feature_correlation.md

Feature Correlation

Feature correlation provides computation of Pearson correlation matrix for local and hetero-federated scenario. To switch between the two modes, set local_only to True or False accordingly.

Pearson Correlation Coefficient is a measure of the linear correlation between two variables, $X$ and $Y$, defined as,

$$\rho_{X,Y} = \frac{cov(X, Y)}{\sigma_X\sigma_Y} = \frac{E[(X-\mu_X)(Y-\mu_Y)]}{\sigma_X\sigma_Y} = E\left[\left(\frac{X-\mu_X}{\sigma_X}\cdot\frac{Y-\mu_Y}{\sigma_Y}\right)\right]$$

Let

$$\tilde{X} = \frac{X-\mu_X}{\sigma_X}, \tilde{Y}=\frac{Y-\mu_Y}{\sigma_Y}$$

then,

$$\rho_{X, Y} = E[\tilde{X}\tilde{Y}]$$

Implementation Detail

We use an MPC protocol called SPDZ for Heterogeneous Pearson Correlation Coefficient calculation. SPDZ(Ivan Damg˚ard, Marcel Keller) is a multiparty computation scheme based on somewhat homomorphic encryption (SHE).

Features

• local Pearson correlation efficient computation
• hetero-federated Pearson correlation efficient computation
• local VIF computation
• computation on select cols only(use skip_col)