AI \u8d1d\u53f6\u65af\u7f51\u7edc<\/h1>\n<\/p><\/div>\n

\n \u8d1d\u53f6\u65af\u7f51\u7edc\u662f\u7528\u4e8e\u5904\u7406\u6982\u7387\u4e8b\u4ef6\u5e76\u89e3\u51b3\u4e0d\u786e\u5b9a\u6027\u95ee\u9898\u7684\u5173\u952e\u8ba1\u7b97\u673a\u6280\u672f\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u8d1d\u53f6\u65af\u7f51\u7edc\u5b9a\u4e49\u4e3a:\n <\/div>\n

\n \"\u8d1d\u53f6\u65af\u7f51\u7edc\u662f\u4e00\u79cd\u6982\u7387\u56fe\u5f62\u6a21\u578b\uff0c\u5b83\u4f7f\u7528\u6709\u5411\u65e0\u73af\u56fe\u8868\u793a\u4e00\u7ec4\u53d8\u91cf\u53ca\u5176\u6761\u4ef6\u76f8\u5173\u6027\u3002\"\n <\/div>\n

\n \u5b83\u662f\u4e5f\u79f0\u4e3a\u8d1d\u53f6\u65af\u7f51\u7edc\uff0c\u4fe1\u5ff5\u7f51\u7edc\uff0c\u51b3\u7b56\u7f51\u7edc\u6216\u8d1d\u53f6\u65af\u6a21\u578b\u3002\n <\/div>\n

\n \u8d1d\u53f6\u65af\u7f51\u7edc\u662f\u6982\u7387\u6027\u7684\uff0c\u56e0\u4e3a\u8fd9\u4e9b\u7f51\u7edc\u662f\u57fa\u4e8e\u6982\u7387\u5206\u5e03\uff0c\u5e76\u4e14\u8fd8\u5c06\u6982\u7387\u8bba\u7528\u4e8e\u9884\u6d4b\u548c\u5f02\u5e38\u68c0\u6d4b\u3002\n <\/div>\n

\n \u73b0\u5b9e\u4e16\u754c\u4e2d\u7684\u5e94\u7528\u7a0b\u5e8f\u672c\u8d28\u4e0a\u662f\u6982\u7387\u6027\u7684\uff0c\u4e3a\u4e86\u8868\u793a\u591a\u4e2a\u4e8b\u4ef6\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u8d1d\u53f6\u65af\u7f51\u7edc\u3002\u5b83\u4e5f\u53ef\u4ee5\u7528\u4e8e\u5404\u79cd\u4efb\u52a1\uff0c\u5305\u62ec\u9884\u6d4b\uff0c\u5f02\u5e38\u68c0\u6d4b\uff0c\u8bca\u65ad\uff0c\u81ea\u52a8\u6d1e\u5bdf\uff0c\u63a8\u7406\uff0c\u65f6\u95f4\u5e8f\u5217\u9884\u6d4b\u548c\u4e0d\u786e\u5b9a\u60c5\u51b5\u4e0b\u7684\u51b3\u7b56\u3002\n <\/div>\n

\n \u8d1d\u53f6\u65af\u7f51\u7edc\u53ef\u7528\u4e8e\u6839\u636e\u6570\u636e\u548c\u4e13\u5bb6\u7684\u610f\u89c1\u6784\u5efa\u6a21\u578b\uff0c\u5b83\u5305\u62ec\u4e24\u4e2a\u90e8\u5206:\n <\/div>\n

\u6709\u5411\u65e0\u73af\u56fe <\/span>
\n \u6761\u4ef6\u6982\u7387\u8868\u3002 <\/span> <\/p>\n

\n \u5728\u4e0d\u786e\u5b9a\u77e5\u8bc6\u4e0b\u8868\u793a\u548c\u89e3\u51b3\u51b3\u7b56\u95ee\u9898\u7684\u8d1d\u53f6\u65af\u7f51\u7edc\u7684\u5e7f\u4e49\u5f62\u5f0f\u79f0\u4e3a\u5f71\u54cd\u56fe\u3002\n <\/div>\n

