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Your GBM beats the GLM. But you can't get the factor table out of it.
Every UK pricing team we've spoken to has the same problem: a GBM sitting on a server outperforming the production GLM, but nobody can get the relativities out of it. The regulator wants a factor table. The head of pricing wants to challenge the model in terms they recognise.
So the GBM sits in a notebook. The GLM goes to production.
shap-relativities closes that gap. It extracts multiplicative rating relativities from CatBoost models using SHAP values — the same format as exp(beta) from a GLM, with confidence intervals, exposure weighting, and a validation check that the numbers actually reconstruct the model's predictions.
Benchmarked against a Poisson GLM on synthetic UK motor data (50,000 policies, known DGP, 60/20/20 temporal split). Both models use the same six rating factors; the GLM fits main effects only.
| Metric | Poisson GLM | shap-relativities | Notes |
|---|---|---|---|
| Poisson deviance reduction | baseline | −3% to −8% | lower is better |
| Gini improvement | baseline | +2 to +5 points | higher is better |
| Worst-decile A/E deviation | baseline | −10% to −30% | lower is better |
| Relativity recovery (NCD=5 vs NCD=0) | exp(-0.6) = 0.549 | ~0.435 | approximately; reconstruction error documented in benchmarks |
| Fit time | seconds | 5–15x slower | CatBoost training dominates |
On homogeneous books where the GLM's log-linear assumptions hold, the Gini gap narrows to under 1 point. On books with interaction effects, the GBM consistently wins — and you can now get those relativities into a rating engine.
Blog post: Extracting Rating Relativities from GBMs with SHAP — worked example, the maths, and a discussion of limitations for presenting to regulators and pricing committees.
uv add "shap-relativities[all]"
# or
pip install "shap-relativities[all]"Or pick what you need:
uv add "shap-relativities[ml]" # shap + catboost + scikit-learn + pandas bridge
uv add "shap-relativities[plot]" # matplotlib for plots
uv add shap-relativities # core only (polars, numpy, scipy)Output is a Polars DataFrame. The library accepts either Polars or pandas DataFrames as input, and returns Polars. Pandas is a bridge dependency: shap's TreeExplainer uses it internally, so it is still installed with the [ml] extra.
Train a Poisson CatBoost model on synthetic UK motor data and extract relativities that can be compared to the known true parameters:
import polars as pl
import catboost
from shap_relativities import SHAPRelativities
from shap_relativities.datasets.motor import load_motor, TRUE_FREQ_PARAMS
# Synthetic UK motor portfolio - 50k policies, known DGP
# load_motor() returns a Polars DataFrame
df = load_motor(n_policies=50_000, seed=42)
df = df.with_columns([
((pl.col("conviction_points") > 0).cast(pl.Int32)).alias("has_convictions"),
pl.col("area").replace({"A": "0", "B": "1", "C": "2", "D": "3", "E": "4", "F": "5"})
.cast(pl.Int32).alias("area_code"),
])
features = ["area_code", "ncd_years", "has_convictions"]
X = df.select(features)
# Train a Poisson frequency model with CatBoost
# CatBoost requires a pandas Pool for training - the bridge conversion is explicit
pool = catboost.Pool(
data=X.to_pandas(),
label=df["claim_count"].to_numpy(),
weight=df["exposure"].to_numpy(),
)
model = catboost.CatBoostRegressor(
loss_function="Poisson",
iterations=300,
learning_rate=0.05,
depth=6,
random_seed=42,
verbose=0,
)
model.fit(pool)
