{"id":519,"date":"2020-10-02T18:13:11","date_gmt":"2020-10-02T10:13:11","guid":{"rendered":"https:\/\/xg1990.com\/blog\/?p=519"},"modified":"2020-10-02T18:32:08","modified_gmt":"2020-10-02T10:32:08","slug":"%e5%b7%ae%e5%88%86%e9%9a%90%e7%a7%81%e9%a1%b9%e7%9b%ae%e5%ae%9e%e8%b7%b5-%e7%bb%9f%e8%ae%a1%e6%95%b0%e6%8d%ae%e9%9a%90%e7%a7%81%e4%bf%9d%e6%8a%a4","status":"publish","type":"post","link":"https:\/\/xg1990.com\/blog\/archives\/519","title":{"rendered":"\u5dee\u5206\u9690\u79c1\u9879\u76ee\u5b9e\u8df5\u2014\u2014\u7edf\u8ba1\u6570\u636e\u9690\u79c1\u4fdd\u62a4"},"content":{"rendered":"\n

0. \u5dee\u5206\u9690\u79c1\u7b80\u4ecb<\/h2>\n\n\n\n

\u968f\u7740GDPR\u6cd5\u89c4\u7684\u5b9e\u65bd\uff0c\u5404\u5927\u516c\u53f8\u4e3a\u4e86\u907f\u514d\u7f5a\u6b3e\uff0c\u5f00\u59cb\u91cd\u89c6\u7528\u6237\u4e2a\u4eba\u9690\u79c1\u7684\u4fdd\u62a4\u3002\u5dee\u5206\u9690\u79c1\u662f\u8fd1\u5e74\u65b0\u5174\u7684\u4e00\u4e2a\u7814\u7a76\u9886\u57df\uff0c\u4e3b\u8981\u7814\u7a76\u5982\u4f55\u4f7f\u7528\u6570\u5b66\u65b9\u6cd5\u4fdd\u62a4\u6570\u636e\u4e2d\u7684\u7528\u6237\u4e2a\u4eba\u9690\u79c1\u3002<\/p>\n\n\n\n

\u7b80\u5355\u800c\u8a00\uff0c\u5dee\u5206\u9690\u79c1\u4e3b\u8981\u901a\u8fc7\u7ed9\u6570\u636e\u589e\u52a0\u968f\u673a\u566a\u97f3\u6765\u6c61\u67d3\u6570\u636e\uff0c\u6765\u8fbe\u5230\u4fdd\u62a4\u9690\u79c1\u7684\u4f5c\u7528\u3002\u4f46\u566a\u97f3\u7684\u591a\u5c11\u81f3\u5173\u91cd\u8981\uff0c\u5982\u679c\u566a\u97f3\u592a\u5c11\u4e0d\u8db3\u4ee5\u8fbe\u5230\u9690\u79c1\u4fdd\u62a4\u7684\u76ee\u7684\uff0c\u5982\u679c\u566a\u97f3\u592a\u591a\u5c31\u4f1a\u63a9\u76d6\u6709\u4ef7\u503c\u4fe1\u606f\u3002\u800c\u5177\u4f53\u5f80\u6570\u636e\u4e2d\u589e\u52a0\u591a\u5c11\u566a\u97f3\uff0c\u5c31\u662f\u5dee\u5206\u9690\u79c1\u9700\u8981\u8ba8\u8bba\u7684\u95ee\u9898<\/p>\n\n\n\n

1. \u95ee\u9898\u80cc\u666f<\/h2>\n\n\n\n

\u6211\u4eec\u5047\u8bbe\u4e00\u4e2a\u4f01\u4e1a\u60f3\u8981\u53d1\u5e03\u81ea\u5df1\u7528\u6237\u7684\u7edf\u8ba1\u4fe1\u606f\uff0c\u4f8b\u5982\uff1aT\u5b9d\u8ba1\u5212\u53d1\u5e03\u7528\u6237\u6bcf\u4e2a\u57ce\u5e02\u7684\u7528\u6237\u6bcf\u5e74\u5e73\u5747\u6d88\u8d39\u91d1\u989d\uff0c\u4f5c\u4e3a\u67d0\u4e2a\u6d3b\u52a8\u7684\u5ba3\u4f20\u6587\u6848\u3002\u76f4\u89c2\u6765\u770b\uff0c\u516c\u5e03\u57ce\u5e02\u7684\u7edf\u8ba1\u6570\u636e\uff08\u6bd4\u5982\u5e73\u5747\u503c\uff09\u5e76\u4e0d\u4f1a\u6cc4\u6f0f\u4efb\u4f55\u4eba\u7684\u9690\u79c1\u3002\u4f46\u5728\u6700\u574f\u7684\u53ef\u80fd\u4e0b\uff0c\u5c11\u6570\u4eba\u7684\u6570\u636e\u4f1a\u56e0\u6b64\u800c\u66b4\u9732\u3002<\/p>\n\n\n\n

