蒙特卡羅方法與人工智能

目 錄
第1 章 蒙特卡羅方法簡介··············································································.1
1.1 引言·······························································································.1
1.2 動機(jī)和目標(biāo)······················································································.1
1.3 蒙特卡羅計算中的任務(wù)·······································································.2
1.3.1 任務(wù)1：采樣和模擬········································································.3
1.3.2 任務(wù)2：通過蒙特卡羅模擬估算未知量···················································.5
1.3.3 任務(wù)3：優(yōu)化和貝葉斯推理································································.7
1.3.4 任務(wù)4：學(xué)習(xí)和模型估計···································································.8
1.3.5 任務(wù)5：可視化能級圖·····································································.9
本章參考文獻(xiàn)··························································································13
第2 章 序貫蒙特卡羅方法··············································································14
2.1 引言·······························································································14
2.2 一維密度采樣···················································································14
2.3 重要性采樣和加權(quán)樣本·······································································15
2.4 序貫重要性采樣（SIS） ······································································18
2.4.1 應(yīng)用：表達(dá)聚合物生長的自避游走························································18
2.4.2 應(yīng)用：目標(biāo)跟蹤的非線性/粒子濾波·······················································20
2.4.3 SMC 方法框架總結(jié)·········································································23
2.5 應(yīng)用：利用SMC 方法進(jìn)行光線追蹤·······················································24
2.6 在重要性采樣中保持樣本多樣性···························································25
2.6.1 基本方法····················································································25
2.6.2 Parzen 窗討論··············································································28
2.7 蒙特卡羅樹搜索················································································29
2.7.1 純蒙特卡羅樹搜索··········································································30
2.7.2 AlphaGo ·····················································································32
2.8 本章練習(xí)·························································································33
本章參考文獻(xiàn)··························································································35
第3 章 馬爾可夫鏈蒙特卡羅方法基礎(chǔ)·······························································36
3.1 引言·······························································································36
蒙特卡羅方法與人工智能
·X ·
3.2 馬爾可夫鏈基礎(chǔ)················································································37
3.3 轉(zhuǎn)移矩陣的拓?fù)洌哼B通與周期······························································38
3.4 Perron-Frobenius 定理··········································································41
3.5 收斂性度量······················································································42
3.6 連續(xù)或異構(gòu)狀態(tài)空間中的馬爾可夫鏈·····················································44
3.7 各態(tài)遍歷性定理················································································45
3.8 通過模擬退火進(jìn)行MCMC 優(yōu)化·····························································46
3.9 本章練習(xí)·························································································49
本章參考文獻(xiàn)··························································································51
第4 章 Metropolis 算法及其變體······································································52
4.1 引言·······························································································52
4.2 Metropolis-Hastings 算法······································································52
4.2.1 原始Metropolis-Hastings 算法······························································53
4.2.2 Metropolis-Hastings 算法的另一形式·······················································54
4.2.3 其他接受概率設(shè)計··········································································55
4.2.4 Metropolis 算法設(shè)計中的關(guān)鍵問題·······························4