# Source code for yellowbrick.classifier.threshold

```
# yellowbrick.classifier.threshold
# DiscriminationThreshold visualizer for probabilistic classifiers.
#
# Author: Nathan Danielsen
# Author: Benjamin Bengfort
# Created: Wed April 26 20:17:29 2017 -0700
#
# Copyright (C) 2017 The scikit-yb developers
# For license information, see LICENSE.txt
#
# ID: threshold.py [] nathan.danielsen@gmail.com $
"""
DiscriminationThreshold visualizer for probabilistic classifiers.
"""
##########################################################################
## Imports
##########################################################################
import bisect
import numpy as np
from scipy.stats import mstats
from collections import defaultdict
from sklearn.base import clone
from sklearn.model_selection import ShuffleSplit
from sklearn.metrics import precision_recall_curve
from sklearn.utils import indexable, safe_indexing
from sklearn.utils.multiclass import type_of_target
from yellowbrick.base import ModelVisualizer
from yellowbrick.style.colors import resolve_colors
from yellowbrick.utils import is_classifier, is_probabilistic, is_monotonic
from yellowbrick.exceptions import YellowbrickTypeError, YellowbrickValueError
# Quantiles for lower bound, curve, and upper bound
QUANTILES_MEDIAN_80 = np.array([0.1, 0.5, 0.9])
# List of threshold metrics
METRICS = ["precision", "recall", "fscore", "queue_rate"]
##########################################################################
# Discrimination Thresholds Visualization
##########################################################################
[docs]class DiscriminationThreshold(ModelVisualizer):
"""
Visualizes how precision, recall, f1 score, and queue rate change as the
discrimination threshold increases. For probabilistic, binary classifiers,
the discrimination threshold is the probability at which you choose the
positive class over the negative. Generally this is set to 50%, but
adjusting the discrimination threshold will adjust sensitivity to false
positives which is described by the inverse relationship of precision and
recall with respect to the threshold.
The visualizer also accounts for variability in the model by running
multiple trials with different train and test splits of the data. The
variability is visualized using a band such that the curve is drawn as the
median score of each trial and the band is from the 10th to 90th
percentile.
The visualizer is intended to help users determine an appropriate
threshold for decision making (e.g. at what threshold do we have a human
review the data), given a tolerance for precision and recall or limiting
the number of records to check (the queue rate).
Parameters
----------
model : estimator
A scikit-learn estimator that should be a classifier. If the model is
not a classifier, an exception is raised. If the internal model is not
fitted, it is fit when the visualizer is fitted, unless otherwise specified
by ``is_fitted``.
ax : matplotlib Axes, default: None
The axes to plot the figure on. If not specified the current axes will be
used (or generated if required).
n_trials : integer, default: 50
Number of times to shuffle and split the dataset to account for noise
in the threshold metrics curves. Note if cv provides > 1 splits,
the number of trials will be n_trials * cv.get_n_splits()
cv : float or cross-validation generator, default: 0.1
Determines the splitting strategy for each trial. Possible inputs are:
- float, to specify the percent of the test split
- object to be used as cross-validation generator
This attribute is meant to give flexibility with stratified splitting
but if a splitter is provided, it should only return one split and
have shuffle set to True.
fbeta : float, 1.0 by default
The strength of recall versus precision in the F-score.
argmax : str, default: 'fscore'
Annotate the threshold maximized by the supplied metric (see exclude
for the possible metrics to use). If None, will not annotate the
graph.
exclude : str or list, optional
Specify metrics to omit from the graph, can include:
- ``"precision"``
- ``"recall"``
- ``"queue_rate"``
- ``"fscore"``
All metrics not excluded will be displayed in the graph, nor will they
be available in ``thresholds_``; however, they will be computed on fit.
quantiles : sequence, default: np.array([0.1, 0.5, 0.9])
Specify the quantiles to view model variability across a number of
trials. Must be monotonic and have three elements such that the first
element is the lower bound, the second is the drawn curve, and the
third is the upper bound. By default the curve is drawn at the median,
and the bounds from the 10th percentile to the 90th percentile.
random_state : int, optional
Used to seed the random state for shuffling the data while composing
different train and test splits. If supplied, the random state is
incremented in a deterministic fashion for each split.
