1.6.14.1 A table🔗ℹ

The predictors by name, the file the table comes from, and a column of the table by name:

> (require glmnet/datasets            glmnet/data/nested            glmnet/data/csv            glmnet/data/math            glmnet/data/polars            (only-in math/matrix build-matrix ->col-matrix matrix-shape)            (only-in polars read-csv))

> (define predictors '("wt" "hp" "qsec"))

> (define file (collection-file-path "mtcars.csv" "glmnet" "datasets"))

> (define (column name) (cdr (assoc name mtcars)))

A table’s numeric columns are a design matrix, and its response column, a vector, is a response as it is. The path has R’s sequence of λ, and R’s coef(fit, s = 0.5):

> (define from-table (table->design-matrix mtcars predictors))

> (define mpg (column "mpg"))

> (define fit (elnet-path from-table mpg))

> (vector-length (glmnet-path-lambda fit))

58

> (coef fit #:lambda 0.5)

'#(33.16562014425745    -3.6829279730390896    -0.02385276160227977    0.12733703169896884)

1.6.14.2 Lists and vectors🔗ℹ

The table’s columns are vectors, which nested->design-matrix takes one per column:

> (define from-nested     (nested->design-matrix (map column predictors) #:by 'columns #:column-names predictors))

> (equal? from-nested from-table)

#t

1.6.14.3 A CSV file🔗ℹ

csv-file->table reads the file into a table of vector columns:

> (define cars (csv-file->table file))

> (define from-csv (table->design-matrix cars predictors))

> (equal? from-csv from-table)

#t

> (equal? (elnet-path from-csv (cdr (assoc "mpg" cars))) fit)

#t

1.6.14.4 A matrix🔗ℹ

A math/matrix matrix has the observations as its rows, and the response can be a column matrix:

> (define M     (build-matrix 32 3 (lambda (i j) (vector-ref (column (list-ref predictors j)) i))))

> (matrix-shape M)

32 3

> (define from-math (matrix->design-matrix M #:column-names predictors))

> (equal? from-math from-table)

#t

> (equal? (elnet-path from-math (array->response (->col-matrix mpg))) fit)

#t

1.6.14.5 A Polars dataframe🔗ℹ

Polars reads the file itself, and the predictors leave it in one copy:

> (define df (read-csv file))

> (define from-polars (polars->design-matrix df predictors))

> (equal? from-polars from-table)

#t

> (equal? (elnet-path from-polars (polars->response df "mpg")) fit)

#t

1.6.14.6 Formulas, and back🔗ℹ

Each source that gives a table, the dataset, the CSV file’s table and the dataframe through polars->table, fits the same formula model:

> (define (fit-formula table)     (coef (formula-fit (mpg . ~ . wt + hp + qsec) table #:lambda 0.5)))

> (fit-formula mtcars)

'(("(Intercept)" . 33.11848756050567)   ("wt" . -3.689045302372365)   ("hp" . -0.02373045877112981)   ("qsec" . 0.1300752214884471))

> (equal? (fit-formula cars) (fit-formula mtcars))

#t

> (equal? (fit-formula (polars->table df)) (fit-formula mtcars))

#t

The design matrix converts back to each of them. A design matrix with column names is a table, which table->csv writes:

> (define first-cars (design-matrix-select-rows from-table '(0 1 2)))

> (design-matrix->nested first-cars)

'((2.62 110.0 16.46) (2.875 110.0 17.02) (2.32 93.0 18.61))

> (design-matrix->matrix first-cars)

(flarray #[#[2.62 110.0 16.46] #[2.875 110.0 17.02] #[2.32 93.0 18.61]])

> (design-matrix->polars first-cars)

shape: (3, 3) ┌───────┬───────┬───────┐ │ wt    ┆ hp    ┆ qsec  │ │ ---   ┆ ---   ┆ ---   │ │ f64   ┆ f64   ┆ f64   │ ╞═══════╪═══════╪═══════╡ │ 2.62  ┆ 110.0 ┆ 16.46 │ │ 2.875 ┆ 110.0 ┆ 17.02 │ │ 2.32  ┆ 93.0  ┆ 18.61 │ └───────┴───────┴───────┘

> (table->csv first-cars)

wt,hp,qsec 2.62,110,16.46 2.875,110,17.02 2.32,93,18.61