np.cov giving unexpected covariance matrix for large datasets with NaN values
I'm relatively new to this, so bear with me... I'm trying to compute the covariance matrix of a large dataset using NumPy's `np.cov`, but I'm running into issues with NaN values skewing my results. I'm working with a dataset of shape `(10000, 50)`, and there are quite a few NaN values scattered throughout. When I use `np.cov`, it seems to return a covariance matrix that doesn't match my expectations, particularly when the NaN values are present. Here's a snippet of what I've tried: ```python import numpy as np # Generating a large dataset with random values and NaNs np.random.seed(42) data = np.random.rand(10000, 50) data[::100] = np.nan # Introduce NaNs every 100th row # Attempting to compute the covariance matrix cov_matrix = np.cov(data, rowvar=False) print(cov_matrix) ``` The resulting covariance matrix seems to include unexpected large values and does not reflect the distributions I observe in the non-NaN data. I also tried using `np.nanmean` to replace NaNs with the mean of their respective columns before computing the covariance: ```python # Replacing NaNs with column-wise means col_means = np.nanmean(data, axis=0) data_filled = np.where(np.isnan(data), col_means, data) cov_matrix_filled = np.cov(data_filled, rowvar=False) print(cov_matrix_filled) ``` This approach seems to give me a more reasonable covariance matrix, but I'm concerned about how the imputation of NaN values might be affecting the results. Is there a recommended best practice for handling NaNs when calculating covariance in large datasets? Should I be using a different method or library for this? Any insights would be greatly appreciated! What's the best practice here? I'm working in a Ubuntu 22.04 environment. I recently upgraded to Python 3.9. What's the best practice here?