correlation.md

Heterogeneous Pearson Correlation Coefficient

Introduction

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. For more details, one can refer [here]

How to Use

• params

• column_indexes
  -1 or list of int. If -1 provided, all columns are used for calculation. If a list of int provided, columns with given indexes are used for calculation.

• column_names
  names of columns use for calculation.

!!! Note

if both params are provided, the union of columns indicated are used for calculation.