The feature engineering process involves selecting the minimum required features to produce a valid model because the more features a model contains, the more complex it is (and the more sparse the data), therefore the more sensitive the model is to errors due to variance. A common approach to eliminating features is to describe their relative importance to a model, then eliminate weak features or combinations of features and re-evalute to see if the model fairs better during cross-validation.
Many model forms describe the underlying impact of features relative to each other. In scikit-learn, Decision Tree models and ensembles of trees such as Random Forest, Gradient Boosting, and Ada Boost provide a feature_importances_ attribute when fitted. The Yellowbrick FeatureImportances visualizer utilizes this attribute to rank and plot relative importances.
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Let's start with an example; first load a classification dataset.
Then we can create a new figure (this is optional, if an Axes isn't specified, Yellowbrick will use the current figure or create one). We can then fit a FeatureImportances visualizer with a GradientBoostingClassifier to visualize the ranked features.
from sklearn.ensemble import RandomForestClassifier
from yellowbrick.datasets import load_occupancy from yellowbrick.model_selection import FeatureImportances
# Load the classification data set X, y = load_occupancy()
model = RandomForestClassifier(n_estimators=10) viz = FeatureImportances(model) viz.fit(X, y) viz.show()
The above figure shows the features ranked according to the explained variance each feature contributes to the model. In this case the features are plotted against their relative importance, that is the percent importance of the most important feature. The visualizer also contains features_ and feature_importances_ attributes to get the ranked numeric values.
For models that do not support a feature_importances_ attribute, the FeatureImportances visualizer will also draw a bar plot for the coef_ attribute that many linear models provide.
When using a model with a coef_ attribute, it is better to set relative=False to draw the true magnitude of the coefficient (which may be negative). We can also specify our own set of labels if the dataset does not have column names or to print better titles. In the example below we title case our features for better readability:
from sklearn.linear_model import Lasso from yellowbrick.datasets import load_concrete from yellowbrick.model_selection import FeatureImportances
# Load the regression dataset dataset = load_concrete(return_dataset=True) X, y = dataset.to_data()
# Title case the feature for better display and create the visualizer labels = list(map(lambda s: s.title(), dataset.meta['features'])) viz = FeatureImportances(Lasso(), labels=labels, relative=False)
# Fit and show the feature importances viz.fit(X, y) viz.show()
Note
The interpretation of the importance of coeficients depends on the model; see the discussion below for more details.
Some estimators return a multi-dimensonal array for either feature_importances_ or coef_ attributes. For example the LogisticRegression classifier returns a coef_ array in the shape of (n_classes, n_features) in the multiclass case. These coefficients map the importance of the feature to the prediction of the probability of a specific class. Although the interpretation of multi-dimensional feature importances depends on the specific estimator and model family, the data is treated the same in the FeatureImportances visualizer -- namely the importances are averaged.
Taking the mean of the importances may be undesirable for several reasons. For example, a feature may be more informative for some classes than others. Multi-output estimators also do not benefit from having averages taken across what are essentially multiple internal models. In this case, use the stack=True parameter to draw a stacked bar chart of importances as follows:
from yellowbrick.model_selection import FeatureImportances from sklearn.linear_model import LogisticRegression from sklearn.datasets import load_iris
data = load_iris() X, y = data.data, data.target
model = LogisticRegression(multi_class="auto", solver="liblinear") viz = FeatureImportances(model, stack=True, relative=False) viz.fit(X, y) viz.show()
It may be more illuminating to the feature engineering process to identify the most or least informative features. To view only the N most informative features, specify the topn argument to the visualizer. Similar to slicing a ranked list by their importance, if topn is a postive integer, then the most highly ranked features are used. If topn is a negative integer, then the lowest ranked features are displayed instead.
from sklearn.linear_model import Lasso from yellowbrick.datasets import load_concrete from yellowbrick.model_selection import FeatureImportances
# Load the regression dataset dataset = load_concrete(return_dataset=True) X, y = dataset.to_data()
# Title case the feature for better display and create the visualizer labels = list(map(lambda s: s.title(), dataset.meta['features'])) viz = FeatureImportances(Lasso(), labels=labels, relative=False, topn=3)
# Fit and show the feature importances viz.fit(X, y) viz.show()
Using topn=3, we can identify the three most informative features in the concrete dataset as splast, cement, and water. This approach to visualization may assist with factor analysis - the study of how variables contribute to an overall model. Note that although water has a negative coefficient, it is the magnitude (absolute value) of the feature that matters since we are closely inspecting the negative correlation of water with the strength of concrete. Alternatively, topn=-3 would reveal the three least informative features in the model. This approach is useful to model tuning similar to rfecv, but instead of automatically removing features, it would allow you to identify the lowest-ranked features as they change in different model instantiations. In either case, if you have many features, using topn can significantly increase the visual and analytical capacity of your analysis.
The topn parameter can also be used when stacked=True. In the context of stacked feature importance graphs, the information of a feature is the width of the entire bar, or the sum of the absolute value of all coefficients contained therein.
from yellowbrick.model_selection import FeatureImportances from sklearn.linear_model import LogisticRegression from sklearn.datasets import load_iris
data = load_iris() X, y = data.data, data.target
model = LogisticRegression(multi_class="auto", solver="liblinear") viz = FeatureImportances(model, stack=True, relative=False, topn=-3) viz.fit(X, y) viz.show()
Generalized linear models compute a predicted independent variable via the linear combination of an array of coefficients with an array of dependent variables. GLMs are fit by modifying the coefficients so as to minimize error and regularization techniques specify how the model modifies coefficients in relation to each other. As a result, an opportunity presents itself: larger coefficients are necessarily "more informative" because they contribute a greater weight to the final prediction in most cases.
Additionally we may say that instance features may also be more or less "informative" depending on the product of the instance feature value with the feature coefficient. This creates two possibilities:
- We can compare models based on ranking of coefficients, such that a higher coefficient is "more informative".
- We can compare instances based on ranking of feature/coefficient products such that a higher product is "more informative".
In both cases, because the coefficient may be negative (indicating a strong negative correlation) we must rank features by the absolute values of their coefficients. Visualizing a model or multiple models by most informative feature is usually done via bar chart where the y-axis is the feature names and the x-axis is numeric value of the coefficient such that the x-axis has both a positive and negative quadrant. The bigger the size of the bar, the more informative that feature is.
This method may also be used for instances; but generally there are very many instances relative to the number models being compared. Instead a heatmap grid is a better choice to inspect the influence of features on individual instances. Here the grid is constructed such that the x-axis represents individual features, and the y-axis represents individual instances. The color of each cell (an instance, feature pair) represents the magnitude of the product of the instance value with the feature's coefficient for a single model. Visual inspection of this diagnostic may reveal a set of instances for which one feature is more predictive than another; or other types of regions of information in the model itself.
The same functionality above can be achieved with the associated quick method feature_importances. This method will build the FeatureImportances object with the associated arguments, fit it, then (optionally) immediately show it.
from sklearn.ensemble import AdaBoostClassifier from yellowbrick.datasets import load_occupancy from yellowbrick.model_selection import feature_importances
# Load dataset X, y = load_occupancy()
# Use the quick method and immediately show the figure feature_importances(AdaBoostClassifier(), X, y)
yellowbrick.model_selection.importances