Understanding the Discrepancy between Python and R Calculation of a Robust Covariance Matrix: A Comparative Analysis of Parameters and Algorithms.

Understanding the Discrepancy between Python and R Calculation of a Robust Covariance Matrix

The discrepancy between the calculation of a robust covariance matrix in Python and R has been observed by several users. In this response, we will delve into the details of the issue, explore possible causes, and provide guidance on how to resolve it.

Background and Context

The problem arises when using different software to calculate a robust covariance matrix. The Python code utilizes the MinCovDet library, while the R code uses the covMcd function from the ncv package. Despite using equivalent input data, the calculated covariance matrices differ significantly between the two programs.

Parameters Affecting Estimation

To understand why the discrepancies occur, we need to examine the parameters that affect estimation in both Python and R. The following parameters are of particular interest:

Python

assume_centered: Whether to assume that the data is centered.
support_fraction: The fraction of rows used for computation.
random_state: A seed value for random number generation.

R

alpha: A parameter controlling the level of robustness.
nsamp: The number of observations used for computation.
nmini: A minimum subset size required for estimation.
scalefn: A function to scale the data.
maxcsteps: Maximum steps allowed in the solver algorithm.
initHsets: Initial values for the Hessian matrix.
seed: A seed value for random number generation.
tolSolve: Tolerance for convergence of the solver algorithm.
use.correction: Whether to use a correction term.
wgtFUN: A function to weight observations.

Identifying the Point of Divergence

To pinpoint where the divergence arises, we need to examine each parameter and determine whether it is the cause of the discrepancy. The following are potential points of divergence:

Sample selection: The method used to select observations for computation.
Weighting: How the selected observations are weighted.
Corrections: Finite sample and consistency correction method.
Algorithms: Instructions passed to the solver algorithm.

Troubleshooting Steps

To resolve the discrepancy, we can follow these troubleshooting steps:

Check the observations used: Verify that the same observations are being used in both Python and R. If different observations were used, check the number and size of samples checked for differences.
Examine raw estimates: Look at the raw estimates before re-weighting and correction. This may help identify whether the discrepancy arises from weighting or corrections.
Compare Python code with R code: Compare the equivalent Python and R code to ensure that they are identical.

Example Code

To illustrate the differences between the two implementations, let’s examine the following example code:

import numpy as np
from mincovdet import MinCovDet

# Create a random dataset
np.random.seed(42)
data = np.random.normal(size=(100, 4))

# Fit MCD with assume_centered=True and support_fraction=0.5
mcd = MinCovDet().fit(data, assume_centered=True, support_fraction=0.5)

# Extract raw location and covariance estimates
raw_location_ = mcd.raw_location_
raw_covariance = mcd.raw_covariance_

print("Raw Location Estimates:")
print(raw_location_)
print("\nRaw Covariance Estimates:")
print(raw_covariance)

# Create a random dataset
set.seed(42)
data <- matrix(rnorm(n = 100 * 4), nrow = 100, byrow = TRUE)

# Fit MCD with alpha=1.5 and nsamp=100
covMcd <- covMcd(data, alpha = 1.5, nsamp = 100)

# Extract raw center and covariance estimates
raw.center <- covMcd$raw.center
raw.cov <- covMcd$raw.cov

print("Raw Center Estimates:")
print(raw.center)
print("\nRaw Covariance Estimates:")
print(raw.cov)

Conclusion

In conclusion, the discrepancy between the calculation of a robust covariance matrix in Python and R arises from differences in parameters affecting estimation. By examining the parameters used in each implementation, we can identify the point of divergence and take steps to resolve it. This may involve adjusting parameters, comparing raw estimates, or re-examining the algorithms used in each implementation.