README.md

Reweighted-FastLTS

The Reweighted-FastLTS is a robust regression algorithm that allows you to detect anomalous observations. A Python implementation of FastLTS (by Michele Cappellari) is based on the analysis of datasets with 3 predictors (p). Inspired by the work of Cappellari and the research of Prof. Peter Rousseeuw I implemented a python version of the Reweighted-FastLTS for (i) p predictors with p < n (n number of observations) (ii) n < 600.

The attributes of Reweighted-FastLTS python class are the same that would be obtained by invoking the ltsReg in RStudio. Some doubts are about the implementation of FastMCD. In particular, I used MinCovDet from the sklearn library, and I realized that the location and the covariance matrix are different from those obtained by RStudio, with the consequence that the Robust Distance is different.

- Reference

• Fast-LTS
• Anomaly detection by robust statistics

- Some examples

Below I report the results of some tests. In particular, in the left column you will see the results obtained with Reweighted-FastLTS, while in the right column you will see the results obtained with ltsReg of RStudio's robustbase library. The datasets used are Hawkins-Bradu-Kass data(HBK) and Stackloss data .

-- Hawkins-Bradu-Kass

	Reweighted-FastLTS	ltsReg
alpha	0.5	0.5
quan	40	40
raw_coefficents	[ 0.27835867, 0.04327558, -0.10558377]	[0.27835868, 0.04327561, -0.10558381]
raw_intercept	-0.62325114	-0.6232511
raw_scale	0.8535975675079938	0.8543587
raw_correction_factor	1.2752919	1.275292
coefficents	[0.08137871, 0.03990183, -0.05166559]	[0.08137871, 0.03990181, -0.05166558]
intercept	-0.18046165	-0.18046163
scale	0.744041162494403	0.7440412
chn_factor	1.34586238	1.345862
correction_factor	1.01626593	1.016266
good leverage points	[11, 12, 13, 14]	[11, 12, 13, 14]
leverage points	[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]	[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
vertical outliers

-- Stackloss data

	Reweighted-FastLTS	ltsReg
alpha	0.5	0.5
quan	13	13
raw_coefficents	[0.7409212, 0.39152664, 0.01113465]	[0.74092106, 0.39152672, 0.01113454]
raw_intercept	-37.32334	-37.32332647
raw_scale	1.863142881084838	1.863146
raw_correction_factor	1.88416645	1.884166
coefficents	[0.7976856, 0.5773405, -0.06706011]	[0.79768556, 0.57734046, -0.06706018]
intercept	-37.652466	-37.65245890
scale	1.9218770928830033	1.921877
chn_factor	1.48689415	1.486894
correction_factor	1.14467424	1.144674
good leverage points	[2, 15, 16, 17, 18, 19]	[2, 15, 16, 17, 18, 19]
bad leverage points	[1, 3, 21]	[1, 3, 21]
vertical outliers	[4]	[4]