Source code for yellowbrick.regressor.residuals

# yellowbrick.regressor.residuals
# Regressor visualizers that score residuals: prediction vs. actual data.
#
# Author:   Rebecca Bilbro
# Author:   Benjamin Bengfort
# Created:  Fri Jun 03 10:30:36 2016 -0700
#
# Copyright (C) 2016 The scikit-yb developers
# For license information, see LICENSE.txt
#
# ID: residuals.py [7d3f5e6] benjamin@bengfort.com $

"""
Regressor visualizers that score residuals: prediction vs. actual data.
"""

##########################################################################
## Imports
##########################################################################


import matplotlib.pyplot as plt

try:
    # Only available in Matplotlib >= 2.0.2
    from mpl_toolkits.axes_grid1 import make_axes_locatable
except ImportError:
    make_axes_locatable = None

from yellowbrick.draw import manual_legend
from yellowbrick.utils.decorators import memoized
from yellowbrick.style.palettes import LINE_COLOR
from yellowbrick.exceptions import YellowbrickValueError
from yellowbrick.regressor.base import RegressionScoreVisualizer
from yellowbrick.bestfit import draw_best_fit, draw_identity_line

## Packages for export
__all__ = ["PredictionError", "prediction_error", "ResidualsPlot", "residuals_plot"]


##########################################################################
## Prediction Error Plots
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[docs]class PredictionError(RegressionScoreVisualizer): """ The prediction error visualizer plots the actual targets from the dataset against the predicted values generated by our model(s). This visualizer is used to detect noise or heteroscedasticity along a range of the target domain. Parameters ---------- model : a Scikit-Learn regressor Should be an instance of a regressor, otherwise will raise a YellowbrickTypeError exception on instantiation. If the estimator 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 None is passed in the current axes will be used (or generated if required). shared_limits : bool, default: True If shared_limits is True, the range of the X and Y axis limits will be identical, creating a square graphic with a true 45 degree line. In this form, it is easier to diagnose under- or over- prediction, though the figure will become more sparse. To localize points, set shared_limits to False, but note that this will distort the figure and should be accounted for during analysis. bestfit : bool, default: True Draw a linear best fit line to estimate the correlation between the predicted and measured value of the target variable. The color of the bestfit line is determined by the ``line_color`` argument. identity : bool, default: True Draw the 45 degree identity line, y=x in order to better show the relationship or pattern of the residuals. E.g. to estimate if the model is over- or under- estimating the given values. The color of the identity line is a muted version of the ``line_color`` argument. alpha : float, default: 0.75 Specify a transparency where 1 is completely opaque and 0 is completely transparent. This property makes densely clustered points more visible. 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. kwargs : dict Keyword arguments that are passed to the base class and may influence the visualization as defined in other Visualizers. Attributes ---------- score_ : float The R^2 score that specifies the goodness of fit of the underlying regression model to the test data. Examples -------- >>> from yellowbrick.regressor import PredictionError >>> from sklearn.linear_model import Lasso >>> model = PredictionError(Lasso()) >>> model.fit(X_train, y_train) >>> model.score(X_test, y_test) >>> model.show() Notes ----- PredictionError is a ScoreVisualizer, meaning that it wraps a model and its primary entry point is the `score()` method. """ def __init__( self, model, ax=None, shared_limits=True, bestfit=True, identity=True, alpha=0.75, is_fitted="auto", **kwargs ): # Whether or not to check if the model is already fitted self.is_fitted = is_fitted # Initialize the visualizer super(PredictionError, self).__init__(model, ax=ax, **kwargs) # Visual arguments self.colors = { "point": kwargs.pop("point_color", None), "line": kwargs.pop("line_color", LINE_COLOR), } # Drawing arguments self.shared_limits = shared_limits self.bestfit = bestfit self.identity = identity self.alpha = alpha
