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关于“因果推断”（Causal Inference）

2020-04-24 耿直 北大数学科学学院

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因果推断（Causal Inference）

因果推断（Causal Inference） 耿直 北京大学数学科学学院 一个现象的出现总是伴随着另一个现象的出现，改变其中之一是否会导致另一个跟着变化？其答案取决于这两个现象之间仅有相关关系？还是有因果关系？自古以来，关于因果关系的研究一直吸引着人们去思考。在科学研究中，人们通过观察和实验发现自然规律、探索现象之间的因果关系是各种科学研究的最终目标。爱因斯坦认为“西方科学是建立在以因果律为基础的形式逻辑之上”。自1888年Galton提出了相关系数的概念以来，“涉及因果推断的问题自始就缠住了统计学的脚后跟”[1]，1911年，Pearson提出用列联表分析因果关系，1921年，Wright提出路径分析模型，1934年，Neyman提出潜在结果模型，1935年，Fisher提出随机化试验方法，1974年，Rubin关于观察性研究提出虚拟事实模型，Pearl[2]和Spirtes等[3]提出因果网络图模型，图1给出了一个设想的关于肺癌的因果网络[4]。Freedman介绍了从相关关系研究到因果关系研究的发展过程。从观察获得的数据中发现，不同因素之间的因果关系是统计学和人工智能领域长期关注

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  1. [GetPortalCommentsPageByObjectIdResponse(id=2201425, encodeId=3ec2220142509, content=此文对因果推断理论发展脉络非常清晰，都详细到具体的年份。, beContent=null, objectType=article, channel=null, level=null, likeNumber=43, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=6baa1634893, createdName=Ruth106, createdTime=Thu May 02 08:08:45 CST 2024, time=2024-05-02, status=1, ipAttribution=上海), GetPortalCommentsPageByObjectIdResponse(id=1668122, encodeId=c3741668122ac, content=<a href='/topic/show?id=2bab405e6c0' target=_blank style='color:#2F92EE;'>#因果推断#</a>, beContent=null, objectType=article, channel=null, level=null, likeNumber=154, replyNumber=0, topicName=null, topicId=null, topicList=[TopicDto(id=40576, encryptionId=2bab405e6c0, topicName=因果推断)], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/aLGWoFXAyMbIu3qymFOyheQLjPSX3OUs5GmkyBlcCOwTPIeq3why9NGibxxUqYo6hcx8qZLHZFgNPnBK1yzWeOFpyg2OnWOt0/0, createdBy=fa4716, createdName=仁心济世, createdTime=Tue Sep 29 22:15:39 CST 2020, time=2020-09-29, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=382177, encodeId=98cc3821e7c3, content=学习了，学习了, beContent=null, objectType=article, channel=null, level=null, likeNumber=97, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/jW482SpianMayicTRbRZ5RzTetibytbqFDmFITWHyBWbxU7S9MYibgPSqvu0sYteH0N6zXqbU0Kf3Mbdb7yWM1Kud3zPgYBibE2SZ/0, createdBy=da7696924, createdName=qingfengqishi5, createdTime=Sat Apr 25 22:38:07 CST 2020, time=2020-04-25, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=382157, encodeId=e12b38215ebc, content=很好的一篇文章，通俗易懂, beContent=null, objectType=article, channel=null, level=null, likeNumber=96, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/oLAjfB7s1ib06iaV3D9Tg5Kzuf9u71gZhPYMiajRtENwicoAABeQtfXOlic8ibhYSy6DvJZWUDVtjRvTfqBffr1XJ6JLtFB5kHicthl/0, createdBy=d41c2055892, createdName=184****9840, createdTime=Sat Apr 25 07:25:04 CST 2020, time=2020-04-25, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=382146, encodeId=7f2738214612, content=学习了，学习了, beContent=null, objectType=article, channel=null, level=null, likeNumber=107, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/jW482SpianMayicTRbRZ5RzTetibytbqFDmFITWHyBWbxU7S9MYibgPSqvu0sYteH0N6zXqbU0Kf3Mbdb7yWM1Kud3zPgYBibE2SZ/0, createdBy=da7696924, createdName=qingfengqishi5, createdTime=Fri Apr 24 23:09:53 CST 2020, time=2020-04-24, status=1, ipAttribution=)]
    2024-05-02 Ruth106 来自上海