\u5177\u4f53\u60c5\u666f\u5982\u4e0b\uff1a
\u5047\u8bbeX\u57ce\u5e02\u603b\u4eba\u6570\u4e3a100\u4eba\uff0cT\u5b9d\u516c\u5e03\u7684\u8be5\u57ce\u5e022018\u5e74\u4eba\u5747\u6d88\u8d39\u91d1\u989d\u662f1\u4e07\u5143\uff0c2019\u5e74\u4eba\u5747\u6d88\u8d39\u91d1\u989d\u66b4\u589e\u52302\u4e07\u5143\u3002
\u540c\u65f6\u4f60\u4ece\u5176\u4ed6\u4fe1\u606f\u6e20\u9053\u5f97\u77e5\uff0c\u67d0\u77e5\u540d\u5bcc\u4e8c\u4ee3Y\u57282019\u5e74\u642c\u5165X\u57ce\u5e02\u3002X\u57ce\u5e02\u73b0\u5728\u7684\u4eba\u53e3\u662f101\u4eba\u3002<\/p>\n\n\n\n

\u90a3\u4e48\u6839\u636e\u5e73\u5747\u503c\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u53ef\u4ee5\u63a8\u7b97\u51fa<\/strong>\uff0c\u5ba2\u6237Y\u7684\u5e74\u6d88\u8d39\u91d1\u989d\u662f 2\u4e07*101-1\u4e07*100=102\u4e07<\/p>\n\n\n\n

\u867d\u7136\u8be5\u516c\u53f8\u53ea\u662f\u516c\u5e03\u4e86X\u57ce\u5e02\u4e24\u5e74\u7684\u4eba\u5c45\u6d88\u8d39\u6570\u636e\uff0c\u4f46\u5728\u4e0d\u7ecf\u610f\u95f4\u66b4\u9732\u4e86\u4e00\u4f4d\u65b0\u6765\u5ba2\u6237\u7684\u4fe1\u606f\u3002\u8fd9\u5c31\u662f\u5dee\u5206\u9690\u79c1\u8981\u89e3\u51b3\u7684\u95ee\u9898\u4e4b\u4e00<\/p>\n\n\n\n

2. \\(\\epsilon\\)-\u5dee\u5206\u9690\u79c1<\/h2>\n\n\n\n

\u5f00\u59cb\u4e4b\u524d\uff0c\u9700\u8981\u5148\u91cf\u5316\u9700\u8981\u89e3\u51b3\u7684\u95ee\u9898\u3002\u5728\u4e0a\u9762\u7684\u4f8b\u5b50\u4e2d\uff0c\u4e3b\u8981\u7684\u95ee\u9898\u6765\u81ea\u4e8e\u8fde\u7eed\u516c\u5e03\u7684\u4e24\u4e2a\u7edf\u8ba1\u91cf\uff081\u4e07\u548c2\u4e07\uff09\u76f8\u5dee\u592a\u5927\uff0c\u5e26\u6765\u4e86\u9690\u79c1\u6cc4\u9732\u3002<\/p>\n\n\n\n

\u6b64\u7c7b\u95ee\u9898\u7684\u89e3\u51b3\u65b9\u6848\u79f0\u4e3a\\(\\epsilon\\)-\u5dee\u5206\u9690\u79c1\u3002\\(\\epsilon\\)-\u5dee\u5206\u9690\u79c1\u662f\u5dee\u5206\u9690\u79c1\u7684\u4e00\u79cd\uff0c\u5b83\u5c06\u9700\u8981\u89e3\u51b3\u7684\u95ee\u9898\u7528\u89c4\u8303\u7684\u6570\u5b66\u5f62\u5f0f\u63cf\u8ff0\u4e3a\uff1a<\/p>\n\n\n\n