Note that if a splitter is provided, it's random state will also be
updated with this random state, even if it was previously set.
is_fitted : bool or str, default="auto"
Specify if the wrapped estimator is already fitted. If False, the estimator
will be fit when the visualizer is fit, otherwise, the estimator will not be
modified. If "auto" (default), a helper method will check if the estimator
is fitted before fitting it again.
force_model : bool, default: False
Do not check to ensure that the underlying estimator is a classifier. This
will prevent an exception when the visualizer is initialized but may result
in unexpected or unintended behavior.
kwargs : dict
Keyword arguments passed to the visualizer base classes.
Attributes
----------
thresholds_ : array
The uniform thresholds identified by each of the trial runs.
cv_scores_ : dict of arrays of ``len(thresholds_)``
The values for all included metrics including the upper and lower
bounds of the metrics defined by quantiles.
Notes
-----
The term "discrimination threshold" is rare in the literature. Here, we
use it to mean the probability at which the positive class is selected
over the negative class in binary classification.
Classification models must implement either a ``decision_function`` or
``predict_proba`` method in order to be used with this class. A
``YellowbrickTypeError`` is raised otherwise.
.. caution:: This method only works for binary, probabilistic classifiers.
.. seealso::
For a thorough explanation of discrimination thresholds, see:
`Visualizing Machine Learning Thresholds to Make Better Business
Decisions
<http://blog.insightdatalabs.com/visualizing-classifier-thresholds/>`_
by Insight Data.
"""
def __init__(
self,
model,
ax=None,
n_trials=50,
cv=0.1,
fbeta=1.0,
argmax="fscore",
exclude=None,
quantiles=QUANTILES_MEDIAN_80,
random_state=None,
is_fitted="auto",
force_model=False,
**kwargs
):
# Perform some quick type checking to help users avoid error.
if not force_model and (
not is_classifier(model) or not is_probabilistic(model)
):
raise YellowbrickTypeError(
"{} requires a probabilistic binary classifier".format(
self.__class__.__name__
)
)
# Check the various inputs
self._check_quantiles(quantiles)
self._check_cv(cv)
self._check_exclude(exclude)
# Initialize the ModelVisualizer
super(DiscriminationThreshold, self).__init__(
model, ax=ax, is_fitted=is_fitted, **kwargs
)
# Set params
self.set_params(
n_trials=n_trials,
cv=cv,
fbeta=fbeta,
argmax=argmax,
exclude=exclude,
quantiles=quantiles,
random_state=random_state,
)
[docs] def fit(self, X, y, **kwargs):
"""
Fit is the entry point for the visualizer. Given instances described
by X and binary classes described in the target y, fit performs n
trials by shuffling and splitting the dataset then computing the
precision, recall, f1, and queue rate scores for each trial. The
scores are aggregated by the quantiles expressed then drawn.
Parameters
----------
X : ndarray or DataFrame of shape n x m
A matrix of n instances with m features
y : ndarray or Series of length n
An array or series of target or class values. The target y must
be a binary classification target.
kwargs: dict
keyword arguments passed to Scikit-Learn API.
Returns
-------
self : instance
Returns the instance of the visualizer
raises: YellowbrickValueError
If the target y is not a binary classification target.