    此文对因果推断理论发展脉络非常清晰，都详细到具体的年份。

    0

  2. [GetPortalCommentsPageByObjectIdResponse(id=2201425, encodeId=3ec2220142509, content=此文对因果推断理论发展脉络非常清晰，都详细到具体的年份。, beContent=null, objectType=article, channel=null, level=null, likeNumber=43, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=6baa1634893, createdName=Ruth106, createdTime=Thu May 02 08:08:45 CST 2024, time=2024-05-02, status=1, ipAttribution=上海), GetPortalCommentsPageByObjectIdResponse(id=1668122, encodeId=c3741668122ac, content=<a href='/topic/show?id=2bab405e6c0' target=_blank style='color:#2F92EE;'>#因果推断#</a>, beContent=null, objectType=article, channel=null, level=null, likeNumber=154, replyNumber=0, topicName=null, topicId=null, topicList=[TopicDto(id=40576, encryptionId=2bab405e6c0, topicName=因果推断)], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/aLGWoFXAyMbIu3qymFOyheQLjPSX3OUs5GmkyBlcCOwTPIeq3why9NGibxxUqYo6hcx8qZLHZFgNPnBK1yzWeOFpyg2OnWOt0/0, createdBy=fa4716, createdName=仁心济世, createdTime=Tue Sep 29 22:15:39 CST 2020, time=2020-09-29, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=382177, encodeId=98cc3821e7c3, content=学习了，学习了, beContent=null, objectType=article, channel=null, level=null, likeNumber=97, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/jW482SpianMayicTRbRZ5RzTetibytbqFDmFITWHyBWbxU7S9MYibgPSqvu0sYteH0N6zXqbU0Kf3Mbdb7yWM1Kud3zPgYBibE2SZ/0, createdBy=da7696924, createdName=qingfengqishi5, createdTime=Sat Apr 25 22:38:07 CST 2020, time=2020-04-25, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=382157, encodeId=e12b38215ebc, content=很好的一篇文章，通俗易懂, beContent=null, objectType=article, channel=null, level=null, likeNumber=96, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/oLAjfB7s1ib06iaV3D9Tg5Kzuf9u71gZhPYMiajRtENwicoAABeQtfXOlic8ibhYSy6DvJZWUDVtjRvTfqBffr1XJ6JLtFB5kHicthl/0, createdBy=d41c2055892, createdName=184****9840, createdTime=Sat Apr 25 07:25:04 CST 2020, time=2020-04-25, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=382146, encodeId=7f2738214612, content=学习了，学习了, beContent=null, objectType=article, channel=null, level=null, likeNumber=107, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/jW482SpianMayicTRbRZ5RzTetibytbqFDmFITWHyBWbxU7S9MYibgPSqvu0sYteH0N6zXqbU0Kf3Mbdb7yWM1Kud3zPgYBibE2SZ/0, createdBy=da7696924, createdName=qingfengqishi5, createdTime=Fri Apr 24 23:09:53 CST 2020, time=2020-04-24, status=1, ipAttribution=)]
    2020-09-29 仁心济世