\\[ \\frac{\\Pr[{\\mathcal {A}}(D)\\in S]}{\\Pr[{\\mathcal {A}}(D\u2018)\\in S]} \\leq \\exp \\left(\\epsilon \\right) \\]<\/p>\n\n\n\n

\u8fd9\u4e2a\u516c\u5f0f\u4e2d\uff0c\u53f3\u4fa7\u7684\u53c2\u6570 \\( \\epsilon \\) \u901a\u5e38\u4e3a\u5927\u4e8e0\u7684\u6b63\u5b9e\u6570\uff0c\u662f\u5bf9\u4e8e\u9690\u79c1\u7684\u91cf\u5316\u7ea6\u675f\u91cf\u3002\u5f0f\u5b50\u53f3\u4fa7\\(\\exp \\left(\\epsilon \\right) \\)\u5219\u4e3a\u4e00\u4e2a\u5927\u4e8e1\u7684\u5b9e\u6570\u3002<\/p>\n\n\n\n

\u5728\u516c\u5f0f\u7684\u5de6\u8fb9\uff0c\\(D\\)\u548c\\(D\u2018\\)\u5206\u522b\u4e3a\u539f\u6570\u636e\u96c6\u548c\u5176\u76f8\u90bb<\/strong>\u6570\u636e\u96c6\uff0c\u8fd9\u91cc\u300c\u76f8\u90bb<\/strong>\u300d\u7684\u5b9a\u4e49\u662f\u5b83\u4eec\u4ec5\u4ec5\u76f8\u5dee\u4e00\u6761\u6570\u636e\uff0c\u53ef\u4ee5\u7c7b\u6bd4\u4e0a\u6587\u4f8b\u5b50\u4e2d2018\u5e74\u7684100\u4eba\u548c2019\u5e74\u7684101\u4eba\uff09\u3002<\/p>\n\n\n\n

\\({\\mathcal {A}}(D)\\) \u4ee3\u8868\u6211\u4eec\u5728\\(D\\) \u8fd9\u4e2a\u6570\u636e\u96c6\u4e0a\u8ba1\u7b97\u7684\u7edf\u8ba1\u91cf\uff0c\u53ef\u4ee5\u7c7b\u6bd4\u4e0a\u6587\u63d0\u5230\u7684\u5e73\u5747\u503c\u51fd\u6570\u3002<\/p>\n\n\n\n

\\(\\Pr[{\\mathcal {A}}(D)\\in S]\\) \u4ee3\u8868\u6211\u4eec\u5728 \\(D\\) \u8fd9\u4e2a\u6570\u636e\u96c6\u4e0a\u8ba1\u7b97\u7684\u7edf\u8ba1\u91cf\u521a\u597d\u662fS\u7684\u6982\u7387\u3002<\/p>\n\n\n\n

\u5f0f\u5b50\u5de6\u8fb9\u5219\u8868\u8fbe\u7684\u662f\uff0c\u5728\\(D\\)\u548c\\(D’\\)\u4e24\u4e2a\u76f8\u90bb\u6570\u636e\u96c6\u4e0a\u8ba1\u7b97\u7edf\u8ba1\u91cf \\({\\mathcal {A}}\\) \u6240\u5f97\u5230\u7684\u7ed3\u679c\u76f8\u540c\uff08\u90fd\u662f\\(S\\)\uff09\u7684\u6982\u7387\u7684\u6bd4\u503c\u5e94\u8be5\u5c0f\u4e8e\u67d0\u4e2a\u5927\u4e8e1\u7684\u5b9e\u6570\uff08\u5373\u4e3a\\(\\exp \\left(\\epsilon \\right) \\)\uff09\u3002\u907f\u514d\u51fa\u73b0\u4e0a\u9762\u7684\u4f8b\u5b50\u91cc\u97621\u4e07\u548c2\u4e07\u8fd9\u79cd\u5de8\u5927\u7684\u5dee\u5f02\u3002<\/p>\n\n\n\n

\u8fd9\u4e2a\u7ea6\u675f\u6761\u4ef6\u80fd\u591f\u4fdd\u8bc1\u4e2a\u4f53\u6570\u636e\u7684\u5dee\u5f02\u7ed9\u603b\u4f53\u7edf\u8ba1\u91cf\u5e26\u6765\u7684\u5f71\u54cd\u5728\u6709\u9650\u8303\u56f4\u5185\uff0c\u786e\u4fdd\u4e86\u4e2a\u4f53\u7684\u9690\u79c1\u5b89\u5168\u3002<\/p>\n\n\n\n