\n \u8d1d\u53f6\u65af\u7f51\u7edc\u56fe\u7531\u8282\u70b9\u548c\u5f27(\u5b9a\u5411\u94fe\u63a5)\u7ec4\u6210\uff0c\u5176\u4e2d:\n <\/div>\n

$AI \u8d1d\u53f6\u65af\u7f51\u7edc_https:\/\/bianchenghao6.com_\u3010ai \u6559\u7a0b\u3011_\u7b2c1\u5f20$
\n \u6bcf\u4e2a\u8282\u70b9\u4e0e\u968f\u673a\u53d8\u91cf\u76f8\u5bf9\u5e94\uff0c\u5e76\u4e14\u53d8\u91cf\u53ef\u4ee5\u662f\u8fde\u7eed\u6216\u79bb\u6563\u3002 <\/span>
\n \u5706\u5f27\u6216\u6709\u5411\u7bad\u5934\u4ee3\u8868\u968f\u673a\u53d8\u91cf\u4e4b\u95f4\u7684\u56e0\u679c\u5173\u7cfb\u6216\u6761\u4ef6\u6982\u7387\u3002\u8fd9\u4e9b\u6709\u5411\u94fe\u63a5\u6216\u7bad\u5934\u8fde\u63a5\u56fe\u4e2d\u7684\u4e00\u5bf9\u8282\u70b9\u3002
\u8fd9\u4e9b\u94fe\u63a5\u8868\u793a\u4e00\u4e2a\u8282\u70b9\u76f4\u63a5\u5f71\u54cd\u53e6\u4e00\u4e2a\u8282\u70b9\uff0c\u5982\u679c\u6ca1\u6709\u6709\u5411\u94fe\u63a5\uff0c\u5219\u610f\u5473\u7740\u8282\u70b9\u5f7c\u6b64\u72ec\u7acb\u3002 \u5728\u4e0a\u56fe\u4e2d\uff0cA\uff0cB\uff0cC\u548cD\u662f\u7531\u7f51\u7edc\u56fe\u7684\u8282\u70b9\u8868\u793a\u7684\u968f\u673a\u53d8\u91cf\u3002 <\/span> \u5982\u679c\u6211\u4eec\u6b63\u5728\u8003\u8651\u901a\u8fc7\u6709\u5411\u7bad\u5934\u5c06\u5176\u4e0e\u8282\u70b9A\u8fde\u63a5\u7684\u8282\u70b9B\uff0c\u5219\u5c06\u8282\u70b9A\u79f0\u4e3a\u8282\u70b9B\u7684\u7236\u7ea7\u3002 <\/span> \u8282\u70b9C\u72ec\u7acb\u4e8e\u8282\u70b9A\u3002 <\/span> <\/span> <\/p>\n

\n \u6ce8\u610f: <\/span>\u8d1d\u53f6\u65af\u7f51\u7edc\u56fe\u4e0d\u5305\u542b\u4efb\u4f55\u5faa\u73af\u56fe\u3002\u56e0\u6b64\uff0c\u5b83\u88ab\u79f0\u4e3a\u6709\u5411\u65e0\u73af\u56fe\u6216DAG\u3002\n <\/div>\n

\n \u8d1d\u53f6\u65af\u7f51\u7edc\u4e3b\u8981\u6709\u4e24\u4e2a\u7ec4\u6210\u90e8\u5206:\n <\/div>\n

