Can scipy.stats identify and mask obvious outliers?

Question

With scipy.stats.linregress I am performing a simple linear regression on some sets of highly correlated x,y experimental data, and initially visually inspecting each x,y sc

Answer 1

It is also possible to limit the effect of outliers using scipy.optimize.least_squares. Especially, take a look at the f_scale parameter:

Value of soft margin between inlier and outlier residuals, default is 1.0. ... This parameter has no effect with loss='linear', but for other loss values it is of crucial importance.

On the page they compare 3 different functions: the normal least_squares, and two methods involving f_scale:

res_lsq =     least_squares(fun, x0, args=(t_train, y_train))
res_soft_l1 = least_squares(fun, x0, loss='soft_l1', f_scale=0.1, args=(t_train, y_train))
res_log =     least_squares(fun, x0, loss='cauchy', f_scale=0.1, args=(t_train, y_train))

As can be seen, the normal least squares is a lot more affected by data outliers, and it can be worth playing around with different loss functions in combination with different f_scales. The possible loss functions are (taken from the documentation):

‘linear’ : Gives a standard least-squares problem.
‘soft_l1’: The smooth approximation of l1 (absolute value) loss. Usually a good choice for robust least squares.
‘huber’  : Works similarly to ‘soft_l1’.
‘cauchy’ : Severely weakens outliers influence, but may cause difficulties in optimization process.
‘arctan’ : Limits a maximum loss on a single residual, has properties similar to ‘cauchy’.

The scipy cookbook has a neat tutorial on robust nonlinear regression.