\u5728\\(\\epsilon\\)-\u5dee\u5206\u9690\u79c1\u4e2d\uff0c\u8fd9\u79cd\u9690\u79c1\u4fdd\u62a4\u7684\u9650\u5ea6\u53d6\u51b3\u4e8e \\(\\epsilon\\)\u7684\u53d6\u503c\u3002\u5f53\\(\\epsilon\\)\u7684\u53d6\u503c\u4e3a0\u65f6\uff0c\u4ee3\u8868\u4e86\u6781\u7aef\u7684\u9690\u79c1\u4fdd\u62a4\u7b56\u7565\uff0c\u516c\u5f0f\u53f3\u4fa7\u4e3a1\uff0c\\(D\\)\u548c\\(D’\\)\u4e24\u4e2a\u6570\u636e\u96c6\u4e0a\u8ba1\u7b97\u7684\u7edf\u8ba1\u91cf\u5fc5\u987b\u4e25\u683c\u4e00\u81f4\u3002\u76f8\u53cd\uff0c\u5f53\\(\\epsilon\\)\u7684\u53d6\u503c\u4e3a\u4e00\u4e2a\u975e\u5e38\u5927\u7684\u6570\u503c\uff08\u6bd4\u5982100\uff09\u65f6\uff0c\u4ee3\u8868\u4e86\u6781\u5ea6\u5bbd\u677e\u7684\u9690\u79c1\u4fdd\u62a4\u7b56\u7565\uff0c\u6b64\u65f6\u516c\u5f0f\u53f3\u4fa7\u975e\u5e38\u5927\uff0c\\(D\\)\u548c\\(D’\\)\u4e24\u4e2a\u6570\u636e\u96c6\u4e0a\u8ba1\u7b97\u7684\u7edf\u8ba1\u91cf\u53ef\u4ee5\u6709\u5f88\u5927\u7684\u5dee\u5f02\u3002<\/p>\n\n\n\n

\u8bf7\u6ce8\u610f\uff0c\\(\\epsilon\\) \u662f\u4e3b\u89c2\u6307\u5b9a\u7684\u4e00\u4e2a\u503c\uff0c\u4e00\u822c\u4e3a1\u5de6\u53f3\uff0c\u5177\u4f53\u7684\u9009\u62e9\u65b9\u6cd5\u4f1a\u5728\u6700\u540e\u8ba8\u8bba\u3002<\/p>\n\n\n\n

\u4ee5\u4e0a\u4ec5\u4ec5\u5b9a\u4e49\u4e86\u6211\u4eec\u7684\u9690\u79c1\u4fdd\u62a4\u76ee\u6807\uff0c\u4f46\u6ca1\u6709\u63d0\u53ca\u5982\u4f55\u5b9e\u73b0\u8fd9\u4e00\u9690\u79c1\u4fdd\u62a4\u76ee\u6807\u3002\u5177\u4f53\u7684\u5b9e\u73b0\u624b\u6bb5\u6709\u5f88\u591a\uff0c\u6700\u5e38\u7528\u7684\u662f\u63a5\u4e0b\u6765\u4ecb\u7ecd\u7684\u62c9\u666e\u62c9\u65af\u673a\u5236<\/p>\n\n\n\n

3. \u62c9\u666e\u62c9\u65af\u673a\u5236(The Laplace mechanism)<\/h2>\n\n\n\n

\u62c9\u666e\u62c9\u65af\u673a\u5236\uff0c\u4e5f\u79f0\u4e3a\u566a\u97f3\u589e\u52a0\u673a\u5236\uff0c\u901a\u8fc7\u7ed9\u6570\u636e\u589e\u52a0\u566a\u97f3\u6765\u4fdd\u62a4\u9690\u79c1\u3002\u566a\u97f3\u7684\u672c\u8d28\u662f\u4e00\u4e2a\u7b26\u5408\u62c9\u666e\u62c9\u65af\u5206\u5e03\u7684\u968f\u673a\u6570\uff1a<\/p>\n\n\n\n

\\[ {\\text{noise}}(x) = {\\frac {1}{2b}}\\exp \\left(-{\\frac {|x|}{b}}\\right) \\]<\/p>\n\n\n\n

