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# Regression

> Metrics used to evaluate numerical prediction tasks in Kumo, including MAE, MSE, RMSE, MAPE, and SMAPE.

> **Prerelease documentation**
>
> This Kumo Studio information is prerelease and is not yet supported. Stay tuned for the Docker and Kubernetes releases.

* [Table of Contents](#)
* * * [Mean Absolute Error (MAE)](#mean-absolute-error-mae)
    * [Mean Squared Error (MSE)](#mean-squared-error-mse)
    * [Root Mean Squared Error (RMSE)](#root-mean-squared-error-rmse)
    * [Mean Absolute Percentage Error (MAPE)](#mean-absolute-percentage-error-mape)
    * [Symmetric Mean Absolute Percentage Error (SMAPE)](#symmetric-mean-absolute-percentage-error-smape)
  * [Heatmap of Predicted vs. Actual Values](#heatmap-of-predicted-vs-actual-values)
  * [Distribution of Predictions Histogram](#distribution-of-predictions-histogram)

For numerical predictions, Kumo provides metrics that measure the distance between predicted values and actual values (called labels).

### Mean Absolute Error (MAE)

**MAE** is calculated by:

![Formula for MAE: sum of absolute differences between predicted and actual values divided by n](file:images/Screenshot2025-06-27at10.44.04AM.png "Formula for MAE: sum of absolute differences between predicted and actual values divided by n")

where **\_yi \_**is the **\_ith \_**label and ***ŷi*** is the **\_ith \_**predicted value.

### Mean Squared Error (MSE)

**MSE** is calculated by:

![Formula for MSE: sum of squared differences between predicted and actual values divided by n](file:images/Screenshot2025-06-27at10.44.27AM.png "Formula for MSE: sum of squared differences between predicted and actual values divided by n")

MSE focuses more on "how wrong" the prediction is. A prediction that is very far from the label contributes more to increasing the MSE than the MAE.

### Root Mean Squared Error (RMSE)

**RMSE** is calculated by:

![Formula for RMSE: square root of MSE](file:images/Screenshot2025-06-27at10.44.48AM.png "Formula for RMSE: square root of MSE")

RMSE is in the same scale as the target and can be used even if a label is `0` or near `0`.

### Mean Absolute Percentage Error (MAPE)

**MAPE** is calculated by:

![Formula for MAPE: mean of absolute percentage differences between actual and forecast values](file:images/Screenshot2025-06-27at10.45.23AM.png "Formula for MAPE: mean of absolute percentage differences between actual and forecast values")

where **M** is the mean absolute percentage error, **At** is the actual value, and **Ft** is the forecast value.

MAPE is a common regression metric that provides an intuitive measure of accuracy.

### Symmetric Mean Absolute Percentage Error (SMAPE)

**SMAPE** is calculated by:

![Formula for SMAPE: symmetric mean absolute percentage error normalizing by the sum of actual and forecast values](file:images/Screenshot2025-06-27at10.45.45AM.png "Formula for SMAPE: symmetric mean absolute percentage error normalizing by the sum of actual and forecast values")

SMAPE normalizes for the scale of the labels and also for the scale of the predictions. Similar to RMSE, SMAPE is especially useful when a label is `0` or near `0`.

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## Heatmap of Predicted vs. Actual Values

Kumo provides a heatmap of predicted values versus actual target labels for all entities in the predictive query, covering the holdout and evaluation sets of the training table.
Use this to spot-check the quality of your trained predictive query.
Kumo generates predictions by applying the trained predictive query to every row in the training table; actuals are the target labels from that same table.

![Heatmap comparing predicted values against actual target labels across the holdout set](/sdgm/_fern-img/e27309a983d8f560753178c4c4aad43027e1e56ed891c48f0b3ecd4b9e66af48.webp)

## Distribution of Predictions Histogram

Kumo also provides a histogram of predicted values alongside actual target labels for all entities in the predictive query, in the holdout and evaluation sets of the training table.
As with the heatmap, use this to spot-check the quality of your trained predictive query.

![Histogram comparing the distribution of predicted values against actual target labels](/sdgm/_fern-img/41b8f7c4364c3f1a9eba72663df32f269e8032b62d80d2e3f5c5e829a8ff7daa.webp)

Ideally, the shape of the two distributions should match; however, some divergence should be expected in normal cases, even for well-written predictive queries.

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