considerable computational effort, making them extremely well suited to parallel, distributed, and even Grid-based computational environments. In these environments, a large QMC problem is broken up into many small subproblems. These subproblems are then scheduled on the parallel, distributed, or Grid-based environment. In a more traditional instantiation, these environments are usually a workstation cluster connected by a local-area network, where the computational workload is cleverly distributed. Recently, peer-to-peer or Grid computing, the cooperative use of geographically distributed resources unified to act as a single powerful computer, has been investigated as an appropriate computational environment for QMC applications. The computational infrastructure developed for quasirandom numbers would be very useful.
Randomized Quasi-Monte Carlo
Quasi-Monte Carlo methods are a variant of ordinary Monte Carlo methods that employ highly uniform quasirandom numbers in place of Monte Carlo's pseudorandom numbers. Quasi-Monte Carlo methods are now widely used in scientific computation, especially in estimating integrals over multidimensional domains and in many different financial computations. While quasirandom numbers do improve the convergence of applications like numerical integration, it is by no means trivial to provide practical error estimates. In order to provide error estimates for quasi-Monte Carlo methods, several researchers proposed the use of Randomized quasi-Monte Carlo methods, where randomness can be brought to bear on quasirandom sequences through scrambling and other related randomization techniques. The core of randomized quasi-Monte Carlo is to find fast and effective algorithms to randomize (scramble) quasirandom sequences. The purpose of scrambling in quasi-Monte Carlo is threefold. Primarily, it provides a practical method to obtain error estimates for quasi-Monte Carlo based by treating each scrambled sequence as a different and independent random sample from a family of randomly scrambled quasirandom numbers. Thus, randomized quasi-Monte Carlo overcomes the main disadvantage of quasi-Monte Carlo while maintaining the favorable convergence rate of quasi-Monte Carlo. Secondarily, scrambling gives us an a simple and unified way to generate quasirandom numbers for parallel, distributed, and Grid-based computational environments. Finally, randomized quasi-Monte Carlo provides many more choices of quality quasirandom sequences for quasi-Monte Carlo applications, and perhaps even optimal choices as a result of derandomization. These promising characteristics have lead to considerable work in the area randomized quasi-Monte Carlo. Thus, a careful exploration of scrambling and derandomization methods coupled with library-level implementations will play central role in the use of randomized quasi-Monte Carlo techniques.

Scrambled Quasirandom Numbers
The Halton sequence along with (t,s)-sequences and lattice points are the standard quasirandom sequences, The critical task for randomizing in QMC is to find fast and effective methods to scramble quasirandom sequences. Various scrambling methods have been studied, and these basically fall into two main categories. One is based on randomized shifting. The other method is based on digital permutations.
Generally speaking, the methods of scrambling quasirandom sequences are based on the construction of the quasirandom numbers. Digital permutations are mainly used for quasirandom sequences which are constructed via digital inversion methods, such as Halton sequences and (t,s)-sequences. Lattice points are constructed by a different method and so digital permutations are not suitable and shifting is used instead. I explore the efficacy of various scrambling methods to build a a library of parallel and distributed quasirandom numbers.

Computational Finance
Numerical methods are used for a variety of purposes of finance. These includes risk analysis, the evaluation of securities, and stress testing of portfolios. The Monte Carlo approach, which uses random sequences, has proved to be a valuable computational tool in modern finance. But, for many applications of computational finance, the use of quasirandom sequences, called quasi-Monte Carlo approach, seems to provide more faster convergent rate than random sequences. Even though it is well-known that the distribution of the quasirandom sequence in high dimensions is not good, the scrambled or optimally scrambled quasirandom sequence can often improve the quality. Thus the scrambled and optimal quasirandom sequence can be widely applied in computational finance.