What is meant by LassoCV (short for “Least Absolute Shrinkage and Selection Operator”)

LassoCV regression is a supervised learning algorithm that uses cross-validation to select the optimal regularization parameter for lasso regression. LassoCV regression is a powerful tool that can be used for a variety of tasks, including feature selection, overfitting prevention, and regression. It is a good choice for situations where these factors are important.

in which our loss function is the standard OLS loss function plus the absolute value of each coefficient multiplied by some constant alpha.Linear regression can overestimate regression coefficients, adding more complexity to the machine learning model. The model becomes unstable, large, and significantly sensitive to input variables.LASSO regression is an extension of linear regression that adds a penalty (L1) to the loss function during model training to restrict (or shrink) the values of the regression coefficients. This process is known as L1 regularization [1].

L1 regularization shrinks the values of regression coefficients for input features that do not make significant contributions to the prediction task. It brings the values of such coefficient down to zero and removes corresponding input variables from the regression equation, encouraging a simpler regression model.

Lasso regression in scikit-learn

To use LassoCV regression in sklearn, you can import the LassoCV class from the linear_model module. The following code shows how to fit a LassoCV model to a dataset of house prices:

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

data = pd.read_csv('kc_house_data.csv')
data = data.drop(['date', 'zipcode'], axis = 1)

features = ['bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', 'waterfront', 'view', 'grade', 'sqft_above', 'sqft_basement', 'condition', 'yr_built', 'yr_renovated', 'lat', 'long', 'sqft_living15', 'sqft_lot15']
X = data[features]
y = data.price
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.30, random_state=0)

from sklearn.linear_model import LassoCV
from sklearn.model_selection import cross_val_score
#Implementation of LassoCV
lasso = LassoCV(alphas=[0.0001, 0.001, 0.01, 0.1, 1, 10, 100])
print("Root Mean Squared Error (Lasso): ", np.sqrt(-
cross_val_score(lasso, X, y, cv=10, 
scoring='neg_mean_squared_error')).mean())
#Results
Root Mean Squared Error (Lasso):       203421.22072610114

This code will fit a lasso regression model to the data using 5-fold cross-validation. The model coefficients will then be printed to the console.

The LassoCV class has a number of parameters that can be used to control the behavior of the model. Some of the most important parameters include:

• cv: The number of folds to use in cross-validation.
• alphas: An array of regularization parameters to try.
• max_iter: The maximum number of iterations to run the solver.
• tol: The convergence tolerance.

import pandas as pd 
from sklearn.linear_model import LassoCV 
# Load the data data = pd.read_csv("house_prices.csv") 
# Split the data into features and target 
features = data.drop("price", axis=1) 
target = data["price"] 
# Fit the LassoCV model 
model = LassoCV(cv=5).fit(features, target) 
# Print the model coefficients print(model.coef_)

# Create a new house object 
new_house = {"square_feet": 1500, "bedrooms": 3, "bathrooms": 2} 
# Convert the new house object to a numpy array
 new_house_array = np.array([new_house]) 
# Make a prediction 
prediction = model.predict(new_house_array) # Print the prediction print(prediction)

Lasso regression for feature selection

One of the really cool aspects of lasso regression is that it can be used to select important features of a dataset. This is because it tends to shrink the coefficients of less important features to be exactly zero. The features whose coefficients are not shrunk to zero are 'selected' by the LASSO algorithm. Let's check this out in practice.

References