Hi, That helped a lot. Thank you very much. I have one more (silly?) doubt though.
Won't an n-sized bootstrapped sample have repeated entries? Say we have an original dataset of size 100. A bootstrap sample (say, B) of size 100 is drawn from this set. Since 32 of the original samples are left out (theoretically at least), some of the samples in B must be repeated? On Tue, Oct 4, 2016 at 12:50 AM, Sebastian Raschka <se.rasc...@gmail.com> wrote: > Or maybe more intuitively, you can visualize this asymptotic behavior > e.g., via > > import matplotlib.pyplot as plt > > vs = [] > for n in range(5, 201, 5): > v = 1 - (1. - 1./n)**n > vs.append(v) > > plt.plot([n for n in range(5, 201, 5)], vs, marker='o', > markersize=6, > alpha=0.5,) > > plt.xlabel('n') > plt.ylabel('1 - (1 - 1/n)^n') > plt.xlim([0, 210]) > plt.show() > > > On Oct 3, 2016, at 3:15 PM, Sebastian Raschka <se.rasc...@gmail.com> > wrote: > > > > Say the probability that a given sample from a dataset of size n is > *not* drawn as a bootstrap sample is > > > > P(not_chosen) = (1 - 1\n)^n > > > > Since you have a 1/n chance to draw a particular sample (since > bootstrapping involves drawing with replacement), which you repeat n times > to get a n-sized bootstrap sample. > > > > This is asymptotically "1/e approx. 0.368” (i.e., for very, very large n) > > > > Then, you can compute the probability of a sample being chosen as > > > > P(chosen) = 1 - (1 - 1/n)^n approx. 0.632 > > > > Best, > > Sebastian > > > >> On Oct 3, 2016, at 3:05 PM, Ibrahim Dalal via scikit-learn < > scikit-learn@python.org> wrote: > >> > >> Hi, > >> > >> Thank you for the reply. Please bear with me for a while. > >> > >> From where did this number, 0.632, come? I have no background in > statistics (which appears to be the case here!). Or let me rephrase my > query: what is this bootstrap sampling all about? Searched the web, but > didn't get satisfactory results. > >> > >> > >> Thanks > >> > >> On Tue, Oct 4, 2016 at 12:02 AM, Sebastian Raschka < > se.rasc...@gmail.com> wrote: > >>> From whatever little knowledge I gained last night about Random > Forests, each tree is trained with a sub-sample of original dataset > (usually with replacement)?. > >> > >> Yes, that should be correct! > >> > >>> Now, what I am not able to understand is - if entire dataset is used > to train each of the trees, then how does the classifier estimates the OOB > error? None of the entries of the dataset is an oob for any of the trees. > (Pardon me if all this sounds BS) > >> > >> If you take an n-size bootstrap sample, where n is the number of > samples in your dataset, you have asymptotically 0.632 * n unique samples > in your bootstrap set. Or in other words 0.368 * n samples are not used for > growing the respective tree (to compute the OOB). As far as I understand, > the random forest OOB score is then computed as the average OOB of each tee > (correct me if I am wrong!). > >> > >> Best, > >> Sebastian > >> > >>> On Oct 3, 2016, at 2:25 PM, Ibrahim Dalal via scikit-learn < > scikit-learn@python.org> wrote: > >>> > >>> Dear Developers, > >>> > >>> From whatever little knowledge I gained last night about Random > Forests, each tree is trained with a sub-sample of original dataset > (usually with replacement)?. > >>> > >>> (Note: Please do correct me if I am not making any sense.) > >>> > >>> RandomForestClassifier has an option of 'bootstrap'. The API states > the following > >>> > >>> The sub-sample size is always the same as the original input sample > size but the samples are drawn with replacement if bootstrap=True (default). > >>> > >>> Now, what I am not able to understand is - if entire dataset is used > to train each of the trees, then how does the classifier estimates the OOB > error? None of the entries of the dataset is an oob for any of the trees. > (Pardon me if all this sounds BS) > >>> > >>> Help this mere mortal. > >>> > >>> Thanks > >>> _______________________________________________ > >>> scikit-learn mailing list > >>> scikit-learn@python.org > >>> https://mail.python.org/mailman/listinfo/scikit-learn > >> > >> _______________________________________________ > >> scikit-learn mailing list > >> scikit-learn@python.org > >> https://mail.python.org/mailman/listinfo/scikit-learn > >> > >> _______________________________________________ > >> scikit-learn mailing list > >> scikit-learn@python.org > >> https://mail.python.org/mailman/listinfo/scikit-learn > > > > _______________________________________________ > > scikit-learn mailing list > > scikit-learn@python.org > > https://mail.python.org/mailman/listinfo/scikit-learn > > _______________________________________________ > scikit-learn mailing list > scikit-learn@python.org > https://mail.python.org/mailman/listinfo/scikit-learn >
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