🌊 PSI (Population Stability Index)

PSI (Population Stability Index)#

A widely used score measuring how much a distribution has shifted.

Important

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What it is#

The Population Stability Index measures how much a variable’s distribution has shifted between a reference (“expected”) sample and a current (“actual”) one — usually training vs production. It bins the variable and sums the per-bin discrepancy:

\[\text{PSI} = \sum_{b} (A_b - E_b)\,\ln\!\frac{A_b}{E_b},\]

over bins \(b\). It is 0 when the distributions match and grows without bound as they diverge.

How it’s computed#

Choose bins (often 10, by quantile or equal width) using the same edges for both samples, take each bin’s proportion in the expected and actual data, and sum the term above across bins. It is closely related to a symmetrized KL divergence.

Reading it#

The rules of thumb are < 0.1 stable, 0.1–0.25 moderate drift (watch), and > 0.25 significant drift (retrain). Two cautions: an empty bin makes PSI undefined or unbounded (so proportions are clipped), and PSI tends to rise with sample size, so thresholds may need tuning.

Theme: Distribution Shift & Drift · All terminology

Hint

Mind map — connected ideas

Covariate Drift (a.k.a. Covariate Shift) · Label Drift (a.k.a. Target Drift) · Kolmogorov–Smirnov (KS) Test · Kullback–Leibler (KL) Divergence · Data Drift · Drift Detection

Hint

More in Distribution Shift & Drift

Cardinality in Categorical Data · Categorical Drift · Categorical Explosions · Classifier Two-Sample Tests (C2STs) · Concept Drift · Covariate Drift (a.k.a. Covariate Shift) · Data Drift · Dataset Shift · Drift Detection · Drift Guardrails · Energy Distance · Jensen–Shannon (JS) Divergence · KS shift (Kolmogorov–Smirnov shift) · Kullback–Leibler (KL) Divergence