214 lines
9.4 KiB
Python
214 lines
9.4 KiB
Python
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# Authors: The scikit-learn developers
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# SPDX-License-Identifier: BSD-3-Clause
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from sklearn.utils._array_api import (
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_find_matching_floating_dtype,
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get_namespace_and_device,
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)
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def _weighted_percentile(
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array, sample_weight, percentile_rank=50, average=False, xp=None
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):
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"""Compute the weighted percentile.
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Implement an array API compatible (weighted version) of NumPy's 'inverted_cdf'
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method when `average=False` (default) and 'averaged_inverted_cdf' when
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`average=True`.
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For an array ordered by increasing values, when the percentile lies exactly on a
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data point:
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* 'inverted_cdf' takes the exact data point.
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* 'averaged_inverted_cdf' takes the average of the exact data point and the one
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above it (this means it gives the same result as `median` for unit weights).
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E.g., for the array [1, 2, 3, 4] the percentile rank at each data point would
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be [25, 50, 75, 100]. Percentile rank 50 lies on '2'. 'average_inverted_cdf'
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computes the average of '2' and '3', making it 'symmetrical' because if you
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reverse the array, rank 50 would fall on '3'. It also matches 'median'.
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On the other hand, 'inverted_cdf', which does not satisfy the symmetry property,
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would give '2'.
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When the requested percentile lies between two data points, both methods return
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the higher data point.
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E.g., for the array [1, 2, 3, 4, 5] the percentile rank at each data point would
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be [20, 40, 60, 80, 100]. Percentile rank 50, lies between '2' and '3'. Taking the
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higher data point is symmetrical because if you reverse the array, 50 would lie
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between '4' and '3'. Both methods match median in this case.
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If `array` is a 2D array, the `values` are selected along axis 0.
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`NaN` values are ignored by setting their weights to 0. If `array` is 2D, this
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is done in a column-isolated manner: a `NaN` in the second column, does not impact
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the percentile computed for the first column even if `sample_weight` is 1D.
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.. versionchanged:: 0.24
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Accepts 2D `array`.
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.. versionchanged:: 1.7
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Supports handling of `NaN` values.
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.. versionchanged:: 1.8
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Supports `average`, which calculates percentile using the
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"averaged_inverted_cdf" method.
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Parameters
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----------
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array : 1D or 2D array
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Values to take the weighted percentile of.
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sample_weight: 1D or 2D array
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Weights for each value in `array`. Must be same shape as `array` or of shape
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`(array.shape[0],)`.
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percentile_rank: scalar or 1D array, default=50
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The probability level(s) of the percentile(s) to compute, in percent. Must be
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between 0 and 100. If a 1D array, computes all percentiles (along each
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axis 0 if `array` is 2D).
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average : bool, default=False
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If `True`, uses the "averaged_inverted_cdf" quantile method, otherwise
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defaults to "inverted_cdf". "averaged_inverted_cdf" is symmetrical with
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unit `sample_weight`, such that the total of `sample_weight` below or equal to
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`_weighted_percentile(percentile_rank)` is the same as the total of
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`sample_weight` above or equal to `_weighted_percentile(100-percentile_rank)`.
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This symmetry is not guaranteed with non-unit weights.
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xp : array_namespace, default=None
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The standard-compatible namespace for `array`. Default: infer.
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Returns
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-------
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percentile : scalar, 1D array, or 2D array
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Weighted percentile at the requested probability level(s).
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If `array` is 1D and `percentile_rank` is scalar, returns a scalar.
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If `array` is 2D and `percentile_rank` is scalar, returns a 1D array
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of shape `(array.shape[1],)`
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If `array` is 1D and `percentile_rank` is 1D, returns a 1D array
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of shape `(percentile_rank.shape[0],)`
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If `array` is 2D and `percentile_rank` is 1D, returns a 2D array
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of shape `(array.shape[1], percentile_rank.shape[0])`
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"""
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xp, _, device = get_namespace_and_device(array)
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# `sample_weight` should follow `array` for dtypes
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floating_dtype = _find_matching_floating_dtype(array, xp=xp)
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array = xp.asarray(array, dtype=floating_dtype, device=device)
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sample_weight = xp.asarray(sample_weight, dtype=floating_dtype, device=device)
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percentile_rank = xp.asarray(percentile_rank, dtype=floating_dtype, device=device)
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n_dim = array.ndim
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if n_dim == 0:
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return array
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if array.ndim == 1:
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array = xp.reshape(array, (-1, 1))
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# When sample_weight 1D, repeat for each array.shape[1]
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if array.shape != sample_weight.shape and array.shape[0] == sample_weight.shape[0]:
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sample_weight = xp.tile(sample_weight, (array.shape[1], 1)).T
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n_dim_percentile = percentile_rank.ndim
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if n_dim_percentile == 0:
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percentile_rank = xp.reshape(percentile_rank, (1,))
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# Sort `array` and `sample_weight` along axis=0:
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sorted_idx = xp.argsort(array, axis=0, stable=False)
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sorted_weights = xp.take_along_axis(sample_weight, sorted_idx, axis=0)
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# Set NaN values in `sample_weight` to 0. Only perform this operation if NaN
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# values present to avoid temporary allocations of size `(n_samples, n_features)`.
