232 lines
11 KiB
Python
232 lines
11 KiB
Python
import quapy as qp
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import numpy as np
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from sklearn.metrics import f1_score
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def from_name(err_name):
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"""Gets an error function from its name. E.g., `from_name("mae")` will return function :meth:`quapy.error.mae`
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:param err_name: string, the error name
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:return: a callable implementing the requested error
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"""
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assert err_name in ERROR_NAMES, f'unknown error {err_name}'
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callable_error = globals()[err_name]
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# if err_name in QUANTIFICATION_ERROR_SMOOTH_NAMES:
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# eps = __check_eps()
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# def bound_callable_error(y_true, y_pred):
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# return callable_error(y_true, y_pred, eps)
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# return bound_callable_error
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return callable_error
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def f1e(y_true, y_pred):
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"""F1 error: simply computes the error in terms of macro :math:`F_1`, i.e., :math:`1-F_1^M`,
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where :math:`F_1` is the harmonic mean of precision and recall, defined as :math:`\\frac{2tp}{2tp+fp+fn}`,
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with `tp`, `fp`, and `fn` standing for true positives, false positives, and false negatives, respectively.
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`Macro` averaging means the :math:`F_1` is computed for each category independently, and then averaged.
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:param y_true: array-like of true labels
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:param y_pred: array-like of predicted labels
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:return: :math:`1-F_1^M`
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"""
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return 1. - f1_score(y_true, y_pred, average='macro')
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def acce(y_true, y_pred):
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"""Computes the error in terms of 1-accuracy. The accuracy is computed as :math:`\\frac{tp+tn}{tp+fp+fn+tn}`, with
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`tp`, `fp`, `fn`, and `tn` standing for true positives, false positives, false negatives, and true negatives,
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respectively
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:param y_true: array-like of true labels
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:param y_pred: array-like of predicted labels
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:return: 1-accuracy
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"""
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return 1. - (y_true == y_pred).mean()
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def mae(prevs, prevs_hat):
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"""Computes the mean absolute error (see :meth:`quapy.error.ae`) across the sample pairs.
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:param prevs: array-like of shape `(n_samples, n_classes,)` with the true prevalence values
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:param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted prevalence values
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:return: mean absolute error
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"""
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return ae(prevs, prevs_hat).mean()
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def ae(prevs, prevs_hat):
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"""Computes the absolute error between the two prevalence vectors.
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Absolute error between two prevalence vectors :math:`p` and :math:`\\hat{p}` is computed as
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:math:`AE(p,\\hat{p})=\\frac{1}{|\\mathcal{Y}|}\\sum_{y\in \mathcal{Y}}|\\hat{p}(y)-p(y)|`,
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where :math:`\\mathcal{Y}` are the classes of interest.
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:param prevs: array-like of shape `(n_classes,)` with the true prevalence values
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:param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values
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:return: absolute error
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"""
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assert prevs.shape == prevs_hat.shape, f'wrong shape {prevs.shape} vs. {prevs_hat.shape}'
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return abs(prevs_hat - prevs).mean(axis=-1)
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def mse(prevs, prevs_hat):
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"""Computes the mean squared error (see :meth:`quapy.error.se`) across the sample pairs.
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:param prevs: array-like of shape `(n_samples, n_classes,)` with the true prevalence values
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:param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted prevalence values
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:return: mean squared error
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"""
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return se(prevs, prevs_hat).mean()
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def se(p, p_hat):
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"""Computes the squared error between the two prevalence vectors.
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Squared error between two prevalence vectors :math:`p` and :math:`\\hat{p}` is computed as
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:math:`SE(p,\\hat{p})=\\frac{1}{|\\mathcal{Y}|}\\sum_{y\in \mathcal{Y}}(\\hat{p}(y)-p(y))^2`, where
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:math:`\\mathcal{Y}` are the classes of interest.
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:param prevs: array-like of shape `(n_classes,)` with the true prevalence values
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:param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values
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:return: absolute error
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"""
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return ((p_hat-p)**2).mean(axis=-1)
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def mkld(prevs, prevs_hat, eps=None):
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"""Computes the mean Kullback-Leibler divergence (see :meth:`quapy.error.kld`) across the sample pairs.
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The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).
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:param prevs: array-like of shape `(n_samples, n_classes,)` with the true prevalence values
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:param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted prevalence values
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:param eps: smoothing factor. KLD is not defined in cases in which the distributions contain zeros; `eps`
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is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size. If `eps=None`, the sample size
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will be taken from the environment variable `SAMPLE_SIZE` (which has thus to be set beforehand).
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:return: mean Kullback-Leibler distribution
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"""
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return kld(prevs, prevs_hat, eps).mean()
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def kld(p, p_hat, eps=None):
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"""Computes the Kullback-Leibler divergence between the two prevalence distributions.
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Kullback-Leibler divergence between two prevalence distributions :math:`p` and :math:`\\hat{p}` is computed as
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:math:`KLD(p,\\hat{p})=D_{KL}(p||\\hat{p})=\\sum_{y\\in \\mathcal{Y}} p(y)\\log\\frac{p(y)}{\\hat{p}(y)}`, where
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:math:`\\mathcal{Y}` are the classes of interest.
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The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).
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:param prevs: array-like of shape `(n_classes,)` with the true prevalence values
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:param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values
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:param eps: smoothing factor. KLD is not defined in cases in which the distributions contain zeros; `eps`
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is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size. If `eps=None`, the sample size
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will be taken from the environment variable `SAMPLE_SIZE` (which has thus to be set beforehand).
