Random forests - Out-of-bag estimates












3














I am reading the chapter on random forests by Leo Breiman (found here: https://www.stat.berkeley.edu/~breiman/randomforest2001.pdf).



In section 3.1 Using out-of-bag estimates to monitor error, strength, and correlation (page 11), it says:




In each bootstrap training set, about one-third of the instances are
left out. Therefore, the out-of-bag estimates are based on combining
only about one-third as many classifiers as in the ongoing main
combination.




I am not sure I understand how the first sentence (that about one-third of cases are left out of each bootstrap sample) implies the second (that each case is OOB in about one-third of the trees)?






random-forest bootstrap







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    3














    I am reading the chapter on random forests by Leo Breiman (found here: https://www.stat.berkeley.edu/~breiman/randomforest2001.pdf).



    In section 3.1 Using out-of-bag estimates to monitor error, strength, and correlation (page 11), it says:




    In each bootstrap training set, about one-third of the instances are
    left out. Therefore, the out-of-bag estimates are based on combining
    only about one-third as many classifiers as in the ongoing main
    combination.




    I am not sure I understand how the first sentence (that about one-third of cases are left out of each bootstrap sample) implies the second (that each case is OOB in about one-third of the trees)?






    random-forest bootstrap







    share|cite|improve this question







    New contributor




    user51462 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.























      3












      3








      3







      I am reading the chapter on random forests by Leo Breiman (found here: https://www.stat.berkeley.edu/~breiman/randomforest2001.pdf).



      In section 3.1 Using out-of-bag estimates to monitor error, strength, and correlation (page 11), it says:




      In each bootstrap training set, about one-third of the instances are
      left out. Therefore, the out-of-bag estimates are based on combining
      only about one-third as many classifiers as in the ongoing main
      combination.




      I am not sure I understand how the first sentence (that about one-third of cases are left out of each bootstrap sample) implies the second (that each case is OOB in about one-third of the trees)?






      random-forest bootstrap







      share|cite|improve this question







      New contributor




      user51462 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      I am reading the chapter on random forests by Leo Breiman (found here: https://www.stat.berkeley.edu/~breiman/randomforest2001.pdf).



      In section 3.1 Using out-of-bag estimates to monitor error, strength, and correlation (page 11), it says:




      In each bootstrap training set, about one-third of the instances are
      left out. Therefore, the out-of-bag estimates are based on combining
      only about one-third as many classifiers as in the ongoing main
      combination.




      I am not sure I understand how the first sentence (that about one-third of cases are left out of each bootstrap sample) implies the second (that each case is OOB in about one-third of the trees)?






      random-forest bootstrap




      random-forest bootstrap






      share|cite|improve this question







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      user51462 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      asked 1 hour ago









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          In a bootstrap sample we replace. The probability of a subject x being sampled with replacement is at about 2/3. If we build for example 1000 trees with different bootstrap samples, we therefore expect that x will be in (2/3)*1000 of these samples. One third of the trees were therefore not build with subject x. The OOB only calculates the error for the trees that have not been build with x, which is (1/3)*1000 in that case.






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          • +1 Nice explanation. I think that you could make your first sentence more clear if you write "Bootstrapping samples from the original data set with replacement." Also, stats.SE supports math typesetting. More information: math.meta.stackexchange.com/questions/5020/…
            – Sycorax
            1 hour ago












          • @Sycorax Ok thanks I will do that next time.
            – Peter Dieter
            1 hour ago











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          In a bootstrap sample we replace. The probability of a subject x being sampled with replacement is at about 2/3. If we build for example 1000 trees with different bootstrap samples, we therefore expect that x will be in (2/3)*1000 of these samples. One third of the trees were therefore not build with subject x. The OOB only calculates the error for the trees that have not been build with x, which is (1/3)*1000 in that case.






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          • +1 Nice explanation. I think that you could make your first sentence more clear if you write "Bootstrapping samples from the original data set with replacement." Also, stats.SE supports math typesetting. More information: math.meta.stackexchange.com/questions/5020/…
            – Sycorax
            1 hour ago












          • @Sycorax Ok thanks I will do that next time.
            – Peter Dieter
            1 hour ago
















          2














          In a bootstrap sample we replace. The probability of a subject x being sampled with replacement is at about 2/3. If we build for example 1000 trees with different bootstrap samples, we therefore expect that x will be in (2/3)*1000 of these samples. One third of the trees were therefore not build with subject x. The OOB only calculates the error for the trees that have not been build with x, which is (1/3)*1000 in that case.






          share|cite|improve this answer








          New contributor




          Peter Dieter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
          Check out our Code of Conduct.


















          • +1 Nice explanation. I think that you could make your first sentence more clear if you write "Bootstrapping samples from the original data set with replacement." Also, stats.SE supports math typesetting. More information: math.meta.stackexchange.com/questions/5020/…
            – Sycorax
            1 hour ago












          • @Sycorax Ok thanks I will do that next time.
            – Peter Dieter
            1 hour ago














          2












          2








          2






          In a bootstrap sample we replace. The probability of a subject x being sampled with replacement is at about 2/3. If we build for example 1000 trees with different bootstrap samples, we therefore expect that x will be in (2/3)*1000 of these samples. One third of the trees were therefore not build with subject x. The OOB only calculates the error for the trees that have not been build with x, which is (1/3)*1000 in that case.






          share|cite|improve this answer








          New contributor




          Peter Dieter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
          Check out our Code of Conduct.









          In a bootstrap sample we replace. The probability of a subject x being sampled with replacement is at about 2/3. If we build for example 1000 trees with different bootstrap samples, we therefore expect that x will be in (2/3)*1000 of these samples. One third of the trees were therefore not build with subject x. The OOB only calculates the error for the trees that have not been build with x, which is (1/3)*1000 in that case.







          share|cite|improve this answer








          New contributor




          Peter Dieter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
          Check out our Code of Conduct.









          share|cite|improve this answer



          share|cite|improve this answer






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          answered 1 hour ago









          Peter Dieter

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          • +1 Nice explanation. I think that you could make your first sentence more clear if you write "Bootstrapping samples from the original data set with replacement." Also, stats.SE supports math typesetting. More information: math.meta.stackexchange.com/questions/5020/…
            – Sycorax
            1 hour ago












          • @Sycorax Ok thanks I will do that next time.
            – Peter Dieter
            1 hour ago


















          • +1 Nice explanation. I think that you could make your first sentence more clear if you write "Bootstrapping samples from the original data set with replacement." Also, stats.SE supports math typesetting. More information: math.meta.stackexchange.com/questions/5020/…
            – Sycorax
            1 hour ago












          • @Sycorax Ok thanks I will do that next time.
            – Peter Dieter
            1 hour ago
















          +1 Nice explanation. I think that you could make your first sentence more clear if you write "Bootstrapping samples from the original data set with replacement." Also, stats.SE supports math typesetting. More information: math.meta.stackexchange.com/questions/5020/…
          – Sycorax
          1 hour ago






          +1 Nice explanation. I think that you could make your first sentence more clear if you write "Bootstrapping samples from the original data set with replacement." Also, stats.SE supports math typesetting. More information: math.meta.stackexchange.com/questions/5020/…
          – Sycorax
          1 hour ago














          @Sycorax Ok thanks I will do that next time.
          – Peter Dieter
          1 hour ago




          @Sycorax Ok thanks I will do that next time.
          – Peter Dieter
          1 hour ago










          user51462 is a new contributor. Be nice, and check out our Code of Conduct.










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