# Mean Square Error (MSE)

Encord Computer Vision Glossary

In the fields of regression analysis and machine learning, the Mean Square Error (MSE) is a crucial metric for evaluating the performance of predictive models. It measures the average squared difference between the predicted and the actual target values within a dataset. The primary objective of the MSE is to assess the quality of a model's predictions by measuring how closely they align with the ground truth.

## Mathematical Formula

The MSE is calculated using the following formula

MSE = Mean Square error

n = Number of Data points

Yi = Observed Values

Y = Predicted Values

## Interpretation

The MSE measures the average of the squared differences between predicted values and actual target values. By squaring the differences, the MSE places a higher weight on larger errors, making it sensitive to outliers. A lower MSE indicates that the model's predictions are closer to the true values, reflecting better overall performance.

## Use Cases

MSE has widespread application in various scenarios:

**Regression Models**: It is extensively used to evaluate the performance of regression models, including linear regression, polynomial regression, and more. The smaller the MSE, the better the model's predictive accuracy.**Model Selection**: In cases where multiple models are considered for a specific problem, the one with the lowest MSE is often preferred as it demonstrates better fitting to the data.**Feature Selection:**By comparing MSE values while including or excluding certain features, you can identify which features contribute significantly to prediction accuracy.

## Limitations

While MSE is a valuable metric, it has certain limitations:

**Sensitivity to Outliers**: MSE is sensitive to outliers due to the squaring of errors.This may cause extreme values to have a significant impact on the model.**Scale Dependenc**e: The magnitude of the MSE depends on the scale of the target variable. This can make it challenging to compare MSE values across different datasets.

Here is a simple Python code snippet to calculate and display the Mean Square Error using the scikit-learn library:

import numpy as np from sklearn.metrics import mean_squared_error # Simulated ground truth and predicted values ground_truth = np.array([2.5, 3.7, 4.2, 5.0, 6.1]) predicted_values = np.array([2.2, 3.5, 4.0, 4.8, 5.8]) # Calculate Mean Square Error mse = mean_squared_error(ground_truth, predicted_values) print(f"Mean Square Error: {mse}")

**Output:** Mean Square Error: 0.06

In this code, the `mean_squared_error()` function from scikit-learn has been used to calculate the MSE between the ground truth and predicted values.

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