"""
# Check target before metrics raise crazy exceptions
# TODO: Switch to using target type from utils.target
if type_of_target(y) != "binary":
raise YellowbrickValueError("multiclass format is not supported")
# Make arrays indexable for cross validation
X, y = indexable(X, y)
# TODO: parallelize trials with joblib (using sklearn utility)
# NOTE: parallelization with matplotlib is tricky at best!
trials = [
metric
for idx in range(self.n_trials)
for metric in self._split_fit_score_trial(X, y, idx)
]
# Compute maximum number of uniform thresholds across all trials
n_thresholds = np.array([len(t["thresholds"]) for t in trials]).min()
self.thresholds_ = np.linspace(0.0, 1.0, num=n_thresholds)
# Filter metrics and collect values for uniform thresholds
metrics = frozenset(METRICS) - self._check_exclude(self.exclude)
uniform_metrics = defaultdict(list)
for trial in trials:
rows = defaultdict(list)
for t in self.thresholds_:
idx = bisect.bisect_left(trial["thresholds"], t)
for metric in metrics:
rows[metric].append(trial[metric][idx])
for metric, row in rows.items():
uniform_metrics[metric].append(row)
# Convert metrics to metric arrays
uniform_metrics = {
metric: np.array(values) for metric, values in uniform_metrics.items()
}
# Perform aggregation and store cv_scores_
quantiles = self._check_quantiles(self.quantiles)
self.cv_scores_ = {}
for metric, values in uniform_metrics.items():
# Compute the lower, median, and upper plots
lower, median, upper = mstats.mquantiles(values, prob=quantiles, axis=0)
# Store the aggregates in cv scores
self.cv_scores_[metric] = median
self.cv_scores_["{}_lower".format(metric)] = lower
self.cv_scores_["{}_upper".format(metric)] = upper
# TODO: fit the underlying estimator with the best decision threshold
# Call super to ensure the underlying estimator is correctly fitted
super(DiscriminationThreshold, self).fit(X, y)
# Draw and always return self
self.draw()
return self
def _split_fit_score_trial(self, X, y, idx=0):
"""
Splits the dataset, fits a clone of the estimator, then scores it
according to the required metrics.
The index of the split is added to the random_state if the
random_state is not None; this ensures that every split is shuffled
differently but in a deterministic fashion for testing purposes.
"""
random_state = self.random_state
if random_state is not None:
random_state += idx
splitter = self._check_cv(self.cv, random_state)
for train_index, test_index in splitter.split(X, y):
# Safe indexing handles multiple types of inputs including
# DataFrames and structured arrays - required for generic splits.
X_train = safe_indexing(X, train_index)
y_train = safe_indexing(y, train_index)
X_test = safe_indexing(X, test_index)
y_test = safe_indexing(y, test_index)
model = clone(self.estimator)
model.fit(X_train, y_train)
if hasattr(model, "predict_proba"):
# Get the probabilities for the positive class
y_scores = model.predict_proba(X_test)[:, 1]
else:
# Use the decision function to get the scores
y_scores = model.decision_function(X_test)
# Compute the curve metrics and thresholds
curve_metrics = precision_recall_curve(y_test, y_scores)
precision, recall, thresholds = curve_metrics
# Compute the F1 score from precision and recall
# Don't need to warn for F, precision/recall would have warned
with np.errstate(divide="ignore", invalid="ignore"):
beta = self.fbeta ** 2
f_score = (1 + beta) * precision * recall / (beta * precision + recall)
# Ensure thresholds ends at 1
thresholds = np.append(thresholds, 1)
# Compute the queue rate
queue_rate = np.array(
[(y_scores >= threshold).mean() for threshold in thresholds]
)
yield {
"thresholds": thresholds,
"precision": precision,
"recall": recall,
"fscore": f_score,
"queue_rate": queue_rate,
}
[docs] def draw(self):
"""
Draws the cv scores as a line chart on the current axes.
