RMSE

Last updated Oct 17, 2024 Edit Source

• Machinelearning
• Math
• Houdini

Root Mean Squared Error (RMSE) is a widely used metric in statistics and machine learning to evaluate the accuracy of a model’s predictions. It measures the average magnitude of the errors between predicted values and actual values, giving more weight to larger errors due to the squaring of differences.

1. Calculate the Errors: For each predicted value $(\hat{y}_i​)$and actual value $({y}_i​)$, compute the difference (error):

   $ei=\hat{y}_i - y_i​$

2. Square the Errors: Square each error to remove negative signs and give more weight to larger errors:

   $e_i^2$

3. Calculate the Mean of Squared Errors: Find the average of these squared errors:

   $\text{MSE} = \frac{1}{n} \sum_{i=1}^{n} e_i^2$

4. Take the Square Root: Finally, take the square root of the mean squared error:

   $\text{RMSE} = \sqrt{\text{MSE}} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} e_i^2}$

// point wrangle

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float input;
float output;

@e = output - input;
@se = pow(@e, 2);

// @e is the local error

Promote the attribute to detail using average mode and rename it to @mse

// detail wrangle

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@rmse = sqrt(@mse);

• Units: The RMSE is in the same units as whatever we’re predicting, making it easier to understand.
• Sensitivity: RMSE really pays attention to outliers; big errors can swing the RMSE value quite a bit.
• Comparison: A lower RMSE means our model is doing a better job. It’s often compared to other metrics, like Mean Absolute Error (MAE), to get a fuller picture of performance.

In short, RMSE is a handy way to summarize how accurate our predictions are, especially in regression tasks!

Here’s a list of other ways to measure error: Measuring Error

sources / further reading:

• What is Root Mean Square Error?