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Residual Diagnostics

Reference for regression-model-trainer · 63 lines

AI & Machine Learning / Classical Machine Learningv1.0.0Updated OCT 25 20264 references2 scripts

Compute on out-of-fold or holdout predictions, never on training predictions.

1. Decile calibration

Sort by prediction, cut into 10 groups, compare mean prediction with mean actual:

python
import pandas as pd
d = pd.DataFrame({"y": y, "p": p})
d["decile"] = pd.qcut(d.p.rank(method="first"), 10, labels=False) + 1
cal = d.groupby("decile").agg(mean_pred=("p", "mean"), mean_true=("y", "mean"))
cal["ratio"] = cal.mean_pred / cal.mean_true

Ratios should be ~1 everywhere. A rising curve below 1 at the top and above 1 at the bottom is "regression to the mean" (shrinkage); common with strong regularisation and squared error on skewed targets.

2. Heteroscedasticity

Correlation between |residual| and prediction (or a binned plot of residual SD by prediction decile). Growing spread means relative errors are roughly constant: log targets or deviance losses fit better, and constant-width intervals are wrong.

3. Residuals vs features

For each important feature, plot mean residual by quantile bin:

python
d["feature_bin"] = pd.qcut(X_valid["sqft"], 10, duplicates="drop")
d.groupby("feature_bin").apply(lambda g: (g.p - g.y).mean())

A systematic pattern means the model misses a non-linearity or interaction in that feature (add splines, interactions, or let the GBM split more).

4. Segment bias

MAE and bias per business segment (region, product line, size band). A small overall bias can hide a large under-prediction for the most valuable segment (the fixture's large segment: −14.8%).

5. Residuals over time

Mean residual by month of the prediction date: drift or a structural break shows up as a trend or step.

6. Worst errors

Read the 20 largest absolute errors row by row: unit errors, duplicated records, outliers that are data issues, or a missing feature that explains them.

7. Influence (linear models)

Cook's distance (statsmodels get_influence().cooks_distance) flags rows that move the fit; inspect them, do not delete them automatically.

Patterns and actions

PatternAction
Under-prediction at the top, over at the bottomless regularisation, log/deviance loss, features for extremes
Spread grows with levellog target / Gamma; relative metrics; adaptive intervals
Residual trend vs a featurenon-linear term or interaction
One segment biasedsegment feature or interaction; separate model
Trend over timeretrain cadence, time features, drift investigation
A few huge errorsdata quality; robust loss
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