Quick Start Guide: Optimal Feature Selection for Regression
This is a Python version of the corresponding OptimalFeatureSelection quick start guide.
In this example we will use Optimal Feature Selection on the Ailerons dataset, which addresses a control problem, namely flying a F16 aircraft. The attributes describe the status of the aeroplane, while the goal is to predict the control action on the ailerons of the aircraft.
First we load in the data and split into training and test datasets:
import pandas as pd
df = pd.read_csv("ailerons.csv")
climbRate Sgz p q ... diffSeTime14 alpha Se goal
0 2 -56 -0.33 -0.09 ... 0.0 0.9 0.032 -0.0009
1 470 -39 0.02 0.12 ... 0.0 0.9 0.034 -0.0011
2 165 4 0.14 0.14 ... 0.0 1.0 0.034 -0.0012
3 -113 5 -0.12 0.11 ... 0.0 0.9 0.033 -0.0011
4 -411 -21 -0.17 0.07 ... 0.0 0.9 0.032 -0.0008
5 -105 -42 0.23 -0.06 ... 0.0 0.8 0.028 -0.0010
6 144 -40 0.31 -0.01 ... 0.0 0.8 0.029 -0.0012
... ... ... ... ... ... ... ... ... ...
13743 -224 -24 -0.22 0.00 ... 0.0 0.7 0.026 -0.0007
13744 -204 -27 -0.25 0.01 ... 0.0 0.7 0.026 -0.0006
13745 399 -22 0.17 0.20 ... 0.0 0.8 0.027 -0.0008
13746 237 -6 0.26 0.10 ... 0.0 0.8 0.027 -0.0010
13747 -148 -3 -0.37 0.09 ... 0.0 0.7 0.026 -0.0006
13748 -237 -11 -0.47 -0.16 ... 0.0 0.7 0.023 -0.0005
13749 128 -14 -0.07 -0.11 ... 0.0 0.6 0.022 -0.0006
[13750 rows x 41 columns]from interpretableai import iai
X = df.iloc[:, 0:-1]
y = df.iloc[:, -1]
(train_X, train_y), (test_X, test_y) = iai.split_data('regression', X, y, seed=1)
Model Fitting
We will use a GridSearch to fit an OptimalFeatureSelectionRegressor:
grid = iai.GridSearch(
iai.OptimalFeatureSelectionRegressor(
random_seed=1,
),
sparsity=range(1, 11),
)
grid.fit(train_X, train_y)
All Grid Results:
│ Row │ sparsity │ train_score │ valid_score │ rank_valid_score │
│ │ Int64 │ Float64 │ Float64 │ Int64 │
├─────┼──────────┼─────────────┼─────────────┼──────────────────┤
│ 1 │ 1 │ 0.502496 │ 0.469551 │ 10 │
│ 2 │ 2 │ 0.664859 │ 0.661475 │ 9 │
│ 3 │ 3 │ 0.75009 │ 0.746062 │ 8 │
│ 4 │ 4 │ 0.808994 │ 0.800123 │ 7 │
│ 5 │ 5 │ 0.814076 │ 0.803629 │ 6 │
│ 6 │ 6 │ 0.816877 │ 0.807073 │ 5 │
│ 7 │ 7 │ 0.819178 │ 0.809386 │ 3 │
│ 8 │ 8 │ 0.819249 │ 0.809528 │ 2 │
│ 9 │ 9 │ 0.819444 │ 0.809719 │ 1 │
│ 10 │ 10 │ 0.818245 │ 0.808777 │ 4 │
Best Params:
sparsity => 9
Best Model - Fitted OptimalFeatureSelectionRegressor:
Constant: 0.000340054
Weights:
SeTime6: -0.00762837
SeTime7: -0.00760919
SeTime8: -0.00533595
SeTime9: -0.00531819
absRoll: 0.0000577878
curRoll: -0.0000863373
diffClb: -0.00000357877
diffRollRate: 0.00253459
p: -0.000428755The model selected a sparsity of 9 as the best parameter, but we observe that the validation scores are close for many of the parameters. We can use the results of the grid search to explore the tradeoff between the complexity of the regression and the quality of predictions:
results = grid.get_grid_result_summary()
ax = results.plot(x='sparsity', y='valid_score', legend=False)
ax.set_xlabel('Sparsity')
ax.set_ylabel('Validation R-Squared')
We see that the quality of the model quickly increases with additional terms until we reach 4, and then only small increases afterwards. Depending on the application, we might decide to choose a lower sparsity for the final model than the value chosen by the grid search.
We can see the relative importance of the selected features with variable_importance:
grid.get_learner().variable_importance()
Feature Importance
0 absRoll 0.339804
1 p 0.184686
2 curRoll 0.119288
3 SeTime6 0.075255
4 SeTime7 0.075074
5 SeTime8 0.052706
6 diffClb 0.052629
.. ... ...
33 diffSeTime4 0.000000
34 diffSeTime5 0.000000
35 diffSeTime6 0.000000
36 diffSeTime7 0.000000
37 diffSeTime8 0.000000
38 diffSeTime9 0.000000
39 q 0.000000
[40 rows x 2 columns]We can make predictions on new data using predict:
grid.predict(test_X)
array([-0.00103273, -0.00124588, -0.00120397, ..., -0.00114447,
-0.00082961, -0.00089865])We can evaluate the quality of the model using score with any of the supported loss functions. For example, the $R^2$ on the training set:
grid.score(train_X, train_y, criterion='mse')
0.816274630679Or on the test set:
grid.score(test_X, test_y, criterion='mse')
0.820105222067