dataframe-learn

Symbolic machine learning for dataframe where a fitted model is a dataframe expression. The API borrows from the now ubiquitous scikit-learn fit + predict convention. fit returns a record containing model information. predict takes that record and returns an Expr over your columns. The expression is a normal dataframe expression that can be:

• applied with derive
• pretty-printed
• manipulated symbolically.

Linear regression

For a linear regression fit returns a record (with regCoef/regIntercept for inspection) and predict compiles it to an Expr Double.

-- cabal: packages: .., ., ../dataframe-core, ../dataframe-parsing, ../dataframe-operations, ../dataframe-csv, ../dataframe-json, ../dataframe-parquet, ../dataframe-lazy, ../dataframe-viz, ../dataframe-expr-serializer, ../dataframe-th, ../dataframe-csv-th, ../dataframe-parquet-th, ../dataframe-huggingface
-- cabal: build-depends: dataframe, dataframe-learn, text, random
-- cabal: default-extensions: OverloadedStrings, TypeApplications, DataKinds, TypeOperators, FlexibleContexts
-- cabal: ghc-options: -w
import qualified DataFrame as D
import DataFrame.Learn

sales = D.fromNamedColumns
    [ ("x", D.fromList ([1, 2, 3, 4, 5, 6] :: [Double]))
    , ("y", D.fromList ([2 * x + 1 | x <- [1, 2, 3, 4, 5, 6]] :: [Double]))
    ]

model = fit defaultLinearConfig (D.col @Double "y") sales
putStrLn (D.prettyPrint (predict model))

2.0 * x + 0.9999999999999989

Type-safe linear regression

fit and predict work on both typed and untyped dataframes. You can have the compiler enforce that you don’t hand the fit function a frame with nullable fields or a non-Double:

import qualified DataFrame.Typed as T
import Data.Maybe (fromJust)

salesT     = T.unsafeFreeze @'[T.Column "x" Double, T.Column "y" Double] sales
typedModel = fit defaultLinearConfig (T.col @"y") salesT
scored     = T.derive @"prediction" (predict typedModel) salesT

putStr (unlines
    [ "typed model:  " ++ D.prettyPrint (T.unTExpr (predict typedModel))
    , "schema after: " ++ show (T.columnNames scored) ])

typed model: 2.0 * x + 0.9999999999999989 schema after: [“x”,“y”,“prediction”]

Decision trees

The tree compiles to nested if/then/else over your columns:

flowers = D.fromNamedColumns
    [ ("petal_length", D.fromList ([1.4, 1.3, 1.5, 1.4, 4.5, 4.7, 4.6, 4.4, 5.5, 5.8, 5.6, 5.7] :: [Double]))
    , ("petal_width",  D.fromList ([0.2, 0.2, 0.1, 0.3, 1.5, 1.4, 1.6, 1.3, 2.0, 2.1, 1.9, 2.2] :: [Double]))
    , ("species",      D.fromList ([0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2] :: [Double]))
    ]

tree = fit defaultTreeConfig (D.col @Double "species") flowers
putStrLn (D.prettyPrint (predict tree))

if petal_length .<=. 2.95 then 0.0 else if petal_length .<=. 5.1 then 1.0 else 2.0

Symbolic regression discovers a formula

Genetic programming searches for an expression that fits the data, and returns it as a dataframe Expr plus the accuracy/complexity Pareto front:

curve = D.fromNamedColumns
    [ ("x", D.fromList xs)
    , ("y", D.fromList [x * x + x | x <- xs])
    ]
  where xs = [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6] :: [Double]

sr = fit
        defaultSRConfig { srSeed = 3, srGenerations = 50, srPopSize = 300, srUnaryOps = [] }
        (D.col @Double "y") curve
putStrLn (D.prettyPrint (srBest sr) ++ "   (mse " ++ show (srBestMSE sr) ++ ")")

x + x * x (mse 0.0)

Deploy: applying an expression to a frame

Because the model is an Expr you can use derive to do inference.

