本論文主要以高斯過程模型（Gaussian Process Model）應用在電腦實驗的研究方向上，主要探討的問題同時包含連續型因子（Quantitative Factors）及類別型因子（Qualitative Factors），並依反應變數含有噪聲（noise）與否分為兩種不同的案例進行研究。而整個實驗流程基本上涵蓋有兩步驟：應用高斯過程模型建模再依填充標準（Infill Criteria）進行序列設計（Sequential Design），整個算法為這兩個步驟依序疊代，直到停止條件滿足為止。

其中不具噪聲的案例為電子元件散熱鰭片之散熱效果分析。此類資料的反應變數不具有噪聲，因此我們選用定量及定性型之高斯過程（QQGP）為替代輔助模型，透過以QQGP建模結合最大期望改進量準則（Expected Improvement Criterion）進行序列設計，得以在控制成本的情況下，從少許實驗樣本找出電子元件散熱鰭片散熱效果較優的配置。

而具有噪聲的案例則應用在卷積神經網路（CNN）的參數優化上。因一般訓練卷積神經網路辨識影像需耗費大量的時間，本論文以樹狀高斯過程模型（tGP）結合期望改進量準則進行最佳化程序，得以在進行迭代的過程中逐步提升模型準確率並優於原作所建議的參數預設值。

This thesis mainly focuses on surrogate-assisted tuning procedures for the different types of the variables and responses. Basically, the surrogate-assisted approach iterates the following two steps until a stop criterion is met. First based on the current explored points, a surrogate surface is constructed and then due to the surrogate model, an infill criterion is adopted to identify the next explored points. Here in addition to quantitative variables, the qualitative variables are also considered, and the responses can be deterministic or contain noise.

Firstly, we study the performance of the heat dissipation fins in electronic components. The response is deterministic. Since qualitative variables are considered in the study, the Gaussian process model with qualitative and quantitative factors (QQGP) is adopted for surrogate construction and a maximum expected improvement criterion is used to identify the next explored points. Due to the cost limitation, the proposed surrogate-assisted approach does find out the configuration with better heat dissipation effect of the heat dissipation fins in electronic components.

Secondly, we consider the parameter tuning in CNN. Since the response involves the random effects, the treed Gaussian process (tGP) with an expected improvement criterion is adopted here for the surrogate-assisted tuning procedure. Due to the numerical experiments, the proposed surrogate-assisted tuning procedure can identify the parameters with better performance.

[1] Ba, S., Myers, W. R., & Brenneman, W. A. (2015). “Optimal sliced Latin hypercube designs.” Technometrics, 57(4), 479-487.
[2] Chen, J. K., Chen, R. B., Fujii, A., Suda, R., & Wang, W. (2018). “Surrogate-assisted tuning for computer experiments with qualitative and quantitative parameters.” Statistica Sinica, 761-789.
[3] Fang, K. T., Li, R., & Sudjianto, A. (2005). “Design and modeling for computer experiments.” CRC press.
[4] Gramacy, R. B. (2007). “tgp: an R package for Bayesian nonstationary, semiparametric nonlinear regression and design by treed Gaussian process models.” Journal of Statistical Software, 19(9), 6.
[5] Gramacy, R. B., & Taddy, M. (2009). “Categorical inputs, sensitivity analysis, optimization and importance tempering with TGP version 2, an R package Ior treed Gaussian process models.” Technical report, R manual.
[6] Gramacy, R. B., & Lee, H. K. H. (2008). “Bayesian treed Gaussian process models with an application to computer modeling.” Journal of the American Statistical Association, 103(483), 1119-1130.
[7] Qian, P. Z. G., Wu, H., & Wu, C. J. (2008). “Gaussian process models for computer experiments with qualitative and quantitative factors.” Technometrics, 50(3), 383-396.
[8] Santner, T. J., Williams, B. J., Notz, W., & Williams, B. J. (2003). “The design and analysis of computer experiments” (Vol. 1). New York: Springer.
[9] Szegedy, C., Liu, W., Jia, Y., Sermanet, P., Reed, S., Anguelov, D., ... & Rabinovich, A. (2015). “Going deeper with convolutions.” In Proceedings of the IEEE conference on computer vision and pattern recognition (pp. 1-9).
[10] Taddy, M. A., Gramacy, R. B., & Polson, N. G. (2011). “Dynamic trees for learning and design.” Journal of the American Statistical Association, 106(493),109-123.
[11] Zhou, Q., Qian, P. Z., & Zhou, S. (2011). “A simple approach to emulation for computer models with qualitative and quantitative factors.” Technometrics, 53(3), 266-273.