# Applied Data Science Coding with Python: Regression with Lasso Algorithm

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Regression with the Lasso algorithm is a method for solving regression problems in machine learning. It is a linear regression model that includes L1 regularization, which is a technique that adds a penalty term to the loss function to reduce the complexity of the model. The Lasso algorithm aims to find the simplest and most interpretable model, by setting some of the coefficients of the model to zero.

The Lasso algorithm starts by defining a linear model with L1 regularization. L1 regularization is also known as Lasso regularization, it adds “absolute value of magnitude” of coefficient as a penalty term to the loss function. The objective of Lasso is to minimize the sum of the residuals and the L1-norm of the coefficients.

After the model is trained, it can be used to make predictions for new data points by passing the new input data through the model. The predicted target variable value is the output of the model for the new data point.

In order to use the Lasso algorithm for regression in Python, you need to have a dataset that includes both the input data and the target variable values. You also need to decide on the parameters such as the regularization strength, etc.

There are several libraries available in Python to implement the Lasso algorithm for regression, such as scikit-learn, NumPy, and Pandas. These libraries provide pre-built functions and methods to build, train, and evaluate a Lasso model for regression.

It is important to note that Lasso algorithm tends to give sparse solutions, so it might be useful for feature selection. Also, Lasso algorithm might be sensitive to the scale of the features, so it’s important to scale the features before using the algorithm.

In summary, Regression with the Lasso algorithm is a linear regression model that includes L1 regularization, which is a technique that adds a penalty term to the loss function to reduce the complexity of the model. It aims to find the simplest and most interpretable model by setting some of the coefficients of the model to zero. Lasso algorithm tends to give sparse solutions, so it might be useful for feature selection and it might be sensitive to the scale of the features, so it’s important to scale the features before using the algorithm.

In this Applied Machine Learning & Data Science Recipe (Jupyter Notebook), the reader will find the practical use of applied machine learning and data science in Python programming: How to apply Lasso Algorithm in regression problems.

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What is Lasso Algorithm?

In statistics and machine learning, lasso (least absolute shrinkage and selection operator; also Lasso or LASSO) is a regression analysis method that performs both variable selection and regularization in order to enhance the prediction accuracy and interpretability of the statistical model it produces. It was originally introduced in geophysics literature in 1986 and later independently rediscovered and popularized in 1996 by Robert Tibshirani who coined the term and provided further insights into the observed performance.

Lasso was originally formulated for least squares models and this simple case reveals a substantial amount about the behavior of the estimator, including its relationship to ridge regression and best subset selection and the connections between lasso coefficient estimates and so-called soft thresholding. It also reveals that (like standard linear regression) the coefficient estimates do not need to be unique if covariates are collinear.

Though originally defined for least squares, lasso regularization is easily extended to a wide variety of statistical models including generalized linear models, generalized estimating equations, proportional hazards models, and M-estimators, in a straightforward fashion. Lasso’s ability to perform subset selection relies on the form of the constraint and has a variety of interpretations including in terms of geometry, Bayesian statistics, and convex analysis.

The LASSO is closely related to basis pursuit denoising. [Source]

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