Table Importability

Study guide: Exam ATPA

Table Importability is whether a model's output can be expressed as rating tables, a base rate and a table of relativities for each rating variable, that an insurer's existing rating or policy administration system can import and apply. A Generalized Linear Model with a log link is table-importable by construction, while a gradient boosting machine generally is not, because its prediction is a sum of hundreds of trees whose splits interact. The ATPA outline lists it among the criteria for choosing a model, alongside accuracy, explainability, stability, analytical effort and computational efficiency.

\hat{\mu}(\mathbf{x}) = B \times \prod_{j=1}^{p} R_j(x_j)

R_j(\ell) = e^{\beta_{j\ell}}

• Symbols: B = e^{\beta_0} is the base rate, the prediction for a risk at every variable's base level, and R_j(\ell) is the relativity for level \ell of rating variable j, which a log-link GLM gives as e^{\beta_{j\ell}}. An interaction term is handled the same way, as a two-way table with one relativity for each pair of levels.
• Why it matters: A rating algorithm made of tables can be loaded into the existing rating engine, filed in a rate manual that a regulator can review, and checked by hand. A model that is not table-importable has to be scored by new software in production, which adds IT cost, delay and a new source of model risk.
• Between the extremes: A boosted model of single-split trees with a log link is additive on the log scale, so each variable's contributions form a one-way table, and trees with two splits give two-way tables. A deeper GBM can be approximated by tables, for example by fitting a GLM to its predictions or by using it to find the interactions worth adding to a GLM, at a cost in accuracy that can be measured on hold-out data.

From GLM Coefficients to Rating Tables A log-link pure premium GLM has an intercept of 6.2146 and coefficients of 0.1823 for territory 2, 0.4700 for a young driver (aged 16–24) and -0.1054 for vehicle group 3. Express the model as tables, price a risk with all three characteristics, and explain why a GBM of 1,500 trees, each with five splits, could not be loaded the same way.

Answer Each coefficient becomes an entry in a table by exponentiation.

\begin{align*}
B &= e^{6.2146} \\
&= 500.00 \\
R_{\text{terr}}(2) &= e^{0.1823} \\
&= 1.20 \\
R_{\text{age}}(\text{young}) &= e^{0.4700} \\
&= 1.60 \\
R_{\text{veh}}(3) &= e^{-0.1054} \\
&= 0.90
\end{align*}

The premium is 500.00 \times 1.20 \times 1.60 \times 0.90 = 864.00, or \$864, and the rating engine needs only the base rate and three one-way tables to reproduce it. In the GBM, five splits can involve up to five different variables, so a risk's prediction depends on combinations of up to five variables at once, summed over 1,500 trees. No small set of one-way or two-way tables reproduces that, and a table of every combination would be far too large to file or review, so the GBM would have to be scored by its own software.

How it appears on the exam

• ATPA asks candidates to select and justify a modeling approach based on accuracy, explainability, stability, analytical effort, computational efficiency and table importability, taking the business context into account. A justification can note that a GLM's output loads straight into the existing rating system, while a more accurate GBM would need new software to deploy.

Exam traps

• Importable is not interpretable: A GLM with many interaction terms can still be imported as tables while being hard to understand. The two criteria are judged separately.
• The business context decides its weight: A model that will never set a filed rate, such as a claims-triage or marketing model, may not need to be table-importable at all. Giving the criterion heavy weight there argues against a model for the wrong reason.