[scikit-learn] Random Forest with Bootstrapping

[Ibrahim Dalal]

So what is the point of having duplicate entries in your training set? This
seems just a pure overhead. Sorry but you will again have to help me here.

On Tue, Oct 4, 2016 at 1:29 AM, Sebastian Raschka <se.raschka at gmail.com>
wrote:

> > 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?
>
> Yeah, you'll definitely have duplications, that’s why (if you have an
> infinitely large n) only 0.632*n samples are unique ;).
>
> Say your dataset is
>
> [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] (where the numbers represent the indices of
> your data points)
>
> then a bootstrap sample could be
>
> [9, 1, 1, 0, 4, 4, 5, 7, 9, 9] and your left out sample is consequently
> [2, 3, 6, 8]
>
>
> > On Oct 3, 2016, at 3:36 PM, Ibrahim Dalal via scikit-learn <
> scikit-learn at python.org> wrote:
> >
> > 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.raschka at 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.raschka at 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 at 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.raschka at 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 at 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
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