感謝貝葉斯網(wǎng)學(xué)習(xí)筆記

問題是這樣描述的：

福爾摩斯先生在他的辦公室工作時接到了他鄰居華生的電話。華生告訴他：他的家里可能進了竊賊， 因為他家的警鈴響了被告知有竊賊闖入，福爾摩斯迅速開車回家。在路上，他聽廣播得知他家那里 發(fā)生了地震。地震也有可能引起警報。這樣，請問福爾摩斯先生應(yīng)該回家抓賊還是迅速撤離該地區(qū) 以躲避地震？

簡單講，在路上的holmes需要判斷是盜賊還是地震導(dǎo)致警鈴？如果是前者，他需要回去抓賊，若是后者，則要逃離地震區(qū)。
所以圖中雖然有5個節(jié)點，地震并不100%導(dǎo)致警鈴，警鈴也不100%導(dǎo)致華生的信號。
但是我們在得到信號，聽到警鈴的情況下，可以通過計算盜賊導(dǎo)致警鈴的概率p1，和地震導(dǎo)致警鈴的概率pp1來進行決策，也可以計算在地震發(fā)生條件下，盜賊導(dǎo)致警鈴的概率p2。

• P1表示在聽到警鈴的條件下，盜賊導(dǎo)致警鈴響的概率
• PP1表示在聽到警鈴的條件下，地震導(dǎo)致警鈴響的概率PP1
• P2，在地震發(fā)生的條件下，盜賊導(dǎo)致警鈴發(fā)生的概率。

如果p2比p1小，說明地震E才是導(dǎo)致A的主要原因。
反過來，如果P2和P1相同，說明地震這個新添加的條件，對警報沒有作用。
添加地震這個條件之后，還是盜賊的概率變小了，說明地震對警報是有影響的。

用用圖像描述如下：

圖片來源于realsa，表示感謝。

==注意：==節(jié)點的狀態(tài)是自己定義的，false = state 1 true = state 2,此處與jbb0523的理解剛好相反。
以下是源代碼分析

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %1、建立貝葉斯網(wǎng)絡(luò)結(jié)構(gòu) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% N = 3; %三個節(jié)點，分別是B、E、A dag = zeros(N,N);%建立一個N*N的0矩陣 B = 1; E = 2; A = 3; % %節(jié)點之間的連接關(guān)系 dag(B,A) = 1;%存在B指向A的邊 dag(E,A) = 1; %存在E指向A的邊 discrete_nodes = 1:N; %離散節(jié)點 node_sizes = 2*ones(1,N);%節(jié)點狀態(tài)數(shù)node_sizes的內(nèi)容為[2,2,2] bnet =mk_bnet(dag,node_sizes,'names',{ 'BB','EE','AAA'},'discrete',discrete_nodes); %name后面的{}里面給出了各個節(jié)點的別名 % % false = state 1 true = state 2,此處與[jbb0523](https://blog.csdn.net/jbb0523/article/details/79438092)的理解剛好相反 bnet.CPD{B} = tabular_CPD(bnet,B,[0.9 0.1]);%手動輸入的條件概率 入室盜竊發(fā)生的概率true 0.1 bnet.CPD{E} = tabular_CPD(bnet,E,[0.99 0.01]); bnet.CPD{A} = tabular_CPD(bnet,A,[0.99 0.1 0.1 0.01 0.01 0.9 0.9 0.99]); %利用tabular_CPD設(shè)置各個變量的邊緣概率，對于B和E，定義順序是False True； %對于T、L和B這類，順序是FF FT TF TT； %對于D這類，順序是FFF FFT FTF FTT TFF TFT TTF TTT%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %2、畫出建好的貝葉斯結(jié)構(gòu) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% draw_graph(dag);%畫圖%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %3、使用聯(lián)合樹引擎對貝葉斯網(wǎng)絡(luò)進行推斷 engine = jtree_inf_engine(bnet); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %4、求解邊緣分布假設(shè) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %我們要計算盜竊導(dǎo)致響鈴的概率 %P1=P(B|A) evidence = cell(1,N);%創(chuàng)建一個1*n的空的矩陣 evidence{A} = 2; % %這里1是false,2是True,等于讓A是True.%C{s}使用這種"{}"形式的返回的是cell中的內(nèi)容[engine, loglik] = enter_evidence(engine, evidence); marg = marginal_nodes(engine, B); %P1=P(B|A) p1 = marg.T(2);%算出p1=0.8412 P1 %現(xiàn)在我們添加地震的證據(jù)觀察它有什么不同P2=P(B|A,E) evidence{E} = 2;% %這里1是false,2是True,等于讓E是True. [engine, loglik] = enter_evidence(engine, evidence);%loglik對數(shù)似然 marg = marginal_nodes(engine, B); p2 = marg.T(2);%算出p2=0.1089 %結(jié)論是地震更能解釋響鈴這個主要事實 %聯(lián)合概率分布%P（ B=True|A=True,E=True） evidence = cell(1,N); evidence{A} = 2; evidence{E} = 2; [engine, ll] = enter_evidence(engine, evidence);%ll m = marginal_nodes(engine, [B E A]);

[engine, ll] = enter_evidence(engine, evidence);里面是LL不是1，也有人選擇loglik，不過也有人直接把這兩個都去掉，但是結(jié)果是相同的，不知道是什么原因。
CPT表如何排列
m的結(jié)果如何輸出，m的結(jié)果如何解讀，是下一步的重點。

總結(jié)

以上是生活随笔為你收集整理的贝叶斯网络经典matlab源代码解析的全部內(nèi)容，希望文章能夠幫你解決所遇到的問題。

如果覺得生活随笔網(wǎng)站內(nèi)容還不錯，歡迎將生活随笔推薦給好友。