\u8fd9\u4e2a\u968f\u673a\u566a\u97f3\u7684\u968f\u673a\u7a0b\u5ea6\uff08\u65b9\u5dee\uff09\u53d6\u51b3\u4e8e\u5b83\u7684\u89c4\u6a21\uff08scale\uff09\u53c2\u6570\\(b\\) \u3002\u4f7f\u7528\u62c9\u666e\u62c9\u65af\u673a\u5236\u524d\u9700\u8981\u5148\u786e\u5b9a\u53c2\u6570\\(b\\)\u7684\u53d6\u503c\u3002<\/p>\n\n\n\n

\u8fd9\u4e2a\u8fc7\u7a0b\u9700\u8981\u5f15\u5165\u4e00\u4e2a\u65b0\u7684\u6982\u5ff5\uff1a\u654f\u611f\u5ea6\uff08sensitivity\uff09\u3002<\/p>\n\n\n\n

4. \u654f\u611f\u5ea6<\/h2>\n\n\n\n

\u5728\u5dee\u5206\u9690\u79c1\u4e2d\uff0c\u6211\u4eec\u628a\u4e24\u4e2a\u76f8\u90bb\u6837\u672c\u96c6\uff08\u4e0a\u6587\u4e2d\u7684\\(D\\)\u548c\\(D’\\)\uff09\u7684\u7edf\u8ba1\u91cf\u7684\u6700\u5927\u5dee\u5f02\u5b9a\u4e49\u4e3a\u654f\u611f\u5ea6\uff08sensitivity\uff09:

\\[ \\Delta f=\\max_{D, D’} \\lVert f(D)-f(D’)\\rVert _{l} \\]<\/p>\n\n\n\n

\u654f\u611f\u5ea6\u7684\u5177\u4f53\u503c\u901a\u8fc7\u5b9e\u9645\u6240\u4f7f\u7528\u7684\u6837\u672c\u96c6 \\(D\\) \u4e0e\u6240\u4f7f\u7528\u7684\u7edf\u8ba1\u51fd\u6570 \\(f(\\cdot)\\)\u6765\u8ba1\u7b97\u5f97\u5230\u3002\u654f\u611f\u5ea6\u7684\u8ba1\u7b97\u65b9\u6cd5\u6709\u5f88\u591a\uff0c\u6700\u539f\u59cb\u7684\u65b9\u6cd5\u5c31\u662f\u4f7f\u7528\u86ee\u529b\u6cd5\uff1a\u5c1d\u8bd5\u4ece\u6837\u672c\u96c6\u4e2d\u53bb\u9664\u6bcf\u4e00\u4e2a\u6837\u672c\uff0c\u8ba1\u7b97\u53bb\u9664\u524d\u540e\u7edf\u8ba1\u51fd\u6570\u7ed3\u679c\u5dee\u5f02\uff0c\u5e76\u8ba1\u7b97\u6700\u5927\u7684\u5dee\u5f02\u4f5c\u4e3a\u654f\u611f\u5ea6\uff0c\u5bf9\u5e94\u7684python\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n\n\n\n