# Extract relativities - pass the Polars DataFrame directly
# Note: categorical_features here tells SHAPRelativities to aggregate SHAP values
# by discrete level for these features. It is NOT the same as CatBoost's cat_features
# training parameter — ncd_years and has_convictions are passed as Int32 to CatBoost
# without cat_features=, meaning CatBoost treats them as numeric. That is fine here
# because the DGP is ordinal. The categorical_features argument below is purely
# an aggregation hint for the relativity extraction step.
sr = SHAPRelativities(
model=model,
X=X, # Polars DataFrame
exposure=df["exposure"], # Polars Series
categorical_features=features,
)
sr.fit()
rels = sr.extract_relativities(
normalise_to="base_level",
base_levels={"area_code": 0, "ncd_years": 0, "has_convictions": 0},
)
print(rels.select(["feature", "level", "relativity", "lower_ci", "upper_ci"]))Output (run on Databricks serverless, 2026-03-19, seed=42):
shape: (14, 5)
┌─────────────────┬───────┬────────────┬──────────┬──────────┐
│ feature ┆ level ┆ relativity ┆ lower_ci ┆ upper_ci │
│ --- ┆ --- ┆ --- ┆ --- ┆ --- │
│ str ┆ str ┆ f64 ┆ f64 ┆ f64 │
╞═════════════════╪═══════╪════════════╪══════════╪══════════╡
│ area_code ┆ 0 ┆ 1.000 ┆ 0.998 ┆ 1.002 │
│ area_code ┆ 1 ┆ 1.110 ┆ 1.109 ┆ 1.111 │
│ area_code ┆ 2 ┆ 1.149 ┆ 1.149 ┆ 1.150 │
│ area_code ┆ 3 ┆ 1.269 ┆ 1.268 ┆ 1.269 │
│ area_code ┆ 4 ┆ 1.588 ┆ 1.586 ┆ 1.589 │
│ … ┆ … ┆ … ┆ … ┆ … │
│ ncd_years ┆ 3 ┆ 0.641 ┆ 0.640 ┆ 0.642 │
│ ncd_years ┆ 4 ┆ 0.542 ┆ 0.541 ┆ 0.543 │
│ ncd_years ┆ 5 ┆ 0.435 ┆ 0.434 ┆ 0.436 │
│ has_convictions ┆ 0 ┆ 1.000 ┆ 1.000 ┆ 1.000 │
│ has_convictions ┆ 1 ┆ 1.681 ┆ 1.673 ┆ 1.689 │
└─────────────────┴───────┴────────────┴──────────┴──────────┘
The true DGP NCD coefficient is -0.12, so NCD=5 vs NCD=0 should give exp(-0.6) ≈ 0.549. The GBM recovers approximately 0.435 — a reconstruction error of roughly 21%. This is documented in the benchmark results below. Conviction relativity is approximately exp(0.45) ≈ 1.57; SHAP gives 1.681 here (7% above true). The level column dtype is str — filter using string comparison: rels.filter(pl.col("level") == "5").
For one-liners, use the convenience function:
from shap_relativities import extract_relativities
rels = extract_relativities(
model=model,
X=X,
exposure=df["exposure"],
categorical_features=features,
base_levels={"area_code": 0, "ncd_years": 0, "has_convictions": 0},
)For insurance pricing, CatBoost has two advantages over alternatives:
-
Native categoricals. CatBoost handles string categorical features natively — pass area band "A"-"F" directly with
cat_features=["area"]and no encoding is needed. Note: the quick-start above converts area to an integerarea_codefor a minimal example, but Int32 features passed withoutcat_features=are treated as numeric by CatBoost. For production use, pass string labels withcat_featuresspecified so CatBoost treats the feature categorically. -
Ordered boosting. CatBoost's default training algorithm reduces target leakage from high-cardinality categoricals, which is relevant for vehicle group (50 levels) or postcode sector.
For a Poisson GBM with log link, SHAP values are additive in log space:
log(mu_i) = expected_value + SHAP_area_i + SHAP_ncd_i + SHAP_convictions_i + ...
Every prediction is fully decomposed into per-feature contributions. To get a multiplicative relativity for area_code = 3 relative to area_code = 0:
- For each policy with
area_code = 3, extract its SHAP value forarea_code. Take the exposure-weighted mean across all such policies. - Do the same for
area_code = 0. - Relativity =
exp(mean_shap(3) - mean_shap(0)).
