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 0.818511 0.808262 4
Best Params:
sparsity => 9
Best Model - Fitted OptimalFeatureSelectionRegressor:
Constant: 0.000340372
Weights:
SeTime1: -0.00724609
SeTime2: -0.00917727
SeTime3: -0.0092368
absRoll: 0.0000578331
curPitch: -0.00000852542
curRoll: -0.0000862067
diffClb: -0.00000312272
diffRollRate: 0.00255865
p: -0.000427066The 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 0.342280
1 p 0.185154
2 curRoll 0.119881
3 SeTime3 0.091496
4 SeTime2 0.090909
5 SeTime1 0.071441
6 diffRollRate 0.048799
.. ... ...
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([-0.00102814, -0.00124873, -0.00120034, ..., -0.00116558,
-0.00079782, -0.00089642])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')
0.816473302178Or on the test set:
grid.score(test_X, test_y, criterion='mse')
0.819417696263