import numpy as np\n\n\ndef sensitivity(data, agg_func):\n    max_diff = 0\n    for i in range(len(data)):\n        max_diff = max(max_diff, abs( agg_func(data) - agg_func(data[:i] + data[(i+1):]) ))\n    return max_diff\n\nsensitivity( [1,2,3,4,5], np.mean)\n# output is 0.5<\/pre>\n\n\n\n
\u5f53\u7136\u8fd9\u79cd\u86ee\u529b\u6cd5\u8ba1\u7b97\u654f\u611f\u5ea6\u975e\u5e38\u4f4e\u6548\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u6839\u636e\u5177\u4f53\u7684\u7edf\u8ba1\u51fd\u6570\u6765\u8fdb\u884c\u4f18\u5316\u3002\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u9700\u8981\u4fdd\u62a4\u7684\u7edf\u8ba1\u91cf\u662f\u5e73\u5747\u503c\uff0c\u90a3\u4e48\u53ef\u4ee5\u5176\u654f\u611f\u5ea6\u5f80\u5f80\u53d6\u51b3\u4e8e\u6570\u636e\u96c6\u4e2d\u6700\u5927\u548c\u6700\u5c0f\u7684\u5143\u7d20\u3002<\/p>\n\n\n\n
\u6b64\u5916\u8fd9\u79cd\u8ba1\u7b97\u53ea\u8003\u8651\u5230\u4e86\u79fb\u9664<\/strong>\u4e00\u6761\u6570\u636e\u7684\u654f\u611f\u5ea6\uff0c\u589e\u52a0<\/strong>\u4e00\u6761\u65b0\u6570\u636e\u7684\u654f\u611f\u5ea6\u540c\u6837\u5e94\u8be5\u8003\u8651\u5728\u5185\u3002\u6bd4\u5982\u539f\u6570\u636e\u96c6\u662f\\([1,2,3,4,5]\\)\uff0c\u6211\u4eec\u65b0\u589e\u4e00\u6761\u6570\u636e 100\u53d8\u6210\\([1,2,3,4,5,100]\\)\uff0c\u654f\u611f\u5ea6\u76f4\u63a5\u98d9\u5347\u523016.16\u3002\u8fd9\u91cc\u5c31\u6709\u4e00\u4e2a\u65b0\u7684\u95ee\u9898\uff1a\u65b0\u589e\u6570\u636e\u4e0d\u53ef\u63a7\u7684\u60c5\u51b5\u4e0b\uff0c\u5982\u4f55\u5408\u7406\u4f30\u8ba1\u654f\u611f\u5ea6\uff1f\u5b9e\u8df5\u4e2d\u53ef\u4ee5\u91c7\u7528\u7684\u65b9\u5f0f\u662f\u7ea6\u5b9a\u4e00\u4e2a\u6570\u636e\u7684\u4e0a\u4e0b\u9650\uff0c\u51e1\u662f\u8d85\u8fc7\u4e0a\u4e0b\u9650\u7684\u6570\u636e\u90fd\u53d6\u8fb9\u754c\u503c\u3002\uff08\u6570\u636e\u6e05\u6d17\u7684\u8fc7\u7a0b\u4e2d\u4e5f\u4f1a\u4f7f\u7528\u7c7b\u4f3c\u7684\u65b9\u6cd5\u6765\u6e05\u9664\u5f02\u5e38\u503c\uff09<\/p>\n\n\n\n
5. \u62c9\u666e\u62c9\u65af\u53c2\u6570\u4f30\u8ba1<\/h2>\n\n\n\n
\u8ba1\u7b97\u5f97\u5230\u4e86\u4e0a\u4e00\u8282\u4e2d\u7684\u654f\u611f\u5ea6\\(\\Delta f\\)\u4ee5\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u5982\u4e0b\u516c\u5f0f\u8bbe\u5b9a\u62c9\u666e\u62c9\u65af\u968f\u673a\u91cf\u7684\u89c4\u6a21\u53c2\u6570(scale) \\(b\\)\uff1a<\/p>\n\n\n\n
\\[ b = \\frac{\\Delta f}{\\epsilon}\\]<\/p>\n\n\n\n
\u6839\u636e\u4ee5\u4e0a\u53c2\u6570\uff0c\u5728\u6570\u636e\u96c6\\(D\\)\u4e0a\u8ba1\u7b97\u7684\u7edf\u8ba1\u91cf\\(f\\)\u9700\u8981\u52a0\u4e0a\u5bf9\u5e94\u7684\u62c9\u666e\u62c9\u65af\u566a\u97f3\uff0c\u5982\u4e0b\uff1a<\/p>\n\n\n\n
