Observability, Covariate Drift & Population Stability Index (PSI)

Ordinary software fails loudly: exceptions, stack traces, 500 errors. ML models usually fail silently: the API keeps returning HTTP 200 with well-formed JSON, latency is fine, dashboards are green — and the predictions are steadily getting worse because the world has changed since training.

So ML monitoring has two layers:

• Service health — uptime, latency, error rates (same as any API).
• Model health — are the inputs still like the training data? Are the outputs behaving as expected? When labels arrive later (did the patient have a stroke?), is accuracy holding?

• Data drift (covariate shift) — the distribution of inputs P(X) changes. The hospital opens a geriatric wing; patient ages shift up. The relationship between features and stroke may be unchanged, but the model now sees regions of feature space it rarely saw in training.
• Concept drift — the relationship P(Y | X) changes. A new treatment lowers stroke risk for hypertensive patients; the same inputs now mean something different.

Data drift can be detected immediately from inputs alone. Concept drift needs ground-truth labels, which arrive with a delay, so you monitor proxies (prediction distribution, rate of high-risk flags) and evaluate properly when labels come in.

PSI compares a feature's production distribution with its training (reference) distribution:

1. Split the reference data into bins — usually 10 quantile bins, so each holds E = 10% of training rows.
2. Count the share A of production rows that fall in each of those same bins.
3. PSI = Σ (A − E) · ln(A / E) over all bins (natural log).

Each term is ≥ 0 and grows when a bin gains or loses share, so PSI is 0 when the distributions match. Industry rule of thumb:

Practical details: use a small floor (e.g. 0.0001) so empty bins don't give ln(0); compute PSI per feature on a rolling window large enough to be stable.

A monitoring pipeline for the stroke model:

1. Log every request's features and prediction (with privacy controls).
2. Each day, compute PSI per feature against the training reference, plus the distribution of predicted risk; the KS test is a common alternative for continuous features.
3. Alert in the 0.10–0.25 band; trigger retraining at ≥ 0.25 or when evaluation on newly labelled cases shows recall dropping.
4. Retrain on recent data, re-validate (recall at the clinical threshold, calibration), and release via canary — never auto-deploy a retrained model straight to 100%.

PSI says that something changed, not whether it matters. A big shift in an unimportant feature may not hurt; a small shift in the most important one might. Pair drift metrics with feature importance and, when labels arrive, real performance.