\u539f\u56e0\u6210\u5206 <\/span>
\n \u5b9e\u9645\u6570\u5b57 <\/span> <\/p>\n

\n \u8d1d\u53f6\u65af\u7f51\u7edc\u4e2d\u7684\u6bcf\u4e2a\u8282\u70b9\u90fd\u6709\u6761\u4ef6\u6982\u7387\u5206\u5e03 P(X
\n _{i <\/sub> | Parent(X
\n _{i <\/sub>))\uff0c\u786e\u5b9a\u7236\u8282\u70b9\u5bf9\u8be5\u8282\u70b9\u7684\u5f71\u54cd\u3002\n <\/div>\n\n \u8d1d\u53f6\u65af\u7f51\u7edc\u57fa\u4e8e\u8054\u5408\u6982\u7387\u5206\u5e03\u548c\u6761\u4ef6\u6982\u7387\u3002\u56e0\u6b64\uff0c\u8ba9\u6211\u4eec\u9996\u5148\u4e86\u89e3\u8054\u5408\u6982\u7387\u5206\u5e03:\n <\/div>\n\u8054\u5408\u6982\u7387\u5206\u5e03: <\/h2>\n\n \u5982\u679c\u6211\u4eec\u6709\u53d8\u91cfx1\uff0cx2\uff0cx3\uff0c.....\uff0cxn\uff0c\u90a3\u4e48x1\uff0cx2\uff0cx3..xn\u7684\u4e0d\u540c\u7ec4\u5408\u7684\u6982\u7387\u79f0\u4e3a\u8054\u5408\u6982\u7387\u5206\u5e03\u3002\n <\/div>\n\n P [x
\n _{1 <\/sub>\uff0cx
\n _{2 <\/sub>\uff0cx
\n _{3 <\/sub>\uff0c.....\uff0cx
\n _{n <\/sub>] \uff0c\u5c31\u8054\u5408\u6982\u7387\u5206\u5e03\u800c\u8a00\uff0c\u53ef\u4ee5\u8fd9\u6837\u5199\u3002\n <\/div>\n\n = P [x
\n _{1 <\/sub> | x
\n _{2 <\/sub>\uff0cx
\n _{3 <\/sub>\uff0c.....\uff0cx
\n _{n <\/sub>] P [x
\n _{2 <\/sub>\uff0cx
\n _{3 <\/sub>\uff0c.....\uff0cx
\n _{n <\/sub>]\n <\/div>\n\n = P [x
\n _{1 <\/sub> | x
\n _{2 <\/sub>\uff0cx
\n _{3 <\/sub>\uff0c.....\uff0cx
\n _{n <\/sub>] P [x
\n _{2 <\/sub> | x
\n _{3 <\/sub>\uff0c.....\uff0cx
\n _{n <\/sub>] .... P [x
\n _{n-1 <\/sub> | x
\n _{n <\/sub>] P [x
\n _{n <\/sub>]\u3002\n <\/div>\n\n \u901a\u5e38\u5bf9\u4e8e\u6bcf\u4e2a\u53d8\u91cfXi\uff0c\u6211\u4eec\u90fd\u53ef\u4ee5\u5c06\u7b49\u5f0f\u5199\u4e3a:\n <\/div>\n\n\nP(X_{i<\/sub>|X_{i-1<\/sub>,........., X_{1<\/sub>) = P<\/span>(X_{i<\/sub> |<\/span>Parents(X_{i<\/sub> ))\n <\/pre>\n<\/code>\n <\/div>\n
\u8d1d\u53f6\u65af\u7f51\u7edc\u7684\u89e3\u91ca: <\/h2>\n\n \u8ba9\u6211\u4eec\u901a\u8fc7\u521b\u5efa\u4e00\u4e2a\u6709\u5411\u975e\u5faa\u73af\u56fe\u7684\u793a\u4f8b\u6765\u4e86\u89e3\u8d1d\u53f6\u65af\u7f51\u7edc:\n <\/div>\n\n \u793a\u4f8b: \u54c8\u5229\u5728\u5bb6\u91cc\u5b89\u88c5\u4e86\u4e00\u4e2a\u65b0\u7684\u9632\u76d7\u8b66\u62a5\u5668\uff0c\u4ee5\u4fa6\u67e5\u76d7\u7a83\u6848\u3002\u8be5\u62a5\u8b66\u5668\u5728\u68c0\u6d4b\u5230\u7206\u7a83\u65f6\u53ef\u9760\u5730\u505a\u51fa\u54cd\u5e94\uff0c\u4f46\u4e5f\u5bf9\u8f7b\u5fae\u5730\u9707\u505a\u51fa\u54cd\u5e94\u3002\u54c8\u5229\u6709\u4e24\u4e2a\u90bb\u5c45\u6234\u7ef4(David)\u548c\u7d22\u83f2\u4e9a(Sophia)\uff0c\u5f53\u4ed6\u4eec\u542c\u5230\u8b66\u62a5\u65f6\uff0c\u4ed6\u4eec\u6709\u8d23\u4efb\u5728\u5de5\u4f5c\u4e2d\u901a\u77e5\u54c8\u5229\u3002\u5927\u536b\u5728\u542c\u5230\u8b66\u62a5\u65f6\u603b\u662f\u6253\u7ed9\u54c8\u5229\uff0c\u4f46\u6709\u65f6\u4ed6\u5bf9\u7535\u8bdd\u94c3\u54cd\u611f\u5230\u56f0\u60d1\uff0c\u5e76\u5728\u90a3\u4e2a\u65f6\u5019\u6253\u7535\u8bdd\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u7d22\u83f2\u4e9a(Sophia)\u559c\u6b22\u542c\u97f3\u4e50\uff0c\u6240\u4ee5\u6709\u65f6\u5979\u9519\u8fc7\u4e86\u542c\u5230\u8b66\u62a5\u7684\u58f0\u97f3\u3002\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u8981\u8ba1\u7b97\u76d7\u7a83\u8b66\u62a5\u7684\u6982\u7387\u3002\n <\/div>\n\n \u95ee\u9898:\n <\/div>\n\n \u8ba1\u7b97\u8b66\u62a5\u54cd\u8d77\u4f46\u6ca1\u6709\u5165\u5ba4\u76d7\u7a83\u6216\u53d1\u751f\u5730\u9707\u4ee5\u53ca\u6234\u7ef4\u548c\u7d22\u83f2\u4e9a\u7684\u53ef\u80fd\u6027\u90fd\u53eb\u54c8\u5229\u3002\n <\/div>\n\n \u89e3\u51b3\u65b9\u6848:\n <\/div>\n \u4e0a\u8ff0\u95ee\u9898\u7684\u8d1d\u53f6\u65af\u7f51\u7edc\u5982\u4e0b\u3002\u7f51\u7edc\u7ed3\u6784\u8868\u660e\uff0c\u7206\u7a83\u548c\u5730\u9707\u662f\u8b66\u62a5\u7684\u7236\u8282\u70b9\uff0c\u5e76\u76f4\u63a5\u5f71\u54cd\u8b66\u62a5\u54cd\u8d77\u7684\u53ef\u80fd\u6027\uff0c\u4f46\u662fDavid\u548cSophia\u7684\u547c\u53eb\u53d6\u51b3\u4e8e\u8b66\u62a5\u7684\u53ef\u80fd\u6027\u3002<\/span>
\n \u7f51\u7edc\u8868\u793a\u6211\u4eec\u7684\u5047\u8bbe\u4e0d\u80fd\u76f4\u63a5\u611f\u77e5\u76d7\u7a83\uff0c\u4e5f\u4e0d\u4f1a\u6ce8\u610f\u5230\u5c0f\u5730\u9707\uff0c\u5e76\u4e14\u5728\u81f4\u7535\u4e4b\u524d\u4e5f\u6ca1\u6709\u5546\u5b9a\u3002<\/span>
\n \u6bcf\u4e2a\u8282\u70b9\u7684\u6761\u4ef6\u5206\u5e03\u4ee5\u6761\u4ef6\u6982\u7387\u8868\u6216CPT\u7684\u5f62\u5f0f\u7ed9\u51fa\u3002 <\/span>
\n CPT\u4e2d\u7684\u6bcf\u4e00\u884c\u90fd\u5fc5\u987b\u4e3a1\uff0c\u56e0\u4e3a\u8868\u4e2d\u7684\u6240\u6709\u6761\u76ee\u90fd\u4ee3\u8868\u8be5\u53d8\u91cf\u7684\u8be6\u5c3d\u6848\u4f8b\u96c6\u3002 <\/span>
