What is Mean Squared Error (MSE)?

Machine Learning

October 17, 2024

Introduction

When working with machine learning models, especially in regression tasks, it’s crucial to evaluate how well your model is performing. One of the most commonly used metrics for this purpose is Mean Squared Error (MSE). In this blog, we’ll break down what MSE is, why it’s important, and walk through a simple Python example to help you calculate and visualize MSE.

Mean Squared Error is a metric used to measure the average of the squares of the errors between predicted values and actual values. Essentially, it shows how far the model’s predictions are from the true values. The formula for MSE is:

Mean Squared Error (MSE): The cost function for linear regression. It calculates the average squared difference between the predicted and actual values.

Tip: Square the errors to make sure negative and positive differences don’t cancel out.

Here’s a sample Python code that demonstrates how to calculate the squared difference between the predicted and actual values and then find the average of the squared differences (i.e., Mean Squared Error, MSE):

import numpy as np

import matplotlib.pyplot as plt

# Sample actual values (y_true) and predicted values (y_pred)

y_true = np.array([3, -0.5, 2, 7])

y_pred = np.array([2.5, 0.0, 2, 8])

# Step 1: Calculate the squared differences between actual and predicted values

squared_diff = (y_true – y_pred) ** 2

print(“Squared differences: “, squared_diff)

# Step 2: Calculate the average of the squared differences (Mean Squared Error)

mse = np.mean(squared_diff)

print(“Mean Squared Error (MSE): “, mse)

# Plotting the actual and predicted values

plt.figure(figsize=(8, 6))

plt.plot(y_true, label=”Actual Values”, marker=’o’, color=’b’, linestyle=’–‘)

plt.plot(y_pred, label=”Predicted Values”, marker=’s’, color=’r’, linestyle=’-‘)

# Highlighting the MSE as a horizontal line in the plot

plt.axhline(y=mse, color=’g’, linestyle=’-.’, label=f’MSE = {mse:.3f}’)

# Annotating the MSE on the graph

plt.text(0.5, mse + 0.2, f’MSE: {mse:.3f}’, color=’g’, fontsize=12)

# Adding the MSE value in yellow on the plot

plt.text(0.5, 6.5, f’Mean Squared Error (MSE): {mse:.3f}’, fontsize=12, color=’black’,

bbox=dict(facecolor=’yellow’, alpha=0.7))

# Highlighting the MSE in the title

plt.title(f’Actual vs Predicted Values’, fontsize=14)

# Labeling the axes

plt.xlabel(‘Index’, fontsize=12)

plt.ylabel(‘Value’, fontsize=12)

# Adding a legend to distinguish between actual and predicted values

plt.legend()

# Show the plot

plt.grid(True)

plt.show()

Introduction

What is Mean Squared Error (MSE)?

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