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# Are You Misinterpreting Correlation for Predictiveness?

### Here’s what you should use instead to measure predictiveness.

Correlation measures how two features vary with one another linearly (or monotonically).

This makes correlation symmetric: `corr(A, B) = corr(B, A)`

.

Yet, associations are often asymmetric.

For instance, given a date, it is easy to tell the month. But given a month, you can never tell the date.

**Correlation, being symmetric, entirely ignores this notion.**

What’s more, it is not meant to quantify how well a feature can predict the outcome, as demonstrated below:

Yet, at times, it is misinterpreted as a measure of “predictiveness”.

Lastly, correlation is mostly limited to numerical data. But categorical data is equally important for predictive models.

**The Predictive Power Score (PPS) addresses each of these limitations.**

As the name suggests, it measures the **predictive power** of a feature.

PPS(a → b) is calculated as follows:

**If the target (b) is numeric:**Train a Decision Tree Regressor that predicts b using a.

Find PPS by comparing its MAE to the MAE of a baseline model (median prediction).

**If the target (b) is categorical:**Train a Decision Tree Classifier that predicts b using a.

Find PPS by comparing its F1 to the F1 of a baseline model (random or most frequent prediction).

Thus, PPS:

is asymmetric, meaning

`PPS(a, b) != PPS(b, a)`

.can be used on categorical targets (b).

can be used to measure the predictive power of categorical features (a).

works well for linear and non-linear relationships.

works well for monotonic and non-monotonic relationships.

Its effectiveness is evident from the image below.

For all three datasets:

Correlation is low.

PPS (x → y) is high.

PPS (y → x) is zero.

**That being said, it is important to note that correlation has its place.**

When selecting between PPS and correlation, first set a clear objective about what you wish to learn about the data:

Do you want to know the general monotonic trend between two variables? Correlation will help.

Do you want to know the predictiveness of a feature? PPS will help.

👉 Over to you: What other points will you add here about PPS vs. Correlation?

Get started with PPS: **GitHub**.

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## Are You Misinterpreting Correlation for Predictiveness?

Mutual information is another good measure.