[docs] def score(self, X, y, **kwargs): """ The score function is the hook for visual interaction. Pass in test data and the visualizer will create predictions on the data and evaluate them with respect to the test values. The evaluation will then be passed to draw() and the result of the estimator score will be returned. Parameters ---------- X : array-like X (also X_test) are the dependent variables of test set to predict y : array-like y (also y_test) is the independent actual variables to score against Returns ------- score : float """ # super will set score_ on the visualizer super(PredictionError, self).score(X, y, **kwargs) y_pred = self.predict(X) self.draw(y, y_pred) return self.score_
[docs] def draw(self, y, y_pred): """ Parameters ---------- y : ndarray or Series of length n An array or series of target or class values y_pred : ndarray or Series of length n An array or series of predicted target values Returns ------- ax : matplotlib Axes The axis with the plotted figure """ label = "$R^2 = {:0.3f}$".format(self.score_) self.ax.scatter( y, y_pred, c=self.colors["point"], alpha=self.alpha, label=label ) # TODO If score happens inside a loop, draw gets called multiple times. # Ideally we'd want the best fit line to be drawn only once if self.bestfit: draw_best_fit( y, y_pred, self.ax, "linear", ls="--", lw=2, c=self.colors["line"], label="best fit", ) # Set the axes limits based on the range of X and Y data # NOTE: shared_limits will be accounted for in finalize() # TODO: do better than add one for really small residuals self.ax.set_xlim(y.min() - 1, y.max() + 1) self.ax.set_ylim(y_pred.min() - 1, y_pred.max() + 1) return self.ax
[docs] def finalize(self, **kwargs): """ Finalizes the figure by ensuring the aspect ratio is correct and adding the identity line for comparison. Also adds a title, axis labels, and the legend. Parameters ---------- kwargs: generic keyword arguments. Notes ----- Generally this method is called from show and not directly by the user. """ # Set the title on the plot self.set_title("Prediction Error for {}".format(self.name)) # Square the axes to ensure a 45 degree line if self.shared_limits: # Get the current limits ylim = self.ax.get_ylim() xlim = self.ax.get_xlim() # Find the range that captures all data bounds = (min(ylim[0], xlim[0]), max(ylim[1], xlim[1])) # Reset the limits self.ax.set_xlim(bounds) self.ax.set_ylim(bounds) # Ensure the aspect ratio is square self.ax.set_aspect("equal", adjustable="box") # Draw the 45 degree line if self.identity: draw_identity_line( ax=self.ax, ls="--", lw=2, c=self.colors["line"], alpha=0.5, label="identity", ) # Set the axes labels self.ax.set_ylabel(r"$\hat{y}$") self.ax.set_xlabel(r"$y$") # Set the legend # Note: it would be nice to be able to use the manual_legend utility # here, since if the user sets a low alpha value, the R2 color in the # legend will also become more translucent. Unfortunately this is a # bit tricky because adding a manual legend here would override the # best fit and 45 degree line legend components. In particular, the # best fit is plotted in draw because it depends on y and y_pred. self.ax.legend(loc="best", frameon=True)
[docs]def prediction_error( model, X_train, y_train, X_test=None, y_test=None, ax=None, shared_limits=True, bestfit=True, identity=True, alpha=0.75, is_fitted="auto", show=True, **kwargs): """Quickly plot a prediction error visualizer Plot the actual targets from the dataset against the predicted values generated by our model(s). This helper function is a quick wrapper to utilize the PredictionError ScoreVisualizer for one-off analysis. Parameters ---------- model : the Scikit-Learn estimator (should be a regressor) Should be an instance of a regressor, otherwise will raise a YellowbrickTypeError exception on instantiation. If the estimator is not fitted, it is fit when the visualizer is fitted, unless otherwise specified by ``is_fitted``. X_train : ndarray or DataFrame of shape n x m A feature array of n instances with m features the model is trained on. Used to fit the visualizer and also to score the visualizer if test splits are not directly specified. y_train : ndarray or Series of length n An array or series of target or class values. Used to fit the visualizer and also to score the visualizer if test splits are not specified. X_test : ndarray or DataFrame of shape n x m, default: None An optional feature array of n instances with m features that the model is scored on if specified, using X_train as the training data. y_test : ndarray or Series of length n, default: None An optional array or series of target or class values that serve as actual labels for X_test for scoring purposes. ax : matplotlib Axes The axes to plot the figure on. shared_limits : bool, default: True If shared_limits is True, the range of the X and Y axis limits will be identical, creating a square graphic with a true 45 degree