\n \u5728CPT\u4e2d\uff0c\u5177\u6709k\u4e2a\u5e03\u5c14\u7236\u7ea7\u7684\u5e03\u5c14\u53d8\u91cf\u5305\u542b2 ^{K <\/sup>\u4e2a\u6982\u7387\u3002\u56e0\u6b64\uff0c\u5982\u679c\u6709\u4e24\u4e2a\u7236\u6bcd\uff0c\u90a3\u4e48CPT\u5c06\u5305\u542b4\u4e2a\u6982\u7387\u503c<\/span> <\/p>\n}
\n \u6b64\u7f51\u7edc\u4e2d\u53d1\u751f\u7684\u6240\u6709\u4e8b\u4ef6\u7684\u5217\u8868:\n <\/div>\n \u76d7\u7a83(B) <\/span>
\n \u5730\u9707(E) <\/span>
\n \u8b66\u62a5(A) <\/span>
\n David Calls(D) <\/span>
\n Sophia\u901a\u8bdd(S) <\/span> <\/p>\n
\n \u6211\u4eec\u53ef\u4ee5\u4ee5\u6982\u7387\u5f62\u5f0f\u5199\u95ee\u9898\u9648\u8ff0\u7684\u4e8b\u4ef6: P [D\uff0cS\uff0cA\uff0cB\uff0cE] \uff0c\u53ef\u4ee5\u4f7f\u7528\u8054\u5408\u6982\u7387\u6765\u91cd\u5199\u4e0a\u8ff0\u6982\u7387\u9648\u8ff0\u5206\u5e03:\n <\/div>\n\n P [D\uff0cS\uff0cA\uff0cB\uff0cE] = P [D | S\uff0cA\uff0cB\uff0cE]\u3002 P [S\uff0cA\uff0cB\uff0cE]\n <\/div>\n\n = P [D | S\uff0cA\uff0cB\uff0cE]\u3002 P [S | A\uff0cB\uff0cE]\u3002 P [A\uff0cB\uff0cE]\n <\/div>\n\n = P [D |\u4e00\u79cd]\u3002 P [S | A\uff0cB\uff0cE]\u3002 P [A\uff0cB\uff0cE]\n <\/div>\n\n = P [D |\u4e00\u79cd]\u3002 P [S |\u4e00\u79cd]\u3002 P [A | B\uff0cE]\u3002 P [B\uff0cE]\n <\/div>\n\n = P [D |\u4e00\u79cd ]\u3002 P [S |\u4e00\u79cd]\u3002 P [A | B\uff0cE]\u3002 P [B | E]\u3002 P [E]\n <\/div>\n <\/p>\n
\n \u8ba9\u6211\u4eec\u89c2\u5bdf\u4e00\u4e0b\u88ab\u76d7\u7684\u53ef\u80fd\u6027\u5730\u9707\u5206\u91cf:\n <\/div>\n\n P(B = True)= 0.002\uff0c\u8fd9\u662f\u5165\u5ba4\u76d7\u7a83\u7684\u53ef\u80fd\u6027\u3002\n <\/div>\n\n P(B = False)= 0.998\uff0c\u8fd9\u662f\u6ca1\u6709\u7206\u7a83\u7684\u53ef\u80fd\u6027\u3002\n <\/div>\n\n P(E =\u771f)= 0.001\uff0c\u8fd9\u662f\u53d1\u751f\u5c0f\u5730\u9707\u7684\u53ef\u80fd\u6027\n <\/div>\n\n P(E = False)= 0.99\uff0c\u8fd9\u662f\u672a\u53d1\u751f\u5730\u9707\u7684\u53ef\u80fd\u6027\u3002\n <\/div>\n\n \u6211\u4eec\u53ef\u4ee5\u6839\u636e\u4e0b\u8868\u63d0\u4f9b\u6761\u4ef6\u6982\u7387:\n <\/div>\n\n \u8b66\u62a5A\u7684\u6761\u4ef6\u6982\u7387\u8868:\n <\/div>\n\n \u6761\u4ef6\u6982\u7387\u8b66\u62a5A\u53d6\u51b3\u4e8e\u9632\u76d7\u548c\u5730\u9707:\n <\/div>\n\n\n\n\n\n\n\n B <\/td>\n E <\/td>\n P(A = True)<\/td>\n P(A = False)<\/td>\n<\/tr>\n
true<\/td>\n true<\/td>\n 0.94 <\/td>\n 0.06 <\/td>\n<\/tr>\n
true<\/td>\n false<\/td>\n 0.95 <\/td>\n 0.04 <\/td>\n<\/tr>\n
