BAM proposes simpler building blocks for inspectable tabular predictions

Transparency is not the same as readability

In BAM: Bivariate Additive Models for Interpretable Tabular Prediction, Atsushi Koike of Tohoku University argues that an inspectable model needs more than visible internal workings. Its individual calculations must also be simple enough for someone to examine against domain knowledge.

The starting point is the generalized additive model, or GAM. It assigns a contribution to each input feature and adds those contributions to a baseline score. An extension, commonly written as GA²M, also includes contributions from pairs of features. That lets a prediction depend on combinations rather than treating every variable separately.

Koike’s concern is that these pairwise contributions can become irregular surfaces with sharp local changes. Plotting them makes the calculation visible, but does not necessarily make its logic easy to grasp. The proposed Bivariate Additive Model, or BAM, restricts the shapes of those surfaces instead of allowing unrestricted complexity.

Predictions assembled from simple shapes

In the implementation studied here, each component is an asymmetric bivariate Gaussian: roughly, a smooth hill or valley over two input variables. Its center, orientation and widths determine where it contributes and how quickly that contribution changes. Allowing different widths on opposite sides makes the shape more flexible while retaining a compact geometric description.

The model adds these component scores to a baseline. For binary classification, that sum is converted into a probability. The displayed contributions therefore belong to the prediction calculation itself, rather than being estimates produced afterward by a separate explanation method.

BAM also learns which features each component uses. During training, a component initially draws on weighted combinations of inputs; selection is progressively sharpened, then fixed while the remaining parameters receive further training. Both inputs can select the same feature, making that component effectively a one-variable function.

Simplicity does not eliminate training difficulties. Koike reports sensitivity to initialization and trains ten random restarts per fold, retaining the model with the lowest training loss.

What the benchmarks show

The study evaluates three regression datasets—California Housing, Bike Sharing and white Wine Quality—and three binary classification datasets—Titanic, Adult and Diabetes Health Indicators. It uses five-fold cross-validation, measuring regression error with RMSE and classification performance with AUC, which assesses how well scores rank the two classes.

The main BAM comparison uses 15 asymmetric components. Alternatives include linear models, a decision tree, additive and pairwise-interaction versions of EBM and NODE-GAM, GRAND-SLAMIN’, a neural network and XGBoost.

Koike reports that BAM achieves accuracy comparable to standard GAMs and approaches pairwise-interaction models on some datasets. Bike Sharing provides a particularly favorable comparison with the one-variable additive models. The author suggests that interactions between inputs help explain this result.

The results are not a general accuracy victory. For example, the extracted table reports Adult AUC of 0.912 for BAM, compared with 0.928 for EBM’s standard GAM configuration. BAM also trails several alternatives on regression tasks. These comparisons support a potential compromise between simplicity and prediction quality, not a claim that simpler components consistently outperform more flexible models.

A separate experiment varies the component count. The author reports that adding components generally improves prediction performance, while increasing the number of plots a reviewer would need to inspect.

An illustration, not a user study

A three-component Titanic example illustrates the intended inspection process. Koike describes contributions involving passenger class and sex, age and class, and sex and the recorded number of siblings or spouses aboard. Those descriptions concern patterns learned by the model; they do not establish causal explanations of survival.

The paper also compares BAM visualizations with EBM plots and SHAP dependence plots. However, it reports no study measuring whether practitioners inspect BAM faster, detect more errors or make better decisions. Its auditability argument rests on the constrained model structure and illustrative comparisons, rather than demonstrated improvements in human performance.

Source status and remaining limits

This account concerns arXiv version 2611.05940v1, submitted on 4 November 2026. It is a preprint; the supplied records do not establish peer-reviewed publication. The evidence available here consists of the landing page, metadata and extracted paper text. PDF extraction can garble equations and tables and omits images, so the visual comparisons cannot be independently assessed from those materials.

The experiments are benchmark evaluations, not deployments in industrial sensing, medicine or other consequential settings. Baselines were not systematically hyperparameter-tuned, and the paper describes changes to GRAND-SLAMIN’ training, limiting conclusions about the methods’ best achievable performance. Koike also leaves component identifiability and overlapping effects for future work. Readable individual shapes therefore should not be mistaken for uniquely determined explanations of the data.