Backward Feature Elimination and its Implementation

Himanshi Singh 07 Apr, 2021
6 min read


In the previous article, we saw another feature selection technique, the Low Variance Filter. So far we’ve seen Missing Value Ratio and Low Variance Filter techniques, In this article, I’m going to cover one more technique use for feature selection know as Backward Feature Elimination.

Let’s Begin!

Note: If you are more interested in learning concepts in an Audio-Visual format, We have this entire article explained in the video below. If not, you may continue reading.



Let’s say we have the same problem statement where we want to predict the fitness level based on the given feature-

Backward Feature Elimination fitness level data

Let’s assume we don’t have any missing values in the dataset. Also, the variance of all the variables is high and the relation between the independent variables is low. These are our assumptions-

Backward Feature Elimination assumptions

So there’s one more technique called Backward Feature Elimination that we can use to select the important features from the dataset. Let’s look at the steps to perform backward feature elimination, which will help us to understand the technique.

The first step is to train the model, using all the variables. You’ll of course not take the ID variable train the model as ID contains a unique value for each observation. So we’ll first train the model using the other three independent variables. And of course, the target variable, which is the Fitness_Level.

Backward Feature Elimination fitness_level

Next, we will calculate the performance of the model. Let’s say we get an accuracy of 92% using all three independent variables.

Next, we will eliminate a variable and train the model on the remaining variables. So let’s say we drop the Calories_Burnt variable and trained the model on the remaining two variables, Gender, and Plays_Sport. Now we will calculate the performance in the model on this new data, which is after dropping that one variable, we get an accuracy of 90% after dropping the Calories_Burnt variable-

Backward Feature Elimination calories_burnt

Similarly, we will drop each variable at a time and train the model on the remaining variables. Here we’ve dropped the Gender variable, as you can see-

Backward Feature Elimination gender variable

and we get an accuracy of 91.6%. Finally, we drop the Plays_Sport variable, and again, train the model on the remaining data-

Backward Feature Elimination remind

and get an accuracy of 88% a slight drop. Now, once the model is trained after dropping each variable at a time, we will identify the eliminated variable, which perhaps did not impact the performance as much.

So if you recall, we got an accuracy of 92% when we used all the variables, and here is the accuracy after dropping each variable-

Backward Feature Elimination accuracy

So when we dropped Calories-Burnt, we got an accuracy of 90%. When we drop the Gender, we got 91.6%. And when we drop Plays_Sport, the accuracy dropped even further to 88%. If you see gender has produced the smallest change in the performance in the model first, it was 92% when we took all the variables and when we dropped gender, it was 91.6%. So we can infer that gender does not have a high impact on the Fitness_Level variable. And hence it can be dropped.

Finally, we will repeat all these steps until no more variables can be dropped. I hope you got a very good sense of how backward feature elimination works. It’s a very simple, but very effective technique.



Now we will see how to implement it in Python. First import Pandas. I’m sure you must have learned this off by heart at this point-

#importing the libraries
import pandas as pd

Next, read the dataset and print the first five observations using the data.head() function-

#reading the file

data = pd.read_csv('backward_feature_elimination.csv')
Backward Feature Elimination holiday

We have the target variable and the other independent variables. Let’s see the shape of our data-

#shape of the data
shape of the data

12,980 observations and 9 columns of variables. Let’s check. If there are any missing values are not-

# checking missing values in the data
checking missing values in the data

There aren’t, Perfect! Now since we will be training a model on our data set, we need to explicitly define the target variable and the independent variables-

# creating the training data

X = data.drop(['ID', 'count'], axis=1)
y = data['count']

X here will be the independent variables after dropping the ID variable and y will be the target variable, “count”. Let me print the shape of both of these-

X.shape, y.shape

and it looks perfect. Now, this is very important. We need to install “the mlxtend” library, which has pre-written codes for both backward feature elimination and forward feature selection techniques. This might take a few moments depending on how fast your internet connection is-

