Random forest - 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)?










share|cite|improve this question





























    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)?










    share|cite|improve this question



























      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)?










      share|cite|improve this question















      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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      share|cite|improve this question













      share|cite|improve this question




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      edited Jan 3 at 4:07







      user51462

















      asked Jan 2 at 0:14









      user51462user51462

      1184




      1184






















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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.






          share|cite|improve this answer





















          • +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
            Jan 2 at 0:53












          • Thank you @Peter, that cleared it up.
            – user51462
            Jan 3 at 4:16











          Your Answer





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          1 Answer
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          1 Answer
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          active

          oldest

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          active

          oldest

          votes






          active

          oldest

          votes









          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





















          • +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
            Jan 2 at 0:53












          • Thank you @Peter, that cleared it up.
            – user51462
            Jan 3 at 4:16
















          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





















          • +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
            Jan 2 at 0:53












          • Thank you @Peter, that cleared it up.
            – user51462
            Jan 3 at 4:16














          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












          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












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 2 at 0:50









          Peter DieterPeter Dieter

          536




          536












          • +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
            Jan 2 at 0:53












          • Thank you @Peter, that cleared it up.
            – user51462
            Jan 3 at 4:16


















          • +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
            Jan 2 at 0:53












          • Thank you @Peter, that cleared it up.
            – user51462
            Jan 3 at 4:16
















          +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
          Jan 2 at 0:53






          +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
          Jan 2 at 0:53














          Thank you @Peter, that cleared it up.
          – user51462
          Jan 3 at 4:16




          Thank you @Peter, that cleared it up.
          – user51462
          Jan 3 at 4:16


















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