# What is the point of redundant samples in bootstrapping? [duplicate]

While studying machine learning I read about different sampling methods. Simple holdout, N-fold cross validation are straightforward. However, I somehow miss the point of bootstrapping. Its definition says that it's just a way to inflate the sample set simply by duplicating some random samples and I cannot figure what is the point in this -- seemingly no additional information in a learning process just by seeing the same instances again and again (on the contrary: others say that omitting redundant points from the training set is recommended for computational efficiency and for some other statistical reason as well).

So what is the explanation here?

• But you're not seeing the same samples again and again. You're taking a different sample each time. With bootstrapping, you're taking a simple random sample with replacement from the original sample. You end up with many different samples. For example, if your original sample was $S={1,2,3}$ some bootstrap samples might be: $S_1^*={1,1,1}$, $S_2^*={1,2,3}$, $S_3^*={3,2,3}$, $S_2^*={2,2,3}$, etc. Dec 11, 2020 at 8:30
• But in case of S1 = 1, 1, 1 I still show my estimator the same 1 instance three times. It's pointless. Dec 11, 2020 at 8:50
• If you want to sample from a distribution defined in terms of samples, redundant samples are equivalent to changing the weighs, or importance, of those redundant samples.
– crlb
Dec 11, 2020 at 8:55
• I see, but in bootstrapping redundant samples are choosen randomly, which in this sense means that we assign weights randomly for certain points. Why, and on what basis? This also seems irrational. Dec 11, 2020 at 9:03
• The distribution $S_1 = \{a,a,b\}$ with equal probability for all elements and the distribution $S_2 = \{a,b\}$ with $p_a = 2/3$ and $p_b = 1/3$ are equivalent when bootstrapping.
– crlb
Dec 11, 2020 at 9:08