!pip install mlxtend
install mlxtend


All right, we have it installed here. Now from the recently installed mlxtend, we’ll import the SequencialFeatureSelector from the sklearn library we’ll important LinearRegression. Why? Because you’re working on a regression problem, where we have to predict the count of bikes rented-

from mlxtend.feature_selection import SequentialFeatureSelector as sfs
from sklearn.linear_model import LinearRegression

Let’s go ahead and train our model. Here, we’ll first call the linear regression model and then we define the feature selector model-

lreg = LinearRegression()

sfs1 = sfs(lreg, k_features=4, forward=False, verbose=1, scoring='neg_mean_squared_error')

Let me explain the different parameters that you’re seeing here. The first parameter here is a model name and hence I’ve passed lreg here, which is the linear regression model.

Then we have to define how many features should be selected. For our example I’ve passed “k_features = 4”, so the model will train until only four features are left.

Next “forward = False” here means that we are training the backward feature elimination and not the forward feature selection method.

The next “verbose = 1” will allow us to print the model summary at each iteration.

And finally, as this is a regression model, scoring will be based on the mean squared error metric hence “scoring = ‘neg_mean_squared_error'”.

Let’s go ahead and fit the model here-

sfs1 =, y)
fit the model


We can see that the model was trained until finally only four features are left. Let’s go ahead and print the features that have been selected-

feat_names = list(sfs1.k_feature_names_)
feature names

These are the selected variables. We’ll put these variables into a new data frame and print the first five observations. So let me go ahead and do that-

new_data = data[feat_names]
new_data['count'] = data['count']


Here we go! Let’s just compare the shape of two datasets-

# shape of new and original data
new_data.shape, data.shape
shape of new and original data

Comparing the shape of the two datasets confirms that we have successfully implemented this method.

End Notes

This was all about Backward Feature Elimination.

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If you have any queries let me know in the comment section!


Himanshi Singh 07 Apr, 2021

I am a data lover and I love to extract and understand the hidden patterns in the data. I want to learn and grow in the field of Machine Learning and Data Science.

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Responses From Readers


Mrinal 08 Apr, 2021

Excellent post. Can I have the dataset source link to practice this?

Mrinal 08 Apr, 2021

I have received it. Many thanks.

Sai 24 May, 2021

Can you please send the dataset?

Vivekanand 22 Dec, 2021

Please share the datasets, Your post is so clean and comprehensible. Thanks you so much for this !

Abhishek 29 Dec, 2021

Hi can u please share me the data set

Anna Thomas
Anna Thomas 03 Feb, 2022

This was so helpful. Thank u so much.

Anwar 19 May, 2022

Can you please send the dataset?

Sourabh Somdeve
Sourabh Somdeve 04 Jun, 2022

Here we have used linear regression and passed the model in SequencialFeatureSelector and it has selected the features acc to linear regression, but what if I want to use Random forest model, so will this 4 features give good accuracy on Random forest or do I need to pass the Random forest and in SequencialFeatureSelector and train again ? Can you pls clear that. And thanks for the article.

bharath 17 Jun, 2022

hey can you please share the dataset please!! Also amazing work!

bharath 17 Jun, 2022

Hi can you please share the dataset , real good work

Roselyn Castrodes
Roselyn Castrodes 05 Oct, 2022

Hi. Can i ask for a copy of the dataset? This post is so helpful. Thanks

Pradeep 22 Dec, 2022

I'd say "THE BEST EXPLAINATION" for this. So very to the point & I have learnt the concept really well. Thanks a lot for sharing your knowledge. I have a question here! In a case where one does not know which model is to be used for the given problem however he/she just knows that it is a regression problem, In that case, does he/she has to do this backward elimination for all the regression algorithms like linear, DT,RF,SVM separately? Or one must finalize the model first & then come to the backward elimination process?

Pradeep 22 Dec, 2022

Thanks for sharing your knowledge!