Statistics and Machine Learning Toolbox: Reference

Complete specification of workbook controls, hyperparameter rules, capacity limits, published output schemas, diagnostic thresholds, tolerances, and troubleshooting.

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Control panel reference

The Start sheet hosts global model execution controls in range Start!A5:B10:

Cell	Control Name	Data Type	Default Value	Allowed Values / Range	Validation Rule	Behavioral Impact
`Start!B6`	Active model	String (List)	`customer_churn_logistic`	`customer_churn_logistic`, `housing_regression_ridge`, `iris_clustering_kmeans`, `credit_default_tree`, `feature_pca`	Excel List validation bound to Start!D5:D10	Selects which dataset rows on Data are ingested and which scikit-learn estimator family is instantiated.
`Start!B7`	Test size	Float	`0.25`	$0.00 \le \text{Test size} < 0.50$	Numeric decimal input	Proportion of active samples held out for testing. When $> 0$, assigns samples to `Train` or `Test` partitions. Classification tasks use stratified holdout.
`Start!B8`	Random seed	Integer	`42`	Integers $\ge 0$	Numeric integer input	Controls pseudo-random number generator for train/test splitting, cross-validation partitioning, k-means++ centroid seeding, and stochastic solvers.
`Start!B9`	CV folds	Integer	`3`	Integers $2 \le K \le 5$	Numeric integer input (clamped in runtime)	Number of cross-validation partitions. Sets out-of-fold evaluation granularity. Clamped to minimum class count if minority count $< K$.
`Start!B10`	Scale features	String (List)	`Standard`	`Standard`, `MinMax`, `None`	Excel List validation	Normalization method applied to predictor columns before fitting.

Hyperparameter reference

Hyperparameters are configured on Model Config!A5:D20. Each parameter has strict boundary validation and automatic clamping:

Model ID	Parameter	Type	Default	Min Bound	Max Bound	Clamping & Fallback Behavior
`customer_churn_logistic`	`C`	Float	`1.0`	$10^{-4}$	$10^4$	Clamped to $[10^{-4}, 10^4]$; if invalid type, defaults to `1.0`. Check 2 flags `FAIL` if unclamped input is out of bounds.
`customer_churn_logistic`	`max_iter`	Integer	`200`	$10$	$5000$	Clamped to $[10, 5000]$; if invalid type, defaults to `200`.
`housing_regression_ridge`	`alpha`	Float	`1.0`	$10^{-5}$	$10^5$	Clamped to $[10^{-5}, 10^5]$; if invalid type, defaults to `1.0`. Check 2 flags `FAIL` if out of bounds.
`housing_regression_ridge`	`max_iter`	Integer	`1000`	$10$	$5000$	Clamped to $[10, 5000]$; if invalid type, defaults to `1000`.
`iris_clustering_kmeans`	`n_clusters`	Integer	`3`	$2$	$\min(n - 1, 10)$	Clamped to $[2, \min(n-1, 10)]$; defaults to `3`. Check 2 flags `FAIL` if out of bounds.
`iris_clustering_kmeans`	`max_iter`	Integer	`300`	$10$	$5000$	Clamped to $[10, 5000]$; defaults to `300`.
`credit_default_tree`	`max_depth`	Integer	`3`	$1$	$20$	Clamped to $[1, 20]$; defaults to `3`. Check 2 flags `FAIL` if out of bounds.
`feature_pca`	`n_components`	Integer	`2`	$1$	$\min(n, p)$	Clamped to $[1, \min(n, p)]$; defaults to `2`. Check 2 flags `FAIL` if out of bounds.

Input boundaries and capacity limits

The notebook ingests fixed worksheet bands defined via bf.ref(...):

Sheet Range	Bound Name	Capacity Limit	Notes
`Start!A5:B10`	`controls`	5 control pairs	Reads global switches.
`Start!D5:H10`	`models`	5 model definitions	Model ID, Label, Task, Algorithm, Description.
`Data!A5:G70`	`data`	Up to 65 observation rows	Model, SampleID, 4 numeric features, Target.
`Model Config!A5:D20`	`config`	15 hyperparameter rows	Model, Hyperparameter, Value, Description.

Capacity and runtime limits

Observation rows: The default reference band reads up to row 70 (approx. 65 observation rows across models). For larger datasets, extend the Data!A5:G... reference range in notebook.py and expand the workbook table.
Maximum recommended dataset size: 1,000 observations and 30 features for interactive browser recalculation.
Pyodide WebAssembly constraints: Execution runs within a single-threaded WebAssembly worker. CPU-intensive operations (such as fine-grained grid searches or deep trees on massive tables) should be partitioned or pre-computed.