    #因果推断#

    0

  3. [GetPortalCommentsPageByObjectIdResponse(id=2201425, encodeId=3ec2220142509, content=此文对因果推断理论发展脉络非常清晰，都详细到具体的年份。, beContent=null, objectType=article, channel=null, level=null, likeNumber=43, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=6baa1634893, createdName=Ruth106, createdTime=Thu May 02 08:08:45 CST 2024, time=2024-05-02, status=1, ipAttribution=上海), GetPortalCommentsPageByObjectIdResponse(id=1668122, encodeId=c3741668122ac, content=<a href='/topic/show?id=2bab405e6c0' target=_blank style='color:#2F92EE;'>#因果推断#</a>, beContent=null, objectType=article, channel=null, level=null, likeNumber=154, replyNumber=0, topicName=null, topicId=null, topicList=[TopicDto(id=40576, encryptionId=2bab405e6c0, topicName=因果推断)], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/aLGWoFXAyMbIu3qymFOyheQLjPSX3OUs5GmkyBlcCOwTPIeq3why9NGibxxUqYo6hcx8qZLHZFgNPnBK1yzWeOFpyg2OnWOt0/0, createdBy=fa4716, createdName=仁心济世, createdTime=Tue Sep 29 22:15:39 CST 2020, time=2020-09-29, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=382177, encodeId=98cc3821e7c3, content=学习了，学习了, beContent=null, objectType=article, channel=null, level=null, likeNumber=97, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/jW482SpianMayicTRbRZ5RzTetibytbqFDmFITWHyBWbxU7S9MYibgPSqvu0sYteH0N6zXqbU0Kf3Mbdb7yWM1Kud3zPgYBibE2SZ/0, createdBy=da7696924, createdName=qingfengqishi5, createdTime=Sat Apr 25 22:38:07 CST 2020, time=2020-04-25, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=382157, encodeId=e12b38215ebc, content=很好的一篇文章，通俗易懂, beContent=null, objectType=article, channel=null, level=null, likeNumber=96, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/oLAjfB7s1ib06iaV3D9Tg5Kzuf9u71gZhPYMiajRtENwicoAABeQtfXOlic8ibhYSy6DvJZWUDVtjRvTfqBffr1XJ6JLtFB5kHicthl/0, createdBy=d41c2055892, createdName=184****9840, createdTime=Sat Apr 25 07:25:04 CST 2020, time=2020-04-25, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=382146, encodeId=7f2738214612, content=学习了，学习了, beContent=null, objectType=article, channel=null, level=null, likeNumber=107, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/jW482SpianMayicTRbRZ5RzTetibytbqFDmFITWHyBWbxU7S9MYibgPSqvu0sYteH0N6zXqbU0Kf3Mbdb7yWM1Kud3zPgYBibE2SZ/0, createdBy=da7696924, createdName=qingfengqishi5, createdTime=Fri Apr 24 23:09:53 CST 2020, time=2020-04-24, status=1, ipAttribution=)]
    2020-04-25 qingfengqishi5

    学习了，学习了

    0

  4. [GetPortalCommentsPageByObjectIdResponse(id=2201425, encodeId=3ec2220142509, content=此文对因果推断理论发展脉络非常清晰，都详细到具体的年份。, beContent=null, objectType=article, channel=null, level=null, likeNumber=43, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=6baa1634893, createdName=Ruth106, createdTime=Thu May 02 08:08:45 CST 2024, time=2024-05-02, status=1, ipAttribution=上海), GetPortalCommentsPageByObjectIdResponse(id=1668122, encodeId=c3741668122ac, content=<a href='/topic/show?id=2bab405e6c0' target=_blank style='color:#2F92EE;'>#因果推断#</a>, beContent=null, objectType=article, channel=null, level=null, likeNumber=154, replyNumber=0, topicName=null, topicId=null, topicList=[TopicDto(id=40576, encryptionId=2bab405e6c0, topicName=因果推断)], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/aLGWoFXAyMbIu3qymFOyheQLjPSX3OUs5GmkyBlcCOwTPIeq3why9NGibxxUqYo6hcx8qZLHZFgNPnBK1yzWeOFpyg2OnWOt0/0, createdBy=fa4716, createdName=仁心济世, createdTime=Tue Sep 29 22:15:39 CST 2020, time=2020-09-29, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=382177, encodeId=98cc3821e7c3, content=学习了，学习了, beContent=null, objectType=article, channel=null, level=null, likeNumber=97, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/jW482SpianMayicTRbRZ5RzTetibytbqFDmFITWHyBWbxU7S9MYibgPSqvu0sYteH0N6zXqbU0Kf3Mbdb7yWM1Kud3zPgYBibE2SZ/0, createdBy=da7696924, createdName=qingfengqishi5, createdTime=Sat Apr 25 22:38:07 CST 2020, time=2020-04-25, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=382157, encodeId=e12b38215ebc, content=很好的一篇文章，通俗易懂, beContent=null, objectType=article, channel=null, level=null, likeNumber=96, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/oLAjfB7s1ib06iaV3D9Tg5Kzuf9u71gZhPYMiajRtENwicoAABeQtfXOlic8ibhYSy6DvJZWUDVtjRvTfqBffr1XJ6JLtFB5kHicthl/0, createdBy=d41c2055892, createdName=184****9840, createdTime=Sat Apr 25 07:25:04 CST 2020, time=2020-04-25, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=382146, encodeId=7f2738214612, content=学习了，学习了, beContent=null, objectType=article, channel=null, level=null, likeNumber=107, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/jW482SpianMayicTRbRZ5RzTetibytbqFDmFITWHyBWbxU7S9MYibgPSqvu0sYteH0N6zXqbU0Kf3Mbdb7yWM1Kud3zPgYBibE2SZ/0, createdBy=da7696924, createdName=qingfengqishi5, createdTime=Fri Apr 24 23:09:53 CST 2020, time=2020-04-24, status=1, ipAttribution=)]
    2020-04-25 184****9840