"""
# Set the colors from the supplied values or reasonable defaults
color_values = resolve_colors(n_colors=4, colors=self.color)
for idx, metric in enumerate(METRICS):
# Skip any excluded labels
if metric not in self.cv_scores_:
continue
# Get the color ensuring every metric has a static color
color = color_values[idx]
# Make the label pretty
if metric == "fscore":
if self.fbeta == 1.0:
label = "$f_1$"
else:
label = "$f_{{\beta={:0.1f}}}".format(self.fbeta)
else:
label = metric.replace("_", " ")
# Draw the metric values
self.ax.plot(
self.thresholds_, self.cv_scores_[metric], color=color, label=label
)
# Draw the upper and lower bounds
lower = self.cv_scores_["{}_lower".format(metric)]
upper = self.cv_scores_["{}_upper".format(metric)]
self.ax.fill_between(
self.thresholds_, upper, lower, alpha=0.35, linewidth=0, color=color
)
# Annotate the graph with the maximizing value
if self.argmax.lower() == metric:
argmax = self.cv_scores_[metric].argmax()
threshold = self.thresholds_[argmax]
self.ax.axvline(
threshold,
ls="--",
c="k",
lw=1,
label="$t_{}={:0.2f}$".format(metric[0], threshold),
)
return self.ax
[docs] def finalize(self, **kwargs):
"""
Sets a title and axis labels on the visualizer and ensures that the
axis limits are scaled to valid threshold values.
Parameters
----------
kwargs: generic keyword arguments.
Notes
-----
Generally this method is called from show and not directly by the user.
"""
super(DiscriminationThreshold, self).finalize(**kwargs)
# Set the title of the threshold visualiztion
self.set_title("Threshold Plot for {}".format(self.name))
self.ax.legend(frameon=True, loc="best")
self.ax.set_xlabel("discrimination threshold")
self.ax.set_ylabel("score")
self.ax.set_xlim(0.0, 1.0)
self.ax.set_ylim(0.0, 1.0)
def _check_quantiles(self, val):
"""
Validate the quantiles passed in. Returns the np array if valid.
"""
if len(val) != 3 or not is_monotonic(val) or not np.all(val < 1):
raise YellowbrickValueError(
"quantiles must be a sequence of three "
"monotonically increasing values less than 1"
)
return np.asarray(val)
def _check_cv(self, val, random_state=None):
"""
Validate the cv method passed in. Returns the split strategy if no
validation exception is raised.
"""
# Use default splitter in this case
if val is None:
val = 0.1
if isinstance(val, float) and val <= 1.0:
return ShuffleSplit(n_splits=1, test_size=val, random_state=random_state)
if hasattr(val, "split") and hasattr(val, "get_n_splits"):
if random_state is not None and hasattr(val, "random_state"):
val.random_state = random_state
return val
raise YellowbrickValueError("'{}' is not a valid cv splitter".format(type(val)))
def _check_exclude(self, val):
"""
Validate the excluded metrics. Returns the set of excluded params.
"""
if val is None:
exclude = frozenset()
elif isinstance(val, str):
exclude = frozenset([val.lower()])
else:
exclude = frozenset(map(lambda s: s.lower(), val))
if len(exclude - frozenset(METRICS)) > 0:
raise YellowbrickValueError(
"'{}' is not a valid metric to exclude".format(repr(val))
)
return exclude
##########################################################################
# Quick Methods
##########################################################################
[docs]def discrimination_threshold(
model,
X,
y,
ax=None,
n_trials=50,
cv=0.1,
fbeta=1.0,
argmax="fscore",
exclude=None,
quantiles=QUANTILES_MEDIAN_80,
random_state=None,
is_fitted="auto",
force_model=False,
show=True,
**kwargs
):
"""Discrimination Threshold
Visualizes how precision, recall, f1 score, and queue rate change as the
discrimination threshold increases. For probabilistic, binary classifiers,
the discrimination threshold is the probability at which you choose the
positive class over the negative. Generally this is set to 50%, but
adjusting the discrimination threshold will adjust sensitivity to false
positives which is described by the inverse relationship of precision and
recall with respect to the threshold.
.. seealso:: See DiscriminationThreshold for more details.
Parameters
----------
model : estimator
A scikit-learn estimator that should be a classifier. If the model is
not a classifier, an exception is raised. If the internal model is not
fitted, it is fit when the visualizer is fitted, unless otherwise specified
by ``is_fitted``.