Published output schemas

The Marimo reactive application exports four dataframes via bf.publish(), anchored to dedicated workbook ranges:

1. Results Summary (`Results!A5:B16`)

Cell Range	Metric Label	Value Type	Description
`A5:B5`	Header	String	`Metric`, `Value`
`A6:B6`	`Active model`	String	Full descriptive model title.
`A7:B7`	`Task`	String	Machine learning task (`Classification`, `Regression`, `Clustering`, `Decomposition`).
`A8:B8`	`Status`	String	Solver status string (`OPTIMAL`).
`A9:B9`	`Algorithm`	String	Scikit-learn estimator class name.
`A10:B10`	`Total samples`	Integer	Number of observations evaluated ($n$).
`A11:B11`	`Feature count`	Integer	Number of predictor columns ($p$).
`A12:B12`	`Primary metric`	Float (6 decimals)	Task primary score (Accuracy, $R^2$, Silhouette, Total Explained Variance).
`A13:B13`	`Secondary metric`	Float (6 decimals)	Task secondary score (F1 score, RMSE, Inertia, PC1 Explained Variance Ratio).
`A14:B14`	`Tertiary metric`	Float (6 decimals)	Task tertiary score (ROC-AUC, MAE, Calinski-Harabasz, PC2 Explained Variance Ratio).
`A15:B15`	`CV score mean`	Float (6 decimals)	Stratified or standard $K$-fold cross-validation arithmetic mean.
`A16:B16`	`Scaling method`	String	Normalization method applied (`Standard`, `Minmax`, `None`).

2. Results Coefficients & Importances (`Results!D5:I16`)

Features are sorted strictly descending by AbsImportance, with alphabetical tie-breaking on Feature:

Column	Header	Type	Format	Description
D	`Feature`	String	Text	Feature name (`Feature1` through `Feature4`).
E	`Weight`	Float	`0.000000`	Signed regression coefficient, PCA loading, or cluster variance fraction.
F	`OddsRatio`	Float	`0.0000`	$\exp(w_j)$ for logistic regression; `0.0` for other models.
G	`AbsImportance`	Float	`0.000000`	Absolute value $\|w_j\|$ used for sorting and ranking.
H	`Rank`	Integer	`0`	Ranking index ($1$ = highest importance).
I	`Significance`	String	Text	Category: `High`, `Moderate`, `ClusterFeature`, `GiniImportance`, `PC1_Loading`.

3. Predictions Table (`Predictions!A5:F55`)

Spills row-level inferences for all observations of the active model:

Column	Header	Type	Description
A	`SampleID`	Integer / String	Sample identifier from `Data!B`.
B	`Actual`	Numeric	Ground truth target from `Data!Target`.
C	`Predicted`	Numeric	Estimated class ($0/1$), price ($k), cluster label ($0/1/2$), or PC1 coordinate.
D	`Probability`	Float	Classification probability $P(y=1)$, regression residual ($y - \hat{y}$), cluster centroid distance, or PC2 coordinate.
E	`Split`	String	Holdout partition assignment: `Train` or `Test`.
F	`Correct`	String	Verification flag: `YES`, `NO`, `Residual`, `ClusterAssigned`, `PCA`.

4. Diagnostics Table (`Diagnostics!A5:C25`)

Spills the complete 7-check health report:

Column	Header	Type	Allowed Values	Description
A	`Check`	String	Fixed check title	Name of the diagnostic test.
B	`Severity`	String	`PASS`, `WARN`, `FAIL`	Standardized alert level.
C	`Detail`	String	Text	Specific quantitative values, thresholds, and diagnostic guidance.

Diagnostic check thresholds reference

The table below documents the exact evaluation rules and thresholds for all seven automated diagnostics:

