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5.2 The Bootstrap
Bootstrap: a method obtain a new sample set without obtaining independent
data sets from the population by repeatedly sampling observations form the
original data set.
It can be applied to a wide range of statistical learning methods, including ones
which a measure of variability is otherwise difficult to obtain and not
automatically output by statistical software.
Estimates of values (e.g. accuracy) of bootstrapped data can perform great, even
comparable to the estimate based o a simulated datasets from the true
population .
Purpose
Bootstrap can be used to estimate and quantify the uncertain value associated
with a given estimator/statistical learning method
Process
1. Assume our sample is representative of the population of interest
2. Bootstrap randomly select n observations from a dataset to produce a
bootstrap data det, Z*1.
The sampling Is performed with replacement: same observation can occur more
than once in the bootstrap data set.
We can use Z*1 to produce a new bootstrap estimate for an estimate of the dataset (e.g.
accuracy as alpha*1).
, 8.2 Bagging, Random Forests, Boosting
Ensemble method/ weak learners: approach that combines many simple “building block”
models to obtain a single powerful model in prediction performance.
Decision tree have low bias but high variance. Averaging many trees improve variance.
(low bias because it has the information of the interactive features)
Ensemble methods that use regression/classification tree as building blocks
1) Bagging
2) Random forests
3) Boosting
8.2.1 Bagging
Bagging : General purpose procedure for reducing he variance of a statistical learning method. –
- Bagging uses bootstrapping: it takes repeated samples from the single training data set,
build a separate prediction model using each training set, and average the resulting
prediction that leads to low variance.
Bagged trees are grown deep + unpruned.
Bagging is particularly useful for many regression methods, particularly decision trees.
Advantage
1. Low bias
a. Trees are grow deep, and not pruned: thanks to the low variance by averaging,
each tree can be fit to each bootstrapped data
2. Low variance
a. Averaging the trees (could be hundreds/thousands trees!) built on bootstrapped
train data reduces the variance: as it does not rely on any single tree
Disadvantage
1. Can be difficult to interpret the resulting model
2. Could result in highly correlated trees when variance importance’s strongly vary among
the predictors, leading to not effective variance reduction (refer to Random Forest)
Process
1. Create B bootstrapped training data sets
2. Construct B regression trees using the bth bootstrapped training set to get the estimates
of y
3. For regression trees: Average them to obtain a single low-variance statistical learning
model, given by
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