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n_features = array.shape[1]
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largest_value_per_column = array[
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sorted_idx[-1, ...], xp.arange(n_features, device=device)
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]
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# NaN values get sorted to end (largest value)
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if xp.any(xp.isnan(largest_value_per_column)):
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sorted_nan_mask = xp.take_along_axis(xp.isnan(array), sorted_idx, axis=0)
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sorted_weights[sorted_nan_mask] = 0
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# Compute the weighted cumulative distribution function (CDF) based on
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# `sample_weight` and scale `percentile_rank` along it.
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#
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# Note: we call `xp.cumulative_sum` on the transposed `sorted_weights` to
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# ensure that the result is of shape `(n_features, n_samples)` so
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# `xp.searchsorted` calls take contiguous inputs as a result (for
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# performance reasons).
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weight_cdf = xp.cumulative_sum(sorted_weights.T, axis=1)
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n_percentiles = percentile_rank.shape[0]
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result = xp.empty((n_features, n_percentiles), dtype=floating_dtype, device=device)
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for p_idx, p_rank in enumerate(percentile_rank):
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adjusted_percentile_rank = p_rank / 100 * weight_cdf[..., -1]
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# Ignore leading `sample_weight=0` observations
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# when `percentile_rank=0` (#20528)
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mask = adjusted_percentile_rank == 0
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adjusted_percentile_rank[mask] = xp.nextafter(
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adjusted_percentile_rank[mask], adjusted_percentile_rank[mask] + 1
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)
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# For each feature with index j, find sample index i of the scalar value
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# `adjusted_percentile_rank[j]` in 1D array `weight_cdf[j]`, such that:
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# weight_cdf[j, i-1] < adjusted_percentile_rank[j] <= weight_cdf[j, i].
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# Note `searchsorted` defaults to equality on the right, whereas Hyndman and Fan
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# reference equation has equality on the left.
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percentile_indices = xp.stack(
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[
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xp.searchsorted(
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weight_cdf[feature_idx, ...], adjusted_percentile_rank[feature_idx]
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)
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for feature_idx in range(weight_cdf.shape[0])
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],
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)
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# `percentile_indices` may be equal to `sorted_idx.shape[0]` due to floating
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# point error (see #11813)
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max_idx = sorted_idx.shape[0] - 1
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percentile_indices = xp.clip(percentile_indices, 0, max_idx)
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col_indices = xp.arange(array.shape[1], device=device)
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percentile_in_sorted = sorted_idx[percentile_indices, col_indices]
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if average:
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# From Hyndman and Fan (1996), `fraction_above` is `g`
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fraction_above = (
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weight_cdf[col_indices, percentile_indices] - adjusted_percentile_rank
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)
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is_fraction_above = fraction_above > xp.finfo(floating_dtype).eps
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percentile_plus_one_indices = xp.clip(percentile_indices + 1, 0, max_idx)
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percentile_plus_one_in_sorted = sorted_idx[
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percentile_plus_one_indices, col_indices
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]
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# Handle case when next index ('plus one') has sample weight of 0
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zero_weight_cols = col_indices[
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sample_weight[percentile_plus_one_in_sorted, col_indices] == 0
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]
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for col_idx in zero_weight_cols:
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cdf_val = weight_cdf[col_idx, percentile_indices[col_idx]]
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# Search for next index where `weighted_cdf` is greater
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next_index = xp.searchsorted(
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weight_cdf[col_idx, ...], cdf_val, side="right"
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)
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# Handle case where there are trailing 0 sample weight samples
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# and `percentile_indices` is already max index
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if next_index >= max_idx:
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# use original `percentile_indices` again
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next_index = percentile_indices[col_idx]
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percentile_plus_one_in_sorted[col_idx] = sorted_idx[next_index, col_idx]
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result[..., p_idx] = xp.where(
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is_fraction_above,
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array[percentile_in_sorted, col_indices],
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(
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array[percentile_in_sorted, col_indices]
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+ array[percentile_plus_one_in_sorted, col_indices]
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)
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/ 2,
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)
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else:
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result[..., p_idx] = array[percentile_in_sorted, col_indices]
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if n_dim_percentile == 0:
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result = result[..., 0]
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return result[0, ...] if n_dim == 1 else result
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