In selecting a loss function for a regression model, which characteristic is most crucial for ensuring that outliers do not disproportionately influence the model's performance?

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Seekh · Accepted Answer

The most important feature is robustness, meaning the loss grows slowly or is capped for large errors so that a single outlier cannot dominate the sum. A loss with bounded influence, such as the Huber or quantile loss, keeps the contribution of a huge residual from blowing up the objective. In a typical linear regression, using squared error lets a single extreme point produce an enormous gradient, but a robust loss limits that effect. For example, if one data point has a residual of 1000, a squared‑error loss adds 1,000,000 to the objective, whereas a Huber loss adds only about 1,000, making the model less sensitive to that outlier. Thus, choosing a loss with bounded or sub‑quadratic growth is key to preventing outliers from skewing the model.

In selecting a loss function for a regression model, which characteristic is most crucial for ensuring that outliers do not disproportionately influence the model's performance?

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