**Before we start:** This Python tutorial is a part of our series of Python Package tutorials.

**Scikit-Learn is one of the most useful Machine Learning (ML) libraries in Python. It includes many supervised and unsupervised algorithms that can be used to analyze datasets and make predictions about the data. Learn more about scikit-learn.**

This post will show you how to make predictions using a variety of algorithms, including:

- Linear regression predictions
- Decision tree predictions
- Random forest predictions
- Neural network predictions
- Bayesian ridge predictions

**Shapley Value Regression**

The Shapley value is a concept in cooperative game theory, and can be used to help explain the output of any machine learning model. In practice, Shapley value regression attempts to resolve a weakness in linear regression reliability when predicting variables that have moderate to high correlation.

In this post, we’ll find Shapley values for each variable in a regression in order to try and find the correct weight for it. The sum of all Shapley values should be the difference between the predictions and average value of the model.

**Linear Regression Example**

In this example, a linear regression model is created with random data, and an estimated regression line is displayed:

# Import the packages and classes needed for this example:import numpy as np import matplotlib.pyplot as plt from sklearn.linear_model import LinearRegression# Create random data with numpy:rnstate = np.random.RandomState(1) x = 10 * rnstate.rand(50) y = 2 * x - 5 + rnstate.randn(50)# Create a linear regression model based on the positioning of the data and Intercept, and predict a Best Fit:model = LinearRegression(fit_intercept=True) model.fit(x[:, np.newaxis], y) xfit = np.linspace(0, 10, 1000) yfit = model.predict(xfit[:, np.newaxis])# Plot the estimated linear regression line with matplotlib:plt.scatter(x, y) plt.plot(xfit, yfit); plt.show()

*Figure 1. Estimated Linear Regression Line*

**Decision Tree Example**

# Import the library required for this example# Create the decision tree regression model:from sklearn import tree dtree = tree.DecisionTreeRegressor(min_samples_split=20) dtree.fit(X_train, y_train) print_accuracy(dtree.predict)# Use Shap explainer to interpret values in the test set:ex = shap.TreeExplainer(dtree) shap_values = ex.shap_values(X_test)# Plot Shap values:shap.summary_plot(shap_values, X_test)

# Plot BMI (Body Mass Index) values:shap.dependence_plot("bmi", shap_values, X_test)

*Figure 2. BMI values distribution in a Shap Decision Tree*

**Random Forest Example**

# Import the library required for this example# Create a Random Forest regression model# that implements aFastTreeExplainer:from sklearn.ensemble import RandomForestRegressor rforest = RandomForestRegressor(n_estimators=1000, max_depth=None, min_samples_split=2, random_state=0) rforest.fit(X_train, y_train) print_accuracy(rforest.predict)#Use Shap explainer to interpret values in the test set:explainer = shap.TreeExplainer(rforest) shap_values = explainer.shap_values(X_test)# Plot Shap values:shap.summary_plot(shap_values, X_test)

# Plot BMI values:shap.dependence_plot("bmi", shap_values, X_test)

*Figure 3. ** BMI values distribution in a Shap Random Forest*

**Neural Network Example**

# Import the library required in this example# Create the Neural Network regression model:from sklearn.neural_network import MLPRegressor nn = MLPRegressor(solver='lbfgs', alpha=1e-1, hidden_layer_sizes=(5, 2), random_state=0) nn.fit(X_train, y_train) print_accuracy(nn.predict)#Use Shap explainer to interpret values in the test set:explainer = shap.KernelExplainer(nn.predict, X_train_summary) shap_values = explainer.shap_values(X_test)# Plot the Shap values:shap.summary_plot(shap_values, X_test)

# Plot BMI values:shap.dependence_plot("bmi", shap_values, X_test)

*Figure 4.* * BMI values distribution in a Shap Neural Network*

**Shap Regression Examples**

**In this set of examples, Shap values are applied to multiple regression models**. Decision Tree, Random Forest, and Neural Network, are displayed in code blocks that share common libraries and classes:

# Import libraries required in the Shap examples, and load some data::import sklearn from sklearn.model_selection import train_test_split import numpy as np import shap import time X,y = shap.datasets.diabetes() X_train,X_test,y_train,y_test = train_test_split(X, y, test_size=0.2, random_state=0)# Summarize the training set with a subset of weighted kmeans,# each weighted by the number of points they represent:X_train_summary = shap.kmeans(X_train, 10) def print_accuracy(f): print("Root mean squared test error ={0}".format(np.sqrt(np.mean((f(X_test) - y_test)**2)))) time.sleep(0.5)# Allow print() to take place before other processes.shap.initjs()

**Ba****yesian Ridge Example**

*Requirement**: *

**Bayesian Ridge regression requires the Python Bayesian-Optimization package. Enter the following command in a command-line or terminal to install the package:**

pip install bayesian-optimizationorpython -m pip install bayesian-optimization

In this example, the BayesianRidge estimator class is used to predict new values in a regression model that lacks sufficient data. A linear regression is formulated using a probable distribution of values in the absence of actual values. The output, response ‘y’, is derived from the probable distribution rather than from actual values.

# Import libraries needed in this example:from sklearn.linear_model import BayesianRidge from sklearn.datasets import load_boston from sklearn.model_selection import train_test_split from sklearn.metrics import mean_squared_error import matplotlib.pyplot as plt from numpy import sqrt# Load the Boston Housing dataset:boston = load_boston()# Split the data into x test, y train sets:x, y = boston.data, boston.target xtrain, xtest, ytrain, ytest=train_test_split(x, y, test_size=0.15)# Define the BayesianRidge model with default parameters:bay_ridge = BayesianRidge()# Fit the model with trained Bayesian data:bay_ridge.fit(xtrain, ytrain)# Use r-squared metrics to measure how close# the data is to the predicted regression line.# Independent variable x^2 = score:score=bay_ridge.score(xtrain, ytrain) print("BayesianRidge regression model - score (r-squared mean): %.2f" % score)# Predict the test data and check for accuracy:ypredict = bay_ridge.predict(xtest) mse = mean_squared_error(ytest, ypredict) # print("Mean squared error level: %.2f" % mse) print("BayesianRidge regression - mean error level: %.2f" % sqrt(mse))# Plot a BayesianRidge regression fitted to probable# Bayesian values in relation to actual values:xaxis = range(len(ytest)) plt.scatter(xaxis, ytest, s=8, color="blue", label="Actual values") plt.plot(xaxis, ypredict, lw=0.8, color="red", label="Predicted regression") plt.legend() plt.show()

**The following tutorials will provide you with step-by-step instructions on how to work with machine learning Python packages:**

- What is Scikit-learn in Python
- How to install Scikit-learn
- How to classify data in Python
- How to display a plot in Python
- How to build a Numpy array
- How to turn a Numpy array into a list
- How to label data for machine learning in Python
- How to run linear regressions in Python Scikit-Learn
- How to classify data in Python using Scikit-Learn

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