line. In this form, it is easier to diagnose under- or over- prediction, though the figure will become more sparse. To localize points, set shared_limits to False, but note that this will distort the figure and should be accounted for during analysis. bestfit : bool, default: True Draw a linear best fit line to estimate the correlation between the predicted and measured value of the target variable. The color of the bestfit line is determined by the ``line_color`` argument. identity: bool, default: True Draw the 45 degree identity line, y=x in order to better show the relationship or pattern of the residuals. E.g. to estimate if the model is over- or under- estimating the given values. The color of the identity line is a muted version of the ``line_color`` argument. alpha : float, default: 0.75 Specify a transparency where 1 is completely opaque and 0 is completely transparent. This property makes densely clustered points more visible. 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. 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 that are passed to the base class and may influence the visualization as defined in other Visualizers. Returns ------- ax : matplotlib Axes Returns the axes that the prediction error plot was drawn on. """ # Instantiate the visualizer visualizer = PredictionError( model, ax, shared_limits=shared_limits, bestfit=bestfit, identity=identity, alpha=alpha, is_fitted=is_fitted, **kwargs) visualizer.fit(X_train, y_train) # Scores the visualizer with X and y test if provided, X and y train if not if X_test is not None and y_test is not None: visualizer.score(X_test, y_test) elif X_test is not None or y_test is not None: raise YellowbrickValueError( "both X_test and y_test are required if one is specified" ) else: visualizer.score(X_train, y_train) if show: visualizer.show() else: visualizer.finalize() # Return the axes object on the visualizer return visualizer
########################################################################## ## Residuals Plots ##########################################################################
[docs]class ResidualsPlot(RegressionScoreVisualizer): """ A residual plot shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a non-linear model is more appropriate. Parameters ---------- model : a Scikit-Learn regressor Should be an instance of a regressor, otherwise will raise a YellowbrickTypeError exception on instantiation. If the estimator 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 None is passed in the current axes will be used (or generated if required). hist : {True, False, None, 'density', 'frequency'}, default: True Draw a histogram showing the distribution of the residuals on the right side of the figure. Requires Matplotlib >= 2.0.2. If set to 'density', the probability density function will be plotted. If set to True or 'frequency' then the frequency will be plotted. train_color : color, default: 'b' Residuals for training data are ploted with this color but also given an opacity of 0.5 to ensure that the test data residuals are more visible. Can be any matplotlib color. test_color : color, default: 'g' Residuals for test data are plotted with this color. In order to create generalizable models, reserved test data residuals are of the most analytical interest, so these points are highlighted by having full opacity. Can be any matplotlib color. line_color : color, default: dark grey Defines the color of the zero error line, can be any matplotlib color. train_alpha : float, default: 0.75 Specify a transparency for traininig data, where 1 is completely opaque and 0 is completely transparent. This property makes densely clustered points more visible. test_alpha : float, default: 0.75 Specify a transparency for test data, where 1 is completely opaque and 0 is completely transparent. This property makes densely clustered points more visible. 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. kwargs : dict Keyword arguments that are passed to the base class and may influence the visualization as defined in other Visualizers. Attributes ---------- train_score_ : float The R^2 score that specifies the goodness of fit of the underlying regression model to the training data. test_score_ : float The R^2 score that specifies the goodness of fit of the underlying regression model to the test data. Examples -------- >>> from yellowbrick.regressor import ResidualsPlot >>> from sklearn.linear_model import Ridge >>> model = ResidualsPlot(Ridge()) >>> model.fit(X_train, y_train) >>> model.score(X_test, y_test) >>> model.show() Notes ----- ResidualsPlot is a ScoreVisualizer, meaning that it wraps a model and its primary entry point is the ``score()`` method. The residuals histogram feature requires matplotlib 2.0.2 or greater. """ def __init__( self, model, ax=None, hist=True, train_color="b", test_color="g", line_color=LINE_COLOR, train_alpha=0.75, test_alpha=0.75, is_fitted="auto", **kwargs ): # Whether or not to check if the model is already fitted self.is_fitted = is_fitted # Initialize the visualizer base super(ResidualsPlot, self).