Unstable behavior of OneClassSVM by changing 'nu'

Question

In the example above, I'm using my dataset to identify outliers. After making slight changes to the nu parameter, there is a huge difference in the number of anomalies identified.

Could this be just a particularity of the dataset? Or a bug in scikit-learn?

P.S. Unfortunately I cannot share the dataset.

Answer 1

If you decrease the value of the tol parameter of the OneClassSVM the result is better although not completely as expected for low values of nu.

import numpy as np
from sklearn.svm import OneClassSVM

import matplotlib.pyplot as plt

X = np.random.rand(100, 1)
nus = np.geomspace(0.0001, 0.5, num=100)

outlier_fraction = np.zeros(len(nus))
for i, nu in enumerate(nus):
    outlier_fraction[i] = (OneClassSVM(nu=nu, tol=1e-12).fit_predict(X) == -1).mean()

plt.plot(nus, outlier_fraction)
plt.xlabel('nu')
plt.ylabel('Outlier fraction')
plt.show()

With the default tol you obtain the following

Answer 2

NOTE: not an answer. Offering a MCVE.

I also recently came across this. I would like to understand the inflection point at the low values

import numpy as np
import pandas as pd
from sklearn.svm import OneClassSVM

X = np.random.rand(100, 1)

nu = np.geomspace(0.0001, 1, num=100)
df = pd.DataFrame(data={'nu': nu})

for i in range(0, len(X)):
    df.loc[i, 'anom_count'] = (OneClassSVM(nu=df.loc[i, 'nu']).fit_predict(X) == -1).sum()

df.set_index('nu').plot();

df.set_index('nu').plot(xlim=(0, 0.2));

df.anom_count.min() # 3
df.anom_count.idxmin() # 62
df.loc[df.anom_count.idxmin(), 'nu'] # 0.031