Close the boundary around one exact table rewrite.
Summarize the rewrite
The displayed rows become X, y, and X plus by exact copying and one pinned intercept column.
raw table → X , y , X + \text{raw table} \rightarrow X,\ y,\ X_+ raw table → X , y , X + Feature Matrix Exactly Exact rows rewritten into X, y, and intercept X plus. rows to X, y, and intercept X plus row id x1 x2 y X row y entry X+ row A 1 2 5 [1,2] 5 [1,1,2] B 2 1 4 [2,1] 4 [1,2,1] C 3 3 8 [3,3] 8 [1,3,3] feature order: x1, x2; row ids stay outside X intercept column is all ones in X+ feature matrix is a table rewrite from displayed rows row IDs stay outside X; intercept column is all ones NOT training; NOT learning; NOT prediction NOT accuracy; NOT generalization; NOT feature importance NOT best features; NOT causal; NOT probability truth
Keep the claims narrow
This matrix does not choose best features, measure feature importance, or prove causality.
matrix layout is not a model claim \text{matrix layout is not a model claim} matrix layout is not a model claim Feature Matrix Exactly Exact rows rewritten into X, y, and intercept X plus. rows to X, y, and intercept X plus row id x1 x2 y X row y entry X+ row A 1 2 5 [1,2] 5 [1,1,2] B 2 1 4 [2,1] 4 [1,2,1] C 3 3 8 [3,3] 8 [1,3,3] feature order: x1, x2; row ids stay outside X intercept column is all ones in X+ feature matrix is a table rewrite from displayed rows row IDs stay outside X; intercept column is all ones NOT training; NOT learning; NOT prediction NOT accuracy; NOT generalization; NOT feature importance NOT best features; NOT causal; NOT probability truth
The honest boundary
This is exact table rewriting only: NOT training, NOT learning, NOT prediction, NOT accuracy, NOT generalization, NOT feature importance, NOT best features, NOT causal, and NOT probability truth.
exact table rewrite only \text{exact table rewrite only} exact table rewrite only Feature Matrix Exactly Exact rows rewritten into X, y, and intercept X plus. rows to X, y, and intercept X plus row id x1 x2 y X row y entry X+ row A 1 2 5 [1,2] 5 [1,1,2] B 2 1 4 [2,1] 4 [1,2,1] C 3 3 8 [3,3] 8 [1,3,3] feature order: x1, x2; row ids stay outside X intercept column is all ones in X+ feature matrix is a table rewrite from displayed rows row IDs stay outside X; intercept column is all ones NOT training; NOT learning; NOT prediction NOT accuracy; NOT generalization; NOT feature importance NOT best features; NOT causal; NOT probability truth