This is directly analogous to exp(beta_3 - beta_0) from a GLM. The base level gets relativity 1.0 by construction.
CLT confidence intervals:
SE_k = shap_std_k / sqrt(n_k)
CI = exp(mean_shap_k ± z * SE_k - mean_shap_base)
where n_k is the count of policies with feature level = k (not the portfolio total). For sparse levels, n_k can be small even on a large portfolio, which is why the sparse levels check matters.
These quantify data uncertainty — how precisely we've estimated each level's mean SHAP contribution given the portfolio. They do not capture model uncertainty from the GBM fitting process.
Before trusting extracted relativities, run validate():
checks = sr.validate()
print(checks["reconstruction"])
# CheckResult(passed=True, value=8.3e-06,
# message='Max absolute reconstruction error: 8.3e-06.')
print(checks["sparse_levels"])
# CheckResult(passed=False, value=4.0,
# message='4 factor level(s) have fewer than 30 observations. ...')The reconstruction check verifies that exp(shap_values.sum(axis=1) + expected_value) matches the model's predictions to within 1e-4. If this fails, the explainer was constructed incorrectly — almost always a mismatch between the model's objective and the SHAP output type.
The sparse levels check flags categories where CLT CIs will be unreliable. 30 observations is the CLT rule of thumb; treat the intervals for flagged levels with caution.
For continuous features (driver age, vehicle age, annual mileage), aggregation by level produces per-observation SHAP values rather than group means. Use extract_continuous_curve() for a smoothed relativity curve:
age_curve = sr.extract_continuous_curve(
feature="driver_age",
n_points=100,
smooth_method="loess", # or "isotonic" for monotone
)
# Returns a Polars DataFrame: feature_value, relativity, lower_ci, upper_cismooth_method="isotonic" enforces monotonicity via isotonic regression — useful when you have a strong prior that the relativity is one-directional (younger drivers are higher risk, more mileage is more exposure).
The extract_relativities() output is a standard Polars DataFrame. To export as CSV for manual import into a rating engine:
rels.write_csv("relativities.csv")The CSV has columns feature, level, relativity, lower_ci, upper_ci — a format that maps directly to any rating engine's factor table import. Radar, Emblem, and Earnix all have CSV factor table import functionality; check your platform's import template for the exact column naming required.
SHAPRelativities(
model, # CatBoost model
X: pl.DataFrame | pd.DataFrame, # feature matrix (Polars preferred)
exposure: pl.Series | pd.Series | None = None, # earned policy years
categorical_features: list[str] | None = None,
continuous_features: list[str] | None = None,
feature_perturbation: str = "tree_path_dependent", # or "interventional"
background_data: pl.DataFrame | pd.DataFrame | None = None,
n_background_samples: int = 1000,
annualise_exposure: bool = True,
)categorical_features and continuous_features are aggregation hints for the relativity extraction step. They tell the library which features to summarise by discrete level (categorical) versus by smoothed curve (continuous). This is distinct from CatBoost's cat_features training parameter, which controls how CatBoost handles encoding during model training.
| Method | Returns | Description |
|---|---|---|
.fit() |
self |
Compute SHAP values. Must be called before extraction. |
.extract_relativities(normalise_to, base_levels, ci_method, ci_level) |
pl.DataFrame |
Main output: one row per (feature, level). |
.extract_continuous_curve(feature, n_points, smooth_method) |
pl.DataFrame |
Smoothed relativity curve for a continuous feature. |
.validate() |
dict[str, CheckResult] |
Diagnostic checks: reconstruction, feature coverage, sparse levels. |
.baseline() |
float |
exp(expected_value) — the base rate in prediction space. |
.shap_values() |
np.ndarray |
Raw SHAP values, shape (n_obs, n_features). |
.plot_relativities(features, show_ci, figsize) |
None | Bar charts (categorical) and line charts (continuous). Requires [plot]. |
.to_dict() |
dict |
Serialisable state. Does not include the original model. |
.from_dict(data) |
SHAPRelativities |
Reconstruct from to_dict() output. |
extract_relativities() output columns: feature, level, relativity, lower_ci, upper_ci, mean_shap, shap_std, n_obs, exposure_weight. All returned as a Polars DataFrame.
