121 lines
3.9 KiB
Python
121 lines
3.9 KiB
Python
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# Sebastian Raschka 2014-2020
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# mlxtend Machine Learning Library Extensions
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#
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# Bootstrap functions
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# Author: Sebastian Raschka <sebastianraschka.com>
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#
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# License: BSD 3 clause
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import numpy as np
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def bootstrap(x, func, num_rounds=1000, ci=0.95, ddof=1, seed=None):
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"""Implements the ordinary nonparametric bootstrap
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Parameters
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----------
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x : NumPy array, shape=(n_samples, [n_columns])
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An one or multidimensional array of data records
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func : <func>
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A function which computes a statistic that is used
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to compute the bootstrap replicates (the statistic computed
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from the bootstrap samples). This function must return a
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scalar value. For example, `np.mean` or `np.median` would be
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an acceptable argument for `func` if `x` is a 1-dimensional array
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or vector.
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num_rounds : int (default=1000)
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The number of bootstrap samples to draw where each
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bootstrap sample has the same number of records as the
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original dataset.
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ci : int (default=0.95)
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An integer in the range (0, 1) that represents the
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confidence level for computing the confidence interval.
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For example, `ci=0.95` (default)
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will compute the 95% confidence
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interval from the bootstrap replicates.
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ddof : int
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The delta degrees of freedom used when computing the
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standard error.
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seed : int or None (default=None)
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Random seed for generating bootstrap samples.
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Returns
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-------
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original, standard_error, (lower_ci, upper_ci) : tuple
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Returns the statistic of the original sample (`original`),
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the standard error of the estimate, and the
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respective confidence interval bounds.
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Examples
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--------
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>>> from mlxtend.evaluate import bootstrap
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>>> rng = np.random.RandomState(123)
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>>> x = rng.normal(loc=5., size=100)
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>>> original, std_err, ci_bounds = bootstrap(x,
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... num_rounds=1000,
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... func=np.mean,
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... ci=0.95,
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... seed=123)
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>>> print('Mean: %.2f, SE: +/- %.2f, CI95: [%.2f, %.2f]' % (original,
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... std_err,
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... ci_bounds[0],
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... ci_bounds[1]))
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Mean: 5.03, SE: +/- 0.11, CI95: [4.80, 5.26]
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>>>
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For more usage examples, please see
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http://rasbt.github.io/mlxtend/user_guide/evaluate/bootstrap/
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"""
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if ci <= 0 or ci >= 1:
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raise AttributeError('ci must be in range (0, 1)')
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check_output = func(x)
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if (not isinstance(check_output, float)
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and not isinstance(check_output, int)
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and len(check_output.shape) != 0):
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raise AttributeError('func must return a scalar')
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rng = np.random.RandomState(seed)
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bootstrap_replicates = np.zeros(shape=num_rounds)
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# quantile function implemented due
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# to the weird behavior of the NumPy equivalent with
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# either nearest or lower interpolation
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def quantile(x, q):
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rank = round(q * x.shape[0]) - 1
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if rank >= x.shape[0]:
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rank = x.shape[0]
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elif rank <= 0:
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rank = 0
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rank = int(round(rank))
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return x[rank]
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sample_idx = np.arange(x.shape[0])
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for i in range(num_rounds):
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bootstrap_idx = rng.choice(sample_idx,
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size=sample_idx.shape[0],
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replace=True)
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bootstrap_replicates[i] = func(x[bootstrap_idx])
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original = check_output
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standard_error = np.std(bootstrap_replicates, ddof=ddof)
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t = np.sort(bootstrap_replicates)
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bound = (1 - ci) / 2.
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upper_ci = quantile(t, q=(ci + bound))
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lower_ci = quantile(t, q=bound)
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return original, standard_error, (lower_ci, upper_ci)
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