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 scatter plot for outliers. More generally (i.e. programmatically) is there a way to identify and mask outliers?

Answer 1

The statsmodels package has what you need. Look at this little code snippet and its output:

# Imports #
import statsmodels.api as smapi
import statsmodels.graphics as smgraphics
# Make data #
x = range(30)
y = [y*10 for y in x]
# Add outlier #
x.insert(6,15)
y.insert(6,220)
# Make graph #
regression = smapi.OLS(x, y).fit()
figure = smgraphics.regressionplots.plot_fit(regression, 0)
# Find outliers #
test = regression.outlier_test()
outliers = ((x[i],y[i]) for i,t in enumerate(test) if t[2] < 0.5)
print 'Outliers: ', list(outliers)

Outliers: [(15, 220)]

Edit

With the newer version of statsmodels, things have changed a bit. Here is a new code snippet that shows the same type of outlier detection.

# Imports #
from random import random
import statsmodels.api as smapi
from statsmodels.formula.api import ols
import statsmodels.graphics as smgraphics
# Make data #
x = range(30)
y = [y*(10+random())+200 for y in x]
# Add outlier #
x.insert(6,15)
y.insert(6,220)
# Make fit #
regression = ols("data ~ x", data=dict(data=y, x=x)).fit()
# Find outliers #
test = regression.outlier_test()
outliers = ((x[i],y[i]) for i,t in enumerate(test.icol(2)) if t < 0.5)
print 'Outliers: ', list(outliers)
# Figure #
figure = smgraphics.regressionplots.plot_fit(regression, 1)
# Add line #
smgraphics.regressionplots.abline_plot(model_results=regression, ax=figure.axes[0])

Outliers: [(15, 220)]

Answer 2

scipy.stats doesn't have anything directly for outliers, so as answer some links and advertising for statsmodels (which is a statistics complement for scipy.stats)

for identifying outliers

http://jpktd.blogspot.ca/2012/01/influence-and-outlier-measures-in.html

http://jpktd.blogspot.ca/2012/01/anscombe-and-diagnostic-statistics.html

http://statsmodels.sourceforge.net/devel/generated/statsmodels.stats.outliers_influence.OLSInfluence.html

instead of masking, a better approach is to use a robust estimator

http://statsmodels.sourceforge.net/devel/rlm.html

with examples, where unfortunately the plots are currently not displayed http://statsmodels.sourceforge.net/devel/examples/generated/tut_ols_rlm.html

RLM downweights outliers. The estimation results have a weights attribute, and for outliers the weights are smaller than 1. This can also be used for finding outliers. RLM is also more robust if the are several outliers.

Answer 3

More generally (i.e. programmatically) is there a way to identify and mask outliers?

Various outlier detection algorithms exist; scikit-learn implements a few of them.

[Disclaimer: I'm a scikit-learn contributor.]

Answer 4

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.