    很好的一篇文章，通俗易懂

    0

  5. [GetPortalCommentsPageByObjectIdResponse(id=2201425, encodeId=3ec2220142509, content=此文对因果推断理论发展脉络非常清晰，都详细到具体的年份。, beContent=null, objectType=article, channel=null, level=null, likeNumber=43, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=, createdBy=6baa1634893, createdName=Ruth106, createdTime=Thu May 02 08:08:45 CST 2024, time=2024-05-02, status=1, ipAttribution=上海), GetPortalCommentsPageByObjectIdResponse(id=1668122, encodeId=c3741668122ac, content=<a href='/topic/show?id=2bab405e6c0' target=_blank style='color:#2F92EE;'>#因果推断#</a>, beContent=null, objectType=article, channel=null, level=null, likeNumber=154, replyNumber=0, topicName=null, topicId=null, topicList=[TopicDto(id=40576, encryptionId=2bab405e6c0, topicName=因果推断)], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/aLGWoFXAyMbIu3qymFOyheQLjPSX3OUs5GmkyBlcCOwTPIeq3why9NGibxxUqYo6hcx8qZLHZFgNPnBK1yzWeOFpyg2OnWOt0/0, createdBy=fa4716, createdName=仁心济世, createdTime=Tue Sep 29 22:15:39 CST 2020, time=2020-09-29, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=382177, encodeId=98cc3821e7c3, content=学习了，学习了, beContent=null, objectType=article, channel=null, level=null, likeNumber=97, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/jW482SpianMayicTRbRZ5RzTetibytbqFDmFITWHyBWbxU7S9MYibgPSqvu0sYteH0N6zXqbU0Kf3Mbdb7yWM1Kud3zPgYBibE2SZ/0, createdBy=da7696924, createdName=qingfengqishi5, createdTime=Sat Apr 25 22:38:07 CST 2020, time=2020-04-25, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=382157, encodeId=e12b38215ebc, content=很好的一篇文章，通俗易懂, beContent=null, objectType=article, channel=null, level=null, likeNumber=96, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/oLAjfB7s1ib06iaV3D9Tg5Kzuf9u71gZhPYMiajRtENwicoAABeQtfXOlic8ibhYSy6DvJZWUDVtjRvTfqBffr1XJ6JLtFB5kHicthl/0, createdBy=d41c2055892, createdName=184****9840, createdTime=Sat Apr 25 07:25:04 CST 2020, time=2020-04-25, status=1, ipAttribution=), GetPortalCommentsPageByObjectIdResponse(id=382146, encodeId=7f2738214612, content=学习了，学习了, beContent=null, objectType=article, channel=null, level=null, likeNumber=107, replyNumber=0, topicName=null, topicId=null, topicList=[], attachment=null, authenticateStatus=null, createdAvatar=https://wx.qlogo.cn/mmopen/jW482SpianMayicTRbRZ5RzTetibytbqFDmFITWHyBWbxU7S9MYibgPSqvu0sYteH0N6zXqbU0Kf3Mbdb7yWM1Kud3zPgYBibE2SZ/0, createdBy=da7696924, createdName=qingfengqishi5, createdTime=Fri Apr 24 23:09:53 CST 2020, time=2020-04-24, status=1, ipAttribution=)]
    2020-04-24 qingfengqishi5

    学习了，学习了

    0

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