\\[\\mathcal{A}(D)= f\\left(D\\right) + {\\frac {\\epsilon}{2\\Delta f}}\\exp \\left(-{\\frac {\\epsilon|x|}{\\Delta f}}\\right) \\]<\/p>\n\n\n\n
\u5176\u4e2d\u654f\u611f\u5ea6\\(\\Delta f\\)\u4f7f\u7528\u4e0a\u6587\u4e2d\u7684\u65b9\u6cd5\u6839\u636e\u5177\u4f53\u7684\u6570\u636e\u96c6\u548c\u7edf\u8ba1\u91cf\u8ba1\u7b97\uff1b\\(\\epsilon\\)\u7531\u4f7f\u7528\u8005\u6839\u636e\u5177\u4f53\u60c5\u51b5\u6307\u5b9a\u3002<\/p>\n\n\n\n
\u53ea\u8981\u4f7f\u7528\u4ee5\u4e0a\u53c2\u6570\u751f\u6210\u566a\u97f3\uff0c\u5c31\u80fd\u591f\u4fdd\u8bc1\u6240\u5f97\u5230\u7684\u7edf\u8ba1\u91cf\u80fd\u591f\u6ee1\u8db3\\(\\epsilon\\)-\u5dee\u5206\u9690\u79c1\u6761\u4ef6<\/p>\n\n\n\n
\\[ \\frac{\\Pr[{\\mathcal {A}}(D)\\in S]}{\\Pr[{\\mathcal {A}}(D’)\\in S]} \\leq \\exp \\left(\\epsilon \\right) \\]<\/p>\n\n\n\n
\u5177\u4f53\u8bc1\u660e\u8fc7\u7a0b\u5982\u4e0b\uff08\u592a\u590d\u6742\u53ef\u4ee5\u8df3\u8fc7\uff09<\/p>\n\n\n\n
\u8003\u8651\u5230\\(\\mathcal{A}(D)\\)\u662f\\(f(D)\\)\u589e\u52a0\u4e86\u566a\u97f3\u7684\u7248\u672c\uff0c\u90a3\u4e48\\(\\Pr[{\\mathcal {A}}(D)\\in S] = {\\frac {\\epsilon}{2\\Delta f}}\\exp \\left(-{\\frac {\\epsilon|f(D)|}{\\Delta f}}\\right) \\)\uff0c\u56e0\u6b64\u6709\uff1a<\/p>\n\n\n\n
\\begin{align}
\\frac{\\Pr[{\\mathcal {A}}(D)\\in S]}{\\Pr[{\\mathcal {A}}(D’)\\in S]} & = \\frac{ {\\frac {\\epsilon}{2\\Delta f}}\\exp \\left(-{\\frac {\\epsilon|f(D)|}{\\Delta f}}\\right)}{ {\\frac {\\epsilon}{2\\Delta f}}\\exp \\left(-{\\frac {\\epsilon|f(D’)|}{\\Delta f}}\\right)}\\\\
& = \\frac{ \\exp \\left(-{\\frac {\\epsilon|f(D)|}{\\Delta f}}\\right)}{ \\exp \\left(-{\\frac {\\epsilon|f(D’)|}{\\Delta f}}\\right)}\\\\
& = \\exp \\left({\\frac {\\epsilon}{\\Delta f}}(|f(D’)| – |f(D)|)\\right)\\\\
& \\leq \\exp \\left({\\frac {\\epsilon}{\\Delta f}}(|f(D) – f(D’)|)\\right) \\\\
& \\leq \\exp \\left({\\frac {\\epsilon}{\\Delta f}}(\\Delta f)\\right) \\\\
& = \\exp \\left(\\epsilon\\right) \\\\
\\end{align}<\/p>\n\n\n\n
6. \u5c0f\u7ed3<\/h2>\n\n\n\n
\u603b\u7ed3\u4ee5\u4e0a\u5185\u5bb9\uff0c\u5728\u5b9e\u8df5\u4e2d\u516c\u5e03\u654f\u611f\u6570\u636e\u96c6\u7684\u7edf\u8ba1\u91cf\u65f6\uff0c\u53ef\u4ee5\u9075\u5faa\u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/p>\n\n\n\n
  1. \u6839\u636e\u6570\u636e\u7684\u654f\u611f\u7a0b\u5ea6\u786e\u5b9a\\(\\epsilon\\)\u7684\u53d6\u503c\uff0c\u5982\u679c\u4e0d\u77e5\u9053\u53d6\u591a\u5c11\u7684\u8bdd 1 \u662f\u4e00\u4e2a\u6bd4\u8f83\u4e2d\u95f4\u7684\u9009\u9879\u3002\u66f4\u654f\u611f\u7684\u6570\u636e\u53ef\u4ee5\u9009\u62e9\u5c0f\u4e8e1\u7684\u503c\uff0c\u4e0d\u90a3\u4e48\u654f\u611f\u7684\u6570\u636e\u53ef\u4ee5\u9009\u62e9\u66f4\u5927\u7684\\(\\epsilon\\)<\/li>