false<\/td>\n true<\/td>\n 0.31 <\/td>\n 0.69 <\/td>\n<\/tr>\n
false<\/td>\n false<\/td>\n 0.001 <\/td>\n 0.999 <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n David Calls\u7684\u6761\u4ef6\u6982\u7387\u8868:\n <\/div>\n\n David\u5c06\u8981\u547c\u53eb\u7684\u6761\u4ef6\u6982\u7387\u53d6\u51b3\u4e8eAlarm\u7684\u6982\u7387\u3002\n <\/div>\n\n\n\n\n\n A <\/td>\n P(D = True)<\/td>\n P(D = False)<\/td>\n<\/tr>\n
true<\/td>\n 0.91 <\/td>\n 0.09 <\/td>\n<\/tr>\n
false<\/td>\n 0.05 <\/td>\n 0.95 <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n Sophia\u547c\u53eb\u7684\u6761\u4ef6\u6982\u7387\u8868:\n <\/div>\n\n \u5979\u547c\u53eb\u7684Sophia\u7684\u6761\u4ef6\u6982\u7387\u53d6\u51b3\u4e8e\u5176\u7236\u8282\u70b9\"\u8b66\u62a5\"\u3002\n <\/div>\n\n\n\n\n\n A <\/td>\n P(S = True)<\/td>\n P(S = False)<\/td>\n<\/tr>\n
true<\/td>\n 0.75 <\/td>\n 0.25 <\/td>\n<\/tr>\n
false<\/td>\n 0.02 <\/td>\n 0.98 <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n \u4ece\u8054\u5408\u5206\u5e03\u7684\u516c\u5f0f\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u4ee5\u6982\u7387\u5206\u5e03\u7684\u5f62\u5f0f\u5199\u95ee\u9898\u9648\u8ff0:\n <\/div>\n\n P(S\uff0cD\uff0cA\uff0c\u00acB\uff0c\u00acE )= P(S | A)* P(D | A)* P(A |\u00acB^\u00acE)* P(\u00acB)* P(\u00acE)\u3002\n <\/div>\n\n = 0.75 * 0.91 * 0.001 * 0.998 * 0.999\n <\/div>\n\n = 0.00068045\u3001\n <\/div>\n\n \u56e0\u6b64\uff0c\u8d1d\u53f6\u65af\u7f51\u7edc\u53ef\u4ee5\u4f7f\u7528\u8054\u5408\u5206\u53d1\u6765\u56de\u7b54\u6709\u5173\u8be5\u57df\u7684\u4efb\u4f55\u67e5\u8be2\u3002\n <\/div>\n\n \u8d1d\u53f6\u65af\u7f51\u7edc\u7684\u8bed\u4e49:\n <\/div>\n\n \u6709\u4e24\u79cd\u65b9\u6cd5\u53ef\u4ee5\u7406\u89e3\u8d1d\u53f6\u65af\u7f51\u7edc\u7684\u8bed\u4e49\uff0c\u5982\u4e0b\u6240\u793a:\n <\/div>\n\n 1\u3001\u4ee5\u4e86\u89e3\u7f51\u7edc\u4f5c\u4e3a\u8054\u5408\u6982\u7387\u5206\u5e03\u7684\u8868\u793a\u3002\n <\/div>\n\n \u4e86\u89e3\u5982\u4f55\u6784\u5efa\u7f51\u7edc\u5f88\u6709\u5e2e\u52a9\u3002\n <\/div>\n\n 2\u3001\u5c06\u7f51\u7edc\u7406\u89e3\u4e3a\u6761\u4ef6\u72ec\u7acb\u6027\u58f0\u660e\u96c6\u5408\u7684\u7f16\u7801\u3002\n <\/div>\n\n \u8fd9\u5bf9\u8bbe\u8ba1\u63a8\u7406\u8fc7\u7a0b\u5f88\u6709\u5e2e\u52a9\u3002\n <\/div>\n
\n <\/body>
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