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:return: Kullback-Leibler divergence between the two distributions
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"""
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eps = __check_eps(eps)
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sp = p+eps
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sp_hat = p_hat + eps
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return (sp*np.log(sp/sp_hat)).sum(axis=-1)
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def mnkld(prevs, prevs_hat, eps=None):
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"""Computes the mean Normalized Kullback-Leibler divergence (see :meth:`quapy.error.nkld`) across the sample pairs.
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The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).
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:param prevs: array-like of shape `(n_samples, n_classes,)` with the true prevalence values
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:param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted prevalence values
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:param eps: smoothing factor. NKLD is not defined in cases in which the distributions contain zeros; `eps`
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is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size. If `eps=None`, the sample size
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will be taken from the environment variable `SAMPLE_SIZE` (which has thus to be set beforehand).
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:return: mean Normalized Kullback-Leibler distribution
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"""
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return nkld(prevs, prevs_hat, eps).mean()
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def nkld(p, p_hat, eps=None):
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"""Computes the Normalized Kullback-Leibler divergence between the two prevalence distributions.
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Normalized Kullback-Leibler divergence between two prevalence distributions :math:`p` and :math:`\\hat{p}`
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is computed as :math:`NKLD(p,\\hat{p}) = 2\\frac{e^{KLD(p,\\hat{p})}}{e^{KLD(p,\\hat{p})}+1}-1`, where
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:math:`\\mathcal{Y}` are the classes of interest.
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The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).
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:param prevs: array-like of shape `(n_classes,)` with the true prevalence values
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:param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values
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:param eps: smoothing factor. NKLD is not defined in cases in which the distributions contain zeros; `eps`
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is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size. If `eps=None`, the sample size
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will be taken from the environment variable `SAMPLE_SIZE` (which has thus to be set beforehand).
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:return: Normalized Kullback-Leibler divergence between the two distributions
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"""
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ekld = np.exp(kld(p, p_hat, eps))
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return 2. * ekld / (1 + ekld) - 1.
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def mrae(p, p_hat, eps=None):
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"""Computes the mean relative absolute error (see :meth:`quapy.error.rae`) across the sample pairs.
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The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).
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:param prevs: array-like of shape `(n_samples, n_classes,)` with the true prevalence values
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:param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted prevalence values
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:param eps: smoothing factor. `mrae` is not defined in cases in which the true distribution contains zeros; `eps`
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is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size. If `eps=None`, the sample size
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will be taken from the environment variable `SAMPLE_SIZE` (which has thus to be set beforehand).
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:return: mean relative absolute error
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"""
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return rae(p, p_hat, eps).mean()
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def rae(p, p_hat, eps=None):
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"""Computes the absolute relative error between the two prevalence vectors.
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Relative absolute error between two prevalence vectors :math:`p` and :math:`\\hat{p}` is computed as
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:math:`RAE(p,\\hat{p})=\\frac{1}{|\\mathcal{Y}|}\\sum_{y\in \mathcal{Y}}\\frac{|\\hat{p}(y)-p(y)|}{p(y)}`,
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where :math:`\\mathcal{Y}` are the classes of interest.
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The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).
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:param prevs: array-like of shape `(n_classes,)` with the true prevalence values
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:param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values
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:param eps: smoothing factor. `rae` is not defined in cases in which the true distribution contains zeros; `eps`
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is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size. If `eps=None`, the sample size
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will be taken from the environment variable `SAMPLE_SIZE` (which has thus to be set beforehand).
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:return: relative absolute error
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"""
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eps = __check_eps(eps)
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p = smooth(p, eps)
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p_hat = smooth(p_hat, eps)
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return (abs(p-p_hat)/p).mean(axis=-1)
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def smooth(prevs, eps):
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""" Smooths a prevalence distribution with :math:`\epsilon` (`eps`) as:
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:math:`\\underline{p}(y)=\\frac{\\epsilon+p(y)}{\\epsilon|\\mathcal{Y}|+\\displaystyle\\sum_{y\\in \\mathcal{Y}}p(y)}`
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:param prevs: array-like of shape `(n_classes,)` with the true prevalence values
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:param eps: smoothing factor
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:return: array-like of shape `(n_classes,)` with the smoothed distribution
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"""
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n_classes = prevs.shape[-1]
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return (prevs + eps) / (eps * n_classes + 1)
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def __check_eps(eps=None):
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if eps is None:
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import quapy as qp
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sample_size = qp.environ['SAMPLE_SIZE']
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if sample_size is None:
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raise ValueError('eps was not defined, and qp.environ["SAMPLE_SIZE"] was not set')
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else:
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eps = 1. / (2. * sample_size)
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return eps
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CLASSIFICATION_ERROR = {f1e, acce}
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QUANTIFICATION_ERROR = {mae, mrae, mse, mkld, mnkld}
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QUANTIFICATION_ERROR_SMOOTH = {kld, nkld, rae, mkld, mnkld, mrae}
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CLASSIFICATION_ERROR_NAMES = {func.__name__ for func in CLASSIFICATION_ERROR}
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QUANTIFICATION_ERROR_NAMES = {func.__name__ for func in QUANTIFICATION_ERROR}
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QUANTIFICATION_ERROR_SMOOTH_NAMES = {func.__name__ for func in QUANTIFICATION_ERROR_SMOOTH}
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ERROR_NAMES = CLASSIFICATION_ERROR_NAMES | QUANTIFICATION_ERROR_NAMES
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f1_error = f1e
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acc_error = acce
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mean_absolute_error = mae
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absolute_error = ae
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mean_relative_absolute_error = mrae
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relative_absolute_error = rae
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