How to efficiently get the correlation matrix (with p-values) of a data frame with NaN values?

Question

I am trying to compute a matrix of correlation, and filter the correlations based on the p-values to find out the highly correlated pairs.

To explain what I mean, say I have a data frame like this.

df

    A       B       C       D
0   2       NaN     2       -2
1   NaN     1       1       1.1
2   1       NaN     NaN     3.2
3   -4      NaN     2       2
4   NaN     1       2.1     NaN
5   NaN     3       1       1
6   3       NaN     0       NaN

For the correlation coefficient. I used pd.corr(). This method can process data frame with NaN values, and more importantly, it tolerates pair of columns having 0 overlap (col A and col B):

rho = df.corr()

       A          B            C           D
A   1.000000     NaN       -0.609994    0.041204
B   NaN          1.0       -0.500000    -1.000000
C   -0.609994    -0.5       1.000000    0.988871
D   0.041204     -1.0       0.988871    1.000000

The challenge is to compute p-value. I didn't find a built-in method to do this. However from pandas columns correlation with statistical significance, @BKay provided a loop way to compute the p-value. This method will complain error if there are fewer than 3 overlaps.So I did some modification by adding error exception.

ValueError: zero-size array to reduction operation maximum which has no identity

pval = rho.copy()
for i in range(df.shape[1]): # rows are the number of rows in the matrix.
    for j in range(df.shape[1]):
        try:
            df_ols = pd.ols(y=df.iloc[:,i], x=df.iloc[:,j], intercept=True)
            pval.iloc[i,j]  = df_ols.f_stat['p-value']
        except ValueError:
            pval.iloc[i,j]  = None

pval
        A        B            C           D
A   0.000000    NaN         0.582343    0.973761
B   NaN         0.000000    0.666667    NaN
C   0.582343    0.666667    0.000000    0.011129
D   0.973761    NaN         0.011129    0.000000

This method outputs a p-value matrix, but it gets extremely slow when the size of the original data frame increase (my real data frame is ~ 5000 rows x 500 columns). What would you suggest to do to get this p-value matrix efficiently for a large size data frame.

Answer 1

This question turned out to be a good solution.