  2. \u6839\u636e\u5177\u4f53\u7684\u6570\u636e\u8ba1\u7b97\u6570\u636e\u96c6\\(D\\)\u7684\u654f\u611f\u5ea6\\( \\Delta f=\\max_{D, D’} \\lVert f(D)-f(D’)\\rVert _{l} \\)\uff0c\u5176\u4e2d\\(D’\\)\u4e0e\\(D\\)\u4ec5\u76f8\u5dee\u4e00\u6761\u6570\u636e<\/li>
  3. \u8ba1\u7b97\u62c9\u666e\u62c9\u65af\u968f\u673a\u6570\u7684\u5c3a\u5ea6(Scale)\u53c2\u6570\\( b = \\frac{\\Delta f}{\\epsilon}\\)<\/li>
  4. \u6700\u540e\u5728\u516c\u5e03\u7684\u6570\u636e\u96c6\u7edf\u8ba1\u91cf\u4e0a\u589e\u52a0\u5bf9\u5e94\u7684\u62c9\u666e\u62c9\u65af\u968f\u673a\u6570\\(\\mathcal{A}(D)= f\\left(D\\right) + {\\frac {\\epsilon}{2\\Delta f}}\\exp \\left(-{\\frac {\\epsilon|x|}{\\Delta f}}\\right) \\)<\/li><\/ol>\n\n\n\n
    \u8fd9\u6837\u5c31\u80fd\u4fdd\u8bc1\u6240\u516c\u5e03\u7684\u6570\u636e\u6709\u8db3\u591f\u7684\u9690\u79c1\u4fdd\u62a4\u3002<\/p>\n\n\n\n
    \u5f53\u7136\u8fd9\u5957\u6d41\u7a0b\u4ec5\u9002\u7528\u4e8e\u6570\u636e\u7684\u4e00\u6b21\u6027\u9759\u6001\u53d1\u5e03\u3002\u5982\u679c\u6709\u7528\u6237\u53cd\u590d\u67e5\u8be2\u540c\u4e00\u4e2a\u6570\u636e\u96c6\u4e0a\u7684\u7edf\u8ba1\u91cf\uff0c\u6bcf\u6b21\u90fd\u5f97\u5230\u4e86\u4f7f\u7528\u4e0d\u540c\u566a\u97f3\u4fdd\u62a4\u7684\u7ed3\u679c\uff0c\u90a3\u4e48\u901a\u8fc7\u5927\u91cf\u7684\u67e5\u8be2\u4f9d\u65e7\u53ef\u4ee5\u4f30\u8ba1\u51fa\u65e0\u566a\u97f3\u7684\u771f\u5b9e\u7ed3\u679c\u3002\u5728\u8fd9\u79cd\u573a\u666f\u4e0b\u5219\u9700\u8981\u5f15\u5165\u9690\u79c1\u9884\u7b97\uff08privacy budget\uff09\u7684\u6982\u5ff5\u6765\u8fdb\u4e00\u6b65\u4fdd\u62a4\u6570\u636e\u9690\u79c1\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
    0. \u5dee\u5206\u9690\u79c1\u7b80\u4ecb \u968f\u7740GDPR\u6cd5\u89c4\u7684\u5b9e\u65bd\uff0c\u5404\u5927\u516c\u53f8\u4e3a\u4e86\u907f\u514d\u7f5a\u6b3e\uff0c\u5f00\u59cb\u91cd\u89c6\u7528\u6237\u4e2a\u4eba\u9690\u79c1\u7684\u4fdd\u62a4\u3002\u5dee\u5206\u9690\u79c1\u662f\u8fd1\u5e74\u65b0… \u9605\u8bfb\u66f4\u591a »\u5dee\u5206\u9690\u79c1\u9879\u76ee\u5b9e\u8df5\u2014\u2014\u7edf\u8ba1\u6570\u636e\u9690\u79c1\u4fdd\u62a4<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"off","neve_meta_content_width":0,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":""},"categories":[1],"tags":[],"translation":{"provider":"WPGlobus","version":"3.0.1","language":"zh","enabled_languages":["zh","en"],"languages":{"zh":{"title":true,"content":true,"excerpt":false},"en":{"title":false,"content":false,"excerpt":false}}},"yoast_head":"\n\u5dee\u5206\u9690\u79c1\u9879\u76ee\u5b9e\u8df5\u2014\u2014\u7edf\u8ba1\u6570\u636e\u9690\u79c1\u4fdd\u62a4 - 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