Nonlinear Regression with Isotonic

Introduction

In this lab, we will explore isotonic regression using scikit-learn. Isotonic regression is a technique that fits a non-decreasing function to one-dimensional data. It is useful when you have data that does not satisfy the assumption of linearity in a regression model.

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Skills Graph

%%%%{init: {'theme':'neutral'}}%%%% flowchart RL sklearn(("`Sklearn`")) -.-> sklearn/ModelSelectionandEvaluationGroup(["`Model Selection and Evaluation`"]) ml(("`Machine Learning`")) -.-> ml/FrameworkandSoftwareGroup(["`Framework and Software`"]) sklearn/ModelSelectionandEvaluationGroup -.-> sklearn/isotonic("`Isotonic Regression`") ml/FrameworkandSoftwareGroup -.-> ml/sklearn("`scikit-learn`") subgraph Lab Skills sklearn/isotonic -.-> lab-71112{{"`Nonlinear Regression with Isotonic`"}} ml/sklearn -.-> lab-71112{{"`Nonlinear Regression with Isotonic`"}} end

Import the necessary libraries

Let's start by importing the IsotonicRegression class from the sklearn.isotonic module.

from sklearn.isotonic import IsotonicRegression

Create sample data

Next, we need to create some sample data to fit our isotonic regression model. In this example, we will generate two arrays, X and y, representing the input data and the target values, respectively.

import numpy as np

## Generate random input data
np.random.seed(0)
X = np.random.rand(100)
y = 4 * X + np.random.randn(100)

Fit the isotonic regression model

Now, we can fit the isotonic regression model to our data. We create an instance of the IsotonicRegression class and call the fit method with our input data and target values.

## Fit isotonic regression model
ir = IsotonicRegression()
ir.fit(X, y)

Predict using the model

After fitting the model, we can use it to make predictions on new data. Let's create a new array X_new and predict the corresponding target values.

## Create new data for prediction
X_new = np.linspace(0, 1, 100)
y_pred = ir.predict(X_new)

Visualize the results

Finally, let's visualize the results of our isotonic regression model. We can plot the original data points as scatter points and the predicted values as a line.

import matplotlib.pyplot as plt

## Plot the original data and predicted values
plt.scatter(X, y, c='b', label='Original Data')
plt.plot(X_new, y_pred, c='r', label='Isotonic Regression')
plt.xlabel('X')
plt.ylabel('y')
plt.legend()
plt.show()

Summary

Isotonic regression is a useful technique when you have non-linear data that does not meet the assumptions of a linear regression model. By fitting a non-decreasing function to the data, isotonic regression provides a piecewise linear approximation that captures the underlying trend in the data. In this lab, we learned how to use scikit-learn's IsotonicRegression class to fit an isotonic regression model, make predictions, and visualize the results.