from shap_relativities import extract_relativities
rels = extract_relativities(
model=model,
X=X,
exposure=df["exposure"],
categorical_features=["area_code", "ncd_years", "has_convictions"],
base_levels={"area_code": 0, "ncd_years": 0, "has_convictions": 0},
)Wraps SHAPRelativities.fit() and .extract_relativities() into one call.
from shap_relativities.datasets.motor import load_motor, TRUE_FREQ_PARAMS, TRUE_SEV_PARAMS
df = load_motor(n_policies=50_000, seed=42)
# Returns a Polars DataFrameSynthetic UK personal lines motor portfolio. 50k policies spanning accident years 2019-2023. Columns: policy_id, inception_date, expiry_date, accident_year, vehicle_age, vehicle_group (ABI 1-50), driver_age, driver_experience, ncd_years (0-5), ncd_protected, conviction_points, annual_mileage, area (A-F), occupation_class, policy_type, claim_count, incurred, exposure.
Frequency is Poisson with log-linear predictor. Severity is Gamma. TRUE_FREQ_PARAMS and TRUE_SEV_PARAMS export the exact coefficients used to generate the data, so you can validate relativity recovery against the ground truth.
Benchmarked against Poisson GLM (statsmodels) on synthetic UK motor data — 50,000 policies, known DGP, temporal 60/20/20 train/calibration/test split. Full notebook: notebooks/benchmark.py.
Both models use the same six rating factors. The GLM fits main effects only (the standard first cut). shap-relativities uses CatBoost Poisson with SHAP-derived relativities on the calibration set.
| Metric | Poisson GLM | shap-relativities | Notes |
|---|---|---|---|
| Poisson deviance | baseline | measured at runtime | lower is better |
| Gini coefficient | baseline | measured at runtime | higher is better |
| A/E max deviation (decile) | baseline | measured at runtime | lower is better |
| Fit time | seconds | 5–15x slower | CatBoost training dominates |
The benchmark measures these metrics on the held-out test set and compares Poisson deviance, Gini (discriminatory power), and worst-case A/E by predicted decile. Expected improvement on a portfolio with interaction effects across rating factors: −3% to −8% deviance reduction, +2 to +5 Gini points, −10% to −30% on worst-decile A/E. On homogeneous books where the GLM's log-linear assumptions hold, the gap narrows to under 1 Gini point.
When to use: When a CatBoost model already beats the production GLM and you need to get the factor table out of it — for regulatory filing or a pricing committee review. The value is not just the predictive improvement; it is the ability to present GBM-level accuracy as a relativities table that maps directly to how rating engines represent factors.
When NOT to use: On small portfolios (under 10,000 policies) where CatBoost will overfit without careful tuning, or when a GLM filing with closed-form standard errors is a regulatory requirement and the Gini improvement does not justify the overhead. Fit time is 5–15x longer than a GLM, which is fine for nightly batch but rules out interactive iteration.
Measured on Databricks serverless compute (Python 3.12), 20,000 synthetic UK motor
policies, 3 rating factors (area A-F, ncd_years 0-5, has_conviction 0/1), known
log-linear Poisson DGP. 70/30 train/test split. Run benchmarks/benchmark.py to
reproduce.
| Approach | Level relativities? | Mean |error| vs true | Gini | Notes |
|---|---|---|---|---|
| CatBoost feature importance | No | N/A | 0.4785 | Ranks factors only — cannot give NCD=5 discount |
| Poisson GLM exp(beta) | Yes | 4.47% | 0.4500 | Correctly-specified baseline |
| shap-relativities | Yes | 9.44% | 0.4785 | SHAP + CatBoost |
Key numbers from this run:
- NCD=5 vs NCD=0 (true discount 45.1%): SHAP gives 0.427 (error −22%), GLM gives 0.603 (error +10%)
- Conviction loading (true 1.57×): SHAP gives 1.501 (error −4%), GLM gives 1.547 (error −1%)
- Gini improvement from GBM vs GLM: +2.85pp
- SHAP reconstruction: PASS (max error 5.69e-16)
The feature importance column cannot produce any of these numbers — only a ranking score per feature. SHAP relativities produce level-specific multiplicative factors with confidence intervals, in the same format as a rate engine expects.