Check Name	Target Condition	Evaluation Rule	Severity
1. Data validation	Sample sufficiency & missing data	$n > p$ and $\sum \mathbf{1}_{\text{missing}} = 0$ $n > p$ and $\sum \mathbf{1}_{\text{missing}} > 0$ $n \le p$	`PASS` `WARN` `FAIL`
2. Convergence & configuration	Estimator convergence & parameter bounds	Solver status `OPTIMAL` and all hyperparameters within documented bounds Solver failure or out-of-bounds parameter	`PASS` `FAIL`
3. Model performance	Viability threshold per task	Classification: $\text{Accuracy} \ge 0.80$ Classification: $0.65 \le \text{Accuracy} < 0.80$ Classification: $\text{Accuracy} < 0.65$ Regression: $R^2 \ge 0.80$ Regression: $0.60 \le R^2 < 0.80$ Regression: $R^2 < 0.60$ Clustering: $\text{Silhouette} \ge 0.40$ Clustering: $0.25 \le \text{Silhouette} < 0.40$ Clustering: $\text{Silhouette} < 0.25$ PCA: $\text{ExpVar} \ge 0.80$ PCA: $0.60 \le \text{ExpVar} < 0.80$ PCA: $\text{ExpVar} < 0.60$	`PASS` `WARN` `FAIL` `PASS` `WARN` `FAIL` `PASS` `WARN` `FAIL` `PASS` `WARN` `FAIL`
4. Generalization & stability	Overfitting gap $\\|M_{\text{train}} - \bar{M}_{\text{CV}}\\|$	Gap $\le 0.15$ $0.15 < \text{Gap} \le 0.25$ Gap $> 0.25$ (K-Means: min cluster size $\ge 2$ = PASS, $< 2$ = WARN) (PCA: cumulative variance $\ge 0.80$ = PASS, $< 0.80$ = WARN)	`PASS` `WARN` `FAIL`
5. Multicollinearity & conditioning	2-norm condition number $\kappa(\mathbf{X})$	$\kappa < 30.0$ $30.0 \le \kappa < 100.0$ $\kappa \ge 100.0$	`PASS` `WARN` `FAIL`
6. Target balance & residual normality	Class balance or residual distribution	Classification minority ratio $\ge 25\%$ Classification minority ratio $10\% \le \rho < 25\%$ Classification minority ratio $< 10\%$ Regression: Shapiro-Wilk $p \ge 0.05$ Regression: Shapiro-Wilk $p < 0.05$ Clustering: min/max cluster ratio $\ge 0.30$ Clustering: min/max cluster ratio $< 0.30$ PCA: Scree dominance confirmed	`PASS` `WARN` `FAIL` `PASS` `WARN` `PASS` `WARN` `PASS`
7. Outlier detection	Standardized residuals $\\|z\\| > 2.5\sigma$	Outlier count $= 0$ Outlier count $\in \{1, 2\}$ Outlier count $> 2$	`PASS` `WARN` `FAIL`

Numerical tolerances and verification benchmarks

All numerical outputs are verified against scikit-learn standard benchmarks under Python 3.14 / Pyodide:

Float precision: Metrics are rounded to 6 decimal places on Results, probabilities to 4 decimal places, and regression currency predictions to 2 decimal places.
Sorting determinism: Feature ranking breaks identical absolute weights by ascending alphabetical feature name.
Validation tolerances:
- Accuracy / F1 / ROC-AUC / $R^2$: $\pm 10^{-4}$
- Coefficients / Weights: $\pm 10^{-4}$
- Cross-validation means: $\pm 10^{-4}$

Troubleshooting guide

Symptom / Warning	Likely Cause	Recommended Remediation
Diagnostic Check 1 flags `FAIL`	Sample count is less than or equal to the number of features ($n \le p$).	Add more observation rows to Data so that $n > p$.
Diagnostic Check 2 flags `FAIL`	A hyperparameter value on Model Config exceeds its mathematical safety bounds, or the solver exceeded `max_iter`.	Check values on Model Config against the allowed bounds above (e.g., ensure $C > 0$, $\alpha > 0$, $n_{\text{clusters}} \ge 2$). Increase `max_iter` to $500$ or $1000$.
Diagnostic Check 4 flags `FAIL` (Generalization gap)	Severe overfitting: training performance is high, but out-of-fold cross-validation drops sharply.	For Decision Trees, decrease `max_depth` (e.g. from 3 to 1). For Logistic/Ridge, increase regularization (decrease $C$ or increase $\alpha$). Enable `Standard` scaling.
Diagnostic Check 5 flags `FAIL` ($\kappa \ge 100$)	Predictor features have widely differing scales or near-perfect collinearity.	On Start!B10, change Scale features to `Standard`. If features are intrinsically redundant, remove collinear columns or switch to `feature_pca`.
Diagnostic Check 6 flags `WARN` / `FAIL` (Class balance)	One class accounts for less than 25% (or 10%) of the observations.	Rebalance the dataset by adding minority class examples or adjust decision threshold probabilities.
Diagnostic Check 7 flags `WARN` / `FAIL` (Outliers)	One or more samples have standardized residuals $\|z\| > 2.5$.	Open the Predictions sheet, find rows with extreme residual/probability values, and verify the data integrity of those specific observations.
Dropdown does not show model options	Excel data validation broken or overwritten.	Restore data validation on `Start!B6` bound to range `Start!D5:D10`.
`#VALUE!` or `#REF!` in output blocks	The spill range was partially overwritten by manual cell entries.	Clear any cells in `Results!A5:B16`, `Results!D5:I16`, `Predictions!A5:F55`, or `Diagnostics!A5:C25` to allow the formulas to spill freely.