Decision tables and PRISM rules

Decision tables and PRISM produce rules for predictable categorical targets. A decision table predicts the target from a small set of columns, with accuracy assessed by cross-validation. PRISM produces rules of the form “if these conditions, then this class.” Their findings use dependencies/predictive and conditional_rules/if_then, respectively. The shared evaluator measures each conditional rule before it enters the report.

Decision tables¶

For each of the most predictable categorical targets (top 6 on standard, 10 on deep), the pass searches for a small feature subset that predicts the target through a lookup table: coarse feature codes (numeric bins folded to 8 buckets, nominal levels kept), cell keys packed into a single u64, cell-majority prediction with a global fallback. The search is greedy over subsets of at most 3 features, drawn from the top 16 by model gain, and each candidate subset is scored by 5-fold cross-validated accuracy (the fold assignment is deterministic).

A table survives when CV accuracy ≥ 0.85 and at least 5 points above the majority baseline. The finding names the subset and both accuracies — the predictive analogue of an approximate dependency. It reports cross-validated error rather than a violation count.

PRISM¶

PRISM (Cendrowska, 1987) induces modular rules one class at a time: start from the rows of one class, repeatedly add the single condition that most increases the class’s share within the covered rows, emit the rule when its precision crosses the bar, remove the covered rows, repeat. The implementation evaluates candidate conditions with precomputed bitset masks — a few hundred word-ANDs per candidate instead of row scans.

PRISM runs only on targets the predictability screen scored ≥ 0.9 with a majority baseline under 0.9, and at most 10 classes. Rules are capped at 3 per class, 4 conditions each, with support ≥ 20 rows and precision ≥ 0.8, drawn from the top 12 features by gain — never the target’s own column. Numeric conditions use the stored bin edge rather than a rounded display value.

The shared rule evaluator¶

Whatever discovers a rule, the report only shows it after a common re-measurement. The evaluator replays the rule’s typed predicates on a deterministic diagnostic partition — one fifth of the sampled rows, chosen by a stable hash of the original row id — and requires:

at least 30 eligible rows (rows where the whole rule is defined),
at least 30 antecedent matches,
at least 20 joint matches,
a conditional rate above the outcome’s baseline rate on the same partition, by at least 0.02 absolute or a lift of at least 1.5.

Surviving rules get the evaluator’s evidence appended — eligible rows, antecedent/outcome/joint counts, conditional rate, baseline rate, lift — and their claim rewritten in those common units. The discovery method’s own numbers stay in its own evidence record: PRISM’s score on uncovered positives is not relabeled as validation precision. Rules that fail the evaluator are dropped; the discovery counts are not a fallback.

import json
import random

import polars as pl

import onceover

rng = random.Random(11)
n = 4_000
segment = ["premium" if rng.random() < 0.5 else "std" for _ in range(n)]
shipping = [
    "express" if (rng.random() < 0.95 if s == "premium" else rng.random() < 0.05)
    else "ground"
    for s in segment
]
df = pl.DataFrame({"segment": segment, "shipping": shipping})

report = onceover.profile(df)
rule = next(f for f in report.findings if f["category"] == "conditional_rules")
print("claim:", rule["claim"])
print()
for e in rule["evidence"]:
    m = e["metrics"]
    keys = [k for k in ("antecedent", "consequent", "conditions",
                        "train_confidence", "holdout_confidence",
                        "discovery_score", "newly_covered_positives",
                        "antecedent_count", "joint_count", "conditional_rate",
                        "baseline_rate", "lift")
            if k in m]
    parts = [f"{k}={m[k]:.3f}" if isinstance(m[k], float) else f"{k}={m[k]}" for k in keys]
    print(f"evidence from {e['method']['detector']:16s} basis={e['basis']:9s} "
          + " ".join(parts))

claim: When segment = "premium", shipping = "express" holds in 362 of 380 matching diagnostic rows (95.26%; baseline 47.28%)

evidence from association_rules basis=estimated antecedent=premium consequent=express train_confidence=0.945 holdout_confidence=0.953
evidence from prism            basis=estimated conditions=['segment = premium'] discovery_score=0.946 newly_covered_positives=1907
evidence from rule_evaluator   basis=measured  antecedent_count=380 joint_count=362 conditional_rate=0.953 baseline_rate=0.473 lift=2.015

Each finding keeps separate evidence from discovery and evaluation. The evaluation partition is diagnostic: miners may have used its rows during discovery, and the evaluation helps select which rules to report. It is not an independent confirmation sample. No multiple-testing correction is applied across the candidate rules.

Report-wide limits apply across rule detectors: at most 20 rules and at most 2 per outcome, configured through the selection policy.

References¶

Cendrowska, J. (1987). PRISM: An algorithm for inducing modular rules. International Journal of Man-Machine Studies 27(4). Kohavi, R. (1995). The power of decision tables. ECML. The evaluator’s counts-and-baseline framing follows standard association-rule vocabulary (support, confidence, lift).