Huber breakpoint parameter in quantile form? about mljlinearmodels.jl HOT 2 OPEN

Hello @BeitianMa, either there's a bit of confusion or I misunderstood your message.

the delta parameter affects the loss function i.e. if you have a $y$ and a $X$ and I give you a coefficient $\beta$, it affects how to compute the loss $L_\delta(\beta; X, y)$. You can see exactly how that loss is computed by considering https://github.com/JuliaAI/MLJLinearModels.jl/blob/27b377257a3de81b899f9fc616c36046fc3942be/src/loss-penalty/robust.jl#L9 and https://github.com/JuliaAI/MLJLinearModels.jl/blob/27b377257a3de81b899f9fc616c36046fc3942be/src/loss-penalty/robust.jl#L39-L45

When the individual residuals are below $\delta$ in absolute value, the loss is quadratic, outside of it the loss is linear.

If I understand your question correctly, you would like to determine the $\delta$ dynamically:

• fix a $\delta$
• find $\beta$ using HuberRegressor
• determine the percentage of outliers by checking the residuals that are $>\delta$
• repeat until the percentage of outliers is $<=0.1%$

this is not supported by this library but should be reasonably easy to do with a for loop even if it's a bit ugly. You can try using the bracketing method to get the $\delta^\star$ (start with a pair of very small and very large delta, compute, split it in two, figure out which half to keep exploring etc until convergence.

from mljlinearmodels.jl.