categoricalInformationValue

Introduced in: v20.1.0

Calculates the information value (IV) for categorical features in relation to a binary target variable.

For each category, the function computes: (P(tag = 1) - P(tag = 0)) × (log(P(tag = 1)) - log(P(tag = 0)))

where:

P(tag = 1) is the probability that the target equals 1 for the given category
P(tag = 0) is the probability that the target equals 0 for the given category

Information Value is a statistic used to measure the strength of a categorical feature’s relationship with a binary target variable in predictive modeling. Higher absolute values indicate stronger predictive power.

The result indicates how much each discrete (categorical) feature [category1, category2, ...] contributes to a learning model which predicts the value of tag.

Syntax

categoricalInformationValue(category1[, category2, ...,]tag)

Arguments

category1, category2, ... — One or more categorical features to analyze. Each category should contain discrete values. UInt8
tag — Binary target variable for prediction. Should contain values 0 and 1. UInt8

Returned value

Returns an array of Float64 values representing the information value for each unique combination of categories. Each value indicates the predictive strength of that category combination for the target variable. Array(Float64)

Examples

Basic usage analyzing age groups vs mobile usage

CREATE TABLE visits (is_young UInt8, is_female UInt8, is_mobile UInt8) ENGINE = Memory;

-- 80 of the 100 young visitors browse on a mobile device, and only 20 of the 100 older ones do,
-- while the sex of a visitor says nothing about the device.
INSERT INTO visits SELECT 1, number % 2, number < 80 FROM numbers(100);
INSERT INTO visits SELECT 0, number % 2, number < 20 FROM numbers(100);

SELECT round(categoricalInformationValue(is_young, is_mobile)[1], 4) AS iv FROM visits;

┌─────iv─┐
│ 0.8318 │
└────────┘

Multiple categorical features with user demographics

-- The age of a visitor predicts the device, the sex of a visitor does not.
SELECT arrayMap(x -> round(x, 4), categoricalInformationValue(is_young, is_female, is_mobile)) AS iv
FROM visits;

┌─iv─────────┐
│ [0.8318,0] │
└────────────┘