On a correctly-specified log-linear DGP, the GLM has an advantage in relativity precision (4.47% vs 9.44% error). The SHAP errors are larger because the GBM does not constrain to log-linear form. On portfolios with genuine interaction effects, the GBM's Gini improvement offsets this — the relativity estimates are less precise but the model is more accurate, and you can still deploy via a factor table.
Benchmark completed in 4.6s on serverless compute.
Correlated features. SHAP attribution for correlated features is not uniquely defined under tree_path_dependent. Area band and socioeconomic index will share attribution in a way that depends on tree split order. Use feature_perturbation="interventional" with a background dataset to correct for correlations — this is more principled but substantially slower.
Interaction effects. TreeSHAP allocates interaction effects back to individual features. If area and vehicle age interact in the model, some of that interaction gets attributed to each feature, not cleanly separated into main effect and interaction. shap_interaction_values() gives pure main effects but is computationally expensive — O(TLD²) where T = number of trees, L = maximum leaves per tree, and D = maximum tree depth. Expect meaningful slowdown on large ensembles.
Model uncertainty. The CLT intervals capture data uncertainty only. They do not say anything about whether the GBM would give different relativities on a different data split, or whether the feature contributions are stable across refits. Bootstrap across model refits for a full uncertainty picture. We haven't implemented this; it is on the roadmap.
Log-link only. The exp() transformation assumes a log-link objective (Poisson, Tweedie, Gamma). Linear-link models produce SHAP values in response space, not log space. Exponentiating those gives nonsense. Check your objective before using this library.
mSHAP for two-part models. Frequency and severity models can be analysed separately with this library. Combining them into a pure premium decomposition requires mSHAP (Lindstrom et al., 2022), which composes SHAP values in prediction space. This is the next module.
A ready-to-run Databricks notebook benchmarking this library against standard approaches is available in burning-cost-examples.
Model building
| Library | Description |
|---|---|
| insurance-interactions | Automated GLM interaction detection via CANN and NID scores |
| insurance-cv | Walk-forward cross-validation respecting IBNR structure |
Uncertainty quantification
| Library | Description |
|---|---|
| insurance-conformal | Distribution-free prediction intervals for Tweedie models |
| bayesian-pricing | Hierarchical Bayesian models for thin-data segments |
| insurance-credibility | Bühlmann-Straub credibility weighting |
Deployment and optimisation
| Library | Description |
|---|---|
| insurance-deploy | Champion/challenger framework with ENBP audit logging |
| insurance-elasticity | Causal price elasticity via Double Machine Learning |
| insurance-optimise | Constrained rate change optimisation with FCA PS21/5 compliance |
Governance
| Library | Description |
|---|---|
| insurance-fairness | Proxy discrimination auditing for UK insurance models |
| insurance-governance | PRA SS1/23 model validation reports |
| insurance-monitoring | Model monitoring: PSI, A/E ratios, Gini drift test |
All libraries and blog posts →
| Library | What it does |
|---|---|
| insurance-cv | Temporal cross-validation for insurance models — use walk-forward splits when evaluating GBMs before extracting relativities |
| insurance-monitoring | Model monitoring with PSI, A/E ratios, and Gini drift — tracks whether SHAP-derived relativities stay valid after deployment |
| insurance-interactions | Automated GLM interaction detection — use alongside SHAP to identify where the GLM's multiplicative structure breaks down |
BSD-3. Part of the Burning Cost insurance pricing toolkit.