[BUG] LOF output mismatch for `fit().predict()` and `fit_predict()`

[notaryanramani]

Describe the bug

LOF as well as PyODAdapter(LOF()) does not seem to be producing same output for fit_predict() as compared to fit().predict().

See #2818

Steps/Code to reproduce the bug

import numpy as np
from aeon.testing.testing_data import FULL_TEST_DATA_DICT
from aeon.base._base import _clone_estimator
from aeon.anomaly_detection import LOF

est = LOF(leaf_size=10, n_neighbors=5, stride=2)
est1 = _clone_estimator(est, random_state=42)
est2 = _clone_estimator(est, random_state=42)

datatype = 'UnivariateSeries-None'
X = FULL_TEST_DATA_DICT[datatype]['train'][0]
y = FULL_TEST_DATA_DICT[datatype]['train'][1]

est1.fit(X, y)
y_pred = est1.predict(X)
y_pred

>>> array([0.99658101, 0.99658101, 0.98995043, 0.98995043, 0.99216063,
       0.99216063, 0.98995043, 0.98995043, 0.99127655, 0.99127655,
       0.98862432, 0.98862432, 0.98995043, 0.98995043, 0.98774024,
       0.98774024, 0.98995043, 0.98995043, 0.98331986, 0.98331986])

y_pred2 = est2.fit_predict(X, y)
y_pred2

>>> array([1.03501792, 1.03501792, 1.02085908, 1.02085908, 1.01276639,
       1.01276639, 1.00540476, 1.00540476, 1.00364001, 1.00364001,
       0.99330039, 0.99330039, 0.98995043, 0.98995043, 0.98774024,
       0.98774024, 0.98995043, 0.98995043, 0.98331986, 0.98331986])

Expected results

np.allclose(y_pred, y_pred2)

>>> True

Actual results

np.allclose(y_pred, y_pred2)

>>> False

Versions

No response

[SebastianSchmidl]

As mentioned here, this is expected:

The non-equal output for LOF et al. is expected because we assume that fit_predict(X) corresponds to an unsupervised usage-scenario and fit(X_train).predict(X_test) to a semi-supervised usage-scenario. LOF uses two different ways to compute the anomaly factor for in-training and out-of-training data (novelty prediction). See this discussion in the PR: #2209 (comment)

If fit(X_train).predict(X_train) should produce the same output as fit_predict(X), we would need to check if the data provided to predict is actually the training data, and thus also need to store the training data (again).