---
title: iScore
tags: teach:MF
---

# iScore

[Chernoff, Lo, and Zheng, 2009](https://www.researchgate.net/publication/46588053_Discovering_influential_variables_A_method_of_partitions) proposed the information score (iScore).

Given a subset $V\in \textsf{N}$, $V=\{v_1,\ldots,v_m\}$, a set of $m$ positive integers.

Suppose $x_i$ has $K$ categories, that is, $x_i$ takes values of category 1 to category $K$. Then,

Let $i$ indicate the $i$-th case of the possible

The I-score of $V$ is calculate as
$$I(V) = \frac{1}{n}\sum_{i=1}^{K^m} n_i^2(\bar{Y}_i-\bar{Y}),$$
where $n_i$ is the number of observation where $x_V$ is exact as the $i$th scenarios, and $\bar{Y}_i$ is the mean of dependent variables when $x_V$ is in the $i$th scenarios, $\bar{Y}$ is the overall mean.

Example: Iris data. Classification.