__init__(model, ax=ax, **kwargs) # TODO: allow more scatter plot arguments for train and test points # See #475 (RE: ScatterPlotMixin) self.colors = { "train_point": train_color, "test_point": test_color, "line": line_color, } self.hist = hist if self.hist not in {True, "density", "frequency", None, False}: raise YellowbrickValueError( "'{}' is an invalid argument for hist, use None, True, " "False, 'density', or 'frequency'".format(hist) ) if self.hist in {True, "density", "frequency"}: self.hax # If hist is True, test the version availability # Store labels and colors for the legend ordered by call self._labels, self._colors = [], [] self.alphas = {"train_point": train_alpha, "test_point": test_alpha} @memoized def hax(self): """ Returns the histogram axes, creating it only on demand. """ if make_axes_locatable is None: raise YellowbrickValueError( ( "residuals histogram requires matplotlib 2.0.2 or greater " "please upgrade matplotlib or set hist=False on the visualizer" ) ) divider = make_axes_locatable(self.ax) hax = divider.append_axes("right", size=1, pad=0.1, sharey=self.ax) hax.yaxis.tick_right() hax.grid(False, axis="x") return hax
[docs] def fit(self, X, y, **kwargs): """ 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 values kwargs: keyword arguments passed to Scikit-Learn API. Returns ------- self : ResidualsPlot The visualizer instance """ # fit the underlying model to the data super(ResidualsPlot, self).fit(X, y, **kwargs) self.score(X, y, train=True) return self
[docs] def score(self, X, y=None, train=False, **kwargs): """ Generates predicted target values using the Scikit-Learn estimator. Parameters ---------- X : array-like X (also X_test) are the dependent variables of test set to predict y : array-like y (also y_test) is the independent actual variables to score against train : boolean If False, `score` assumes that the residual points being plotted are from the test data; if True, `score` assumes the residuals are the train data. Returns ------- score : float The score of the underlying estimator, usually the R-squared score for regression estimators. """ # Do not call super in order to differentiate train and test scores. score = self.estimator.score(X, y, **kwargs) if train: self.train_score_ = score else: self.test_score_ = score y_pred = self.predict(X) residuals = y_pred - y self.draw(y_pred, residuals, train=train) return score
[docs] def draw(self, y_pred, residuals, train=False, **kwargs): """ Draw the residuals against the predicted value for the specified split. It is best to draw the training split first, then the test split so that the test split (usually smaller) is above the training split; particularly if the histogram is turned on. Parameters ---------- y_pred : ndarray or Series of length n An array or series of predicted target values residuals : ndarray or Series of length n An array or series of the difference between the predicted and the target values train : boolean, default: False If False, `draw` assumes that the residual points being plotted are from the test data; if True, `draw` assumes the residuals are the train data. Returns ------- ax : matplotlib Axes The axis with the plotted figure """ if train: color = self.colors["train_point"] label = "Train $R^2 = {:0.3f}$".format(self.train_score_) alpha = self.alphas["train_point"] else: color = self.colors["test_point"] label = "Test $R^2 = {:0.3f}$".format(self.test_score_) alpha = self.alphas["test_point"] # Update the legend information self._labels.append(label) self._colors.append(color) # Draw the residuals scatter plot self.ax.scatter(y_pred, residuals, c=color, alpha=alpha, label=label) # Add residuals histogram if self.hist in {True, "frequency"}: self.hax.hist(residuals, bins=50, orientation="horizontal", color=color) elif self.hist == "density": self.hax.hist( residuals, bins=50, orientation="horizontal", density=True, color=color ) # Ensure the current axes is always the main residuals axes plt.sca(self.ax) return self.ax