X : ndarray or DataFrame of shape n x m
A matrix of n instances with m features
y : ndarray or Series of length n
An array or series of target or class values. The target y must
be a binary classification target.
ax : matplotlib Axes, default: None
The axes to plot the figure on. If not specified the current axes will be
used (or generated if required).
n_trials : integer, default: 50
Number of times to shuffle and split the dataset to account for noise
in the threshold metrics curves. Note if cv provides > 1 splits,
the number of trials will be n_trials * cv.get_n_splits()
cv : float or cross-validation generator, default: 0.1
Determines the splitting strategy for each trial. Possible inputs are:
- float, to specify the percent of the test split
- object to be used as cross-validation generator
This attribute is meant to give flexibility with stratified splitting
but if a splitter is provided, it should only return one split and
have shuffle set to True.
fbeta : float, 1.0 by default
The strength of recall versus precision in the F-score.
argmax : str, default: 'fscore'
Annotate the threshold maximized by the supplied metric (see exclude
for the possible metrics to use). If None, will not annotate the
graph.
exclude : str or list, optional
Specify metrics to omit from the graph, can include:
- ``"precision"``
- ``"recall"``
- ``"queue_rate"``
- ``"fscore"``
All metrics not excluded will be displayed in the graph, nor will they
be available in ``thresholds_``; however, they will be computed on fit.
quantiles : sequence, default: np.array([0.1, 0.5, 0.9])
Specify the quantiles to view model variability across a number of
trials. Must be monotonic and have three elements such that the first
element is the lower bound, the second is the drawn curve, and the
third is the upper bound. By default the curve is drawn at the median,
and the bounds from the 10th percentile to the 90th percentile.
random_state : int, optional
Used to seed the random state for shuffling the data while composing
different train and test splits. If supplied, the random state is
incremented in a deterministic fashion for each split.
Note that if a splitter is provided, it's random state will also be
updated with this random state, even if it was previously set.
is_fitted : bool or str, default="auto"
Specify if the wrapped estimator is already fitted. If False, the estimator
will be fit when the visualizer is fit, otherwise, the estimator will not be
modified. If "auto" (default), a helper method will check if the estimator
is fitted before fitting it again.
force_model : bool, default: False
Do not check to ensure that the underlying estimator is a classifier. This
will prevent an exception when the visualizer is initialized but may result
in unexpected or unintended behavior.
show : bool, default: True
If True, calls ``show()``, which in turn calls ``plt.show()`` however you cannot
call ``plt.savefig`` from this signature, nor ``clear_figure``. If False, simply
calls ``finalize()``
kwargs : dict
Keyword arguments passed to the visualizer base classes.
Notes
-----
The term "discrimination threshold" is rare in the literature. Here, we
use it to mean the probability at which the positive class is selected
over the negative class in binary classification.
Classification models must implement either a ``decision_function`` or
``predict_proba`` method in order to be used with this class. A
``YellowbrickTypeError`` is raised otherwise.
.. seealso::
For a thorough explanation of discrimination thresholds, see:
`Visualizing Machine Learning Thresholds to Make Better Business
Decisions
<http://blog.insightdatalabs.com/visualizing-classifier-thresholds/>`_
by Insight Data.
Examples
--------
>>> from yellowbrick.classifier.threshold import discrimination_threshold
>>> from sklearn.linear_model import LogisticRegression
>>> from yellowbrick.datasets import load_occupancy
>>> X, y = load_occupancy()
>>> model = LogisticRegression(multi_class="auto", solver="liblinear")
>>> discrimination_threshold(model, X, y)
Returns
-------
viz : DiscriminationThreshold
Returns the fitted and finalized visualizer object.
"""
# Instantiate the visualizer
visualizer = DiscriminationThreshold(
model,
ax=ax,
n_trials=n_trials,
cv=cv,
fbeta=fbeta,
argmax=argmax,
exclude=exclude,
quantiles=quantiles,
random_state=random_state,
is_fitted=is_fitted,
force_model=force_model,
**kwargs
)
# Fit and transform the visualizer (calls draw)
visualizer.fit(X, y)
if show:
visualizer.show()
else:
visualizer.finalize()
# Return the visualizer
return visualizer
```