Yizao Wang

Modifications of UCT and sequence-like simulations for Monte-Carlo Go

Algorithm UCB1 for multi-armed bandit problem has already been extended to algorithm UCT which works for minimax tree search. We have developed a Monte-Carlo program, MoGo, which is the first computer Go program using UCT. We explain our modification of UCT for Go application and also the sequence-like random simulation with patterns which has improved significantly the performance of MoGo. UCT combined with pruning techniques for large Go board is discussed, as well as parallelization of UCT. MoGo is now a top-level computer-Go program on 9 times 9 Go board

On the structure and representations of max-stable processes

We develop classification results for max-stable processes, based on their spectral representations. The structure of max-linear isometries and minimal spectral representations play important roles. We propose a general classification strategy for measurable max-stable processes based on the notion of co-spectral functions. In particular, we discuss the spectrally continuous-discrete, the conservative-dissipative, and the positive-null decompositions. For stationary max-stable processes, the latter two decompositions arise from connections to nonsingular flows and are closely related to the classification of stationary sum-stable processes. The interplay between the introduced decompositions of max-stable processes is further explored. As an example, the Brown-Resnick stationary processes, driven by fractional Brownian motions, are shown to be dissipative.

Conditional sampling for spectrally discrete max-stable random fields

Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a consequence, we develop an algorithm for efficient and exact sampling from the conditional distributions. Our method provides a computational solution to the prediction problem for spectrally discrete max-stable random fields. This work offers new tools and a new perspective to many statistical inference problems for spatial extremes, arising, for example, in meteorology, geology, and environmental applications.

Ergodic properties of sum- and max-stable stationary random fields via null and positive group actions

We establish characterization results for the ergodicity of stationary symmetric

From infinite urn schemes to decompositions of self-similar Gaussian processes

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On the asymptotic normality of kernel density estimators for causal linear random fields

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Invariance principles for operator-scaling Gaussian random fields

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Dual representations of Laplace transforms of Brownian excursion and generalized meanders

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Modification of UCT with Patterns in Monte-Carlo Go

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Exploration exploitation in Go: UCT for Monte-Carlo Go

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