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  "body": "\n## Summary\n\nThe Huber loss is a [[loss function|3BTG6VVCGZ]] that is quadratic for small residuals and linear for large ones.\nIt combines the efficiency of [[least squares|0BYTQ4X1HC]] for well-behaved data with the resistance of absolute loss to outliers.\nPeter Huber introduced it in 1964 to define a robust [[M-estimator|4503R8BVF8]] of location, and it is now also common in regression and machine learning.\n\n## Explanations\n\n### L1 human\n\nSquared error punishes a residual of $10$ a hundred times as much as a residual of $1$, so a single outlier can dominate a fit.\nAbsolute error is gentler on outliers but has a sharp corner at zero.\nThe Huber loss uses squared error near zero and switches to a straight line beyond a cutoff $\\delta$.\nSo small errors are treated as in least squares, while large errors count only in proportion to their size.\n",
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