隨著資訊科技的進步，處理高維度數據已成為當代統計學與機器學習的核 心挑戰。傳統支援向量機（Support Vector Machine， SVM）在處理變數間複雜 共線性時，往往會面臨過度擬合與解釋性不足的問題。為了克服這些限制，本 研究提出了一種兼具特徵過濾與降維效果的整合型統計架構：貝氏主成分支援 向量機。 本研究的方法論基礎建立在充分維度削減之上。首先，我們借鑒了 Li (1991) 提出的切片逆迴歸以及 Li et al. (2011) 的主成分支援向量機之核心幾 何思想，透過將響應變數切片並求解最佳分離超平面，以對齊並捕捉核心中心 子空間。為了進一步提升模型在極高維度環境下的強健性，我們導入了三參數 Beta 常態先驗作為全域—區域縮減先驗，這使得模型即便在參數空間隨樣本量 增長時，仍能保持後驗一致性並精準實現變數篩選，有效剔除隨機噪聲。 在分類器的機率化建構上，本研究參考 Henao et al. (2014) 提出的貝氏 SVM 框架，將傳統的損失函數轉化為正態分佈的縮放混合模型。此一處理方式 不僅容許我們利用馬可夫鏈蒙地卡羅抽樣演算法進行高效後驗推論，更讓模型 具備了量化預測不確定性的能力。 模擬實驗結果顯示，在面對高維噪聲污染時，BPSVM 在 Frobenius 距離模 擬表現上優於傳統的 SIR 與 PSVM。變數選取靈敏度與稀疏壓制力上則持平甚 至在一些維度設定上稍占優勢。最後，透過實際人類活動識別高維數據集的案 例應用驗證，本模型展現了卓越的子空間邊界解析度，為高維數據分析提供了 一個兼具統計理論支持與運算效率的新路徑。;With the advancement of information technology， the analysis of high-dimensional data has become a central challenge in contemporary statistics and machine learning. Traditional Support Vector Machines (SVMs)， when applied to data with complex multicollinearity among variables， often suffer from overfitting and limited interpretability. To overcome these limitations， this study proposes an integrated statistical framework that combines feature screening and dimension reduction: the Bayesian Principal Support Vector Machine. The methodological foundation of this study is built upon sufficient dimension reduction. First， we draw on the core geometric ideas of Sliced Inverse Regression proposed by Li (1991) and the Principal Support Vector Machine introduced by Li et al. (2011). By slicing the response variable and solving for optimal separating hyperplanes， the proposed method aims to align with and capture the central subspace. To further enhance the robustness of the model in ultra-high-dimensional settings， we introduce the three-parameter beta normal prior as a global-local shrinkage prior. This enables the model to maintain posterior consistency even when the parameter space grows with the sample size， while accurately performing variable selection and effectively eliminating random noise. For the probabilistic construction of the classifier， this study follows the Bayesian SVM framework proposed by Henao et al. (2014)， transforming the traditional loss function into a scale mixture of normal distributions. This formulation not only allows efficient posterior inference through Markov chain Monte Carlo sampling algorithms， but also enables the model to quantify predictive uncertainty. Simulation results show that， under high-dimensional noise contamination， the proposed BPSVM outperforms traditional SIR and PSVM methods in terms of Frobenius distance across the simulation settings. In terms of variable selection sensitivity and sparsity-inducing capability， BPSVM performs comparably to， or slightly better than， the competing methods. Finally， an application to a high-dimensional human activity recognition dataset further validates the proposed model， demonstrating superior subspace boundary resolution and predictive robustness. Overall， this study provides a new approach to high-dimensional data analysis that combines statistical theoretical support with computational efficiency.