[docs] def finalize(self, **kwargs): """ Prepares the plot for renderig by adding a title, legend, and axis labels. Also draws a line at the zero residuals to show the baseline. Parameters ---------- kwargs: generic keyword arguments. Notes ----- Generally this method is called from show and not directly by the user. """ # Add the title to the plot self.set_title("Residuals for {} Model".format(self.name)) # Set the legend with full opacity patches using manual legend manual_legend(self, self._labels, self._colors, loc="best", frameon=True) # Create a full line across the figure at zero error. self.ax.axhline(y=0, c=self.colors["line"]) # Set the axes labels self.ax.set_ylabel("Residuals") self.ax.set_xlabel("Predicted Value") # Finalize the histogram axes if self.hist: self.hax.axhline(y=0, c=self.colors["line"]) self.hax.set_xlabel("Distribution")
########################################################################## ## Quick Method ##########################################################################
[docs]def residuals_plot( model, X_train, y_train, X_test=None, y_test=None, ax=None, hist=True, train_color="b", test_color="g", line_color=LINE_COLOR, train_alpha=0.75, test_alpha=0.75, is_fitted="auto", show=True, **kwargs ): """ResidualsPlot quick method: A residual plot shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a non-linear model is more appropriate. Parameters ---------- model : a Scikit-Learn regressor Should be an instance of a regressor, otherwise will raise a YellowbrickTypeError exception on instantiation. If the estimator is not fitted, it is fit when the visualizer is fitted, unless otherwise specified by ``is_fitted``. X_train : ndarray or DataFrame of shape n x m A feature array of n instances with m features the model is trained on. Used to fit the visualizer and also to score the visualizer if test splits are not directly specified. y_train : ndarray or Series of length n An array or series of target or class values. Used to fit the visualizer and also to score the visualizer if test splits are not specified. X_test : ndarray or DataFrame of shape n x m, default: None An optional feature array of n instances with m features that the model is scored on if specified, using X_train as the training data. y_test : ndarray or Series of length n, default: None An optional array or series of target or class values that serve as actual labels for X_test for scoring purposes. ax : matplotlib Axes, default: None The axes to plot the figure on. If None is passed in the current axes will be used (or generated if required). hist : {True, False, None, 'density', 'frequency'}, default: True Draw a histogram showing the distribution of the residuals on the right side of the figure. Requires Matplotlib >= 2.0.2. If set to 'density', the probability density function will be plotted. If set to True or 'frequency' then the frequency will be plotted. train_color : color, default: 'b' Residuals for training data are ploted with this color but also given an opacity of 0.5 to ensure that the test data residuals are more visible. Can be any matplotlib color. test_color : color, default: 'g' Residuals for test data are plotted with this color. In order to create generalizable models, reserved test data residuals are of the most analytical interest, so these points are highlighted by having full opacity. Can be any matplotlib color. line_color : color, default: dark grey Defines the color of the zero error line, can be any matplotlib color. train_alpha : float, default: 0.75 Specify a transparency for traininig data, where 1 is completely opaque and 0 is completely transparent. This property makes densely clustered points more visible. test_alpha : float, default: 0.75 Specify a transparency for test data, where 1 is completely opaque and 0 is completely transparent. This property makes densely clustered points more visible. 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. 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 that are passed to the base class and may influence the visualization as defined in other Visualizers. Returns ------- viz : ResidualsPlot Returns the fitted ResidualsPlot that created the figure. """ # Instantiate the visualizer viz = ResidualsPlot( model=model, ax=ax, hist=hist, train_color=train_color, test_color=test_color, line_color=line_color, train_alpha=train_alpha, test_alpha=test_alpha, is_fitted=is_fitted, **kwargs ) # Fit the visualizer viz.fit(X_train, y_train) # Score the visualizer if X_test is not None and y_test is not None: viz.score(X_test, y_test) elif X_test is not None or y_test is not None: raise YellowbrickValueError( "both X_test and y_test are required if one is specified" ) else: viz.score(X_train, y_train) # Draw the final visualization if show: viz.show() else: viz.finalize() # Return the visualizer return viz