D.columnNames (D.derive "prediction" (predict model) sales)

[“x”,“y”,“prediction”]

A model and its preprocessing compose by substitution

Preprocessing is an expression too, so a model trained in a transformed space and the transform that produced it compose. Composition of expressions is substitution of one into the other. compileThrough performs that composition, folding a fitted transform into a prediction so the result is a single formula over the raw inputs. Below we standardize x, fit in the scaled space, then fold the scaler back in to recover a raw-column model:

scaler      = standardScaler ["x"] sales
scaledSales = applyTransform (scalerTransform scaler) sales
scaledModel = fit defaultLinearConfig (D.col @Double "y") scaledSales

deployed = compileThrough (scalerTransform scaler) (predict scaledModel)
putStr (unlines
    [ "trained in scaled space: " ++ D.prettyPrint (predict scaledModel)
    , "folded to raw columns:   " ++ D.prettyPrint deployed ])

trained in scaled space: 3.4156502553198655 * x + 8.0 folded to raw columns: 3.4156502553198655 * (x - 3.5) / 1.707825127659933 + 8.0

The folded expression is a function of the raw x alone, so it scores the original frame with no preprocessing step at inference time.

evaluate rmse deployed (D.col @Double "y") sales

3.6259732146947156e-16

Splitting the data, and evaluation

import qualified DataFrame as D

realistic = D.fromNamedColumns
    [ ("id", D.fromList [fromIntegral ((i * 7919) `mod` 97) | i <- [1 .. 40 :: Int]])
    , ("x",  D.fromList xs)
    , ("y",  D.fromList [2 * x + 1 + noise i | (i, x) <- zip [0 :: Int ..] xs])
    ]
  where
    xs      = map fromIntegral [1 .. 40 :: Int] :: [Double]
    noise i = fromIntegral ((i * 2654435761 + 12345) `mod` 1000) / 100 - 5

clean = D.select ["x", "y"] realistic

Hold-out evaluation. randomSplit (seeded, deterministic) keeps the score honest — evaluate on rows the model never saw, and the metrics are realistic, not the 1e-15 of an in-sample toy:

import System.Random (mkStdGen)

(train, test) = D.randomSplit (mkStdGen 7) 0.75 clean
heldModel     = fit defaultLinearConfig (D.col @Double "y") train
putStr (unlines
    [ "held-out R^2:  " ++ show (evaluate r2   (predict heldModel) (D.col @Double "y") test)
    , "held-out RMSE: " ++ show (evaluate rmse (predict heldModel) (D.col @Double "y") test) ])

held-out R^2: 0.9671190074242891 held-out RMSE: 3.56674709632647

Cross-validation. crossValidate is scikit-learn’s cross_val_score: it fits on each training fold and scores the prediction expression on the held-out fold. You pass a train -> Expr closure, so it works with any model:

cv = crossValidate 5 0 rmse (D.col @Double "y")
         (\tr -> predict (fit defaultLinearConfig (D.col @Double "y") tr))
         clean
putStrLn ("5-fold RMSE: " ++ show (sum cv / fromIntegral (length cv)))

5-fold RMSE: 3.0325616706245713

gridSearch tunes hyperparameters the same way, over a list of configs.

Reporting metrics

Metrics are plain functions (rmse, mse, r2, accuracy, multiclass precision/recall/f1), and classificationReport bundles the common numbers with a scikit-learn-style layout (per-class precision/recall/F1/support plus macro/weighted averages):

clf = fit defaultLogisticConfig (D.col @Double "species") flowers
putStr (show (classificationReportExpr (predict clf) (D.col @Double "species") flowers))

class precision recall f1 support
0.0 1.0 1.0 1.0 4
1.0 1.0 1.0 1.0 4
2.0 1.0 1.0 1.0 4

accuracy = 1.0 macro f1 = 1.0 weighted f1 = 1.0

Pipelines compose as a monoid

A fitted preprocessing step is a Transform, and transforms compose with <>. applyTransform runs the whole pipeline; compileThrough folds it into a single expression over the raw columns for export:

features = ["petal_length", "petal_width"]
scalerF  = standardScaler features flowers
pca      = fit (PCAConfig (NComp 2) True) (map (D.col @Double) features) flowers
pipeline = scalerTransform scalerF <> pcaTransform pca

D.columnNames (applyTransform pipeline flowers)

[“petal_length”,“petal_width”,“species”,“pc1”,“pc2”]

Synthesize the feature you would have hand-engineered

DataFrame.Synthesis is automated feature engineering: a bottom-up enumerative search (with observational-equivalence pruning) for a small, interpretable expression over your columns that tracks the target. Here y is the interaction a * b, which a linear model on the raw columns cannot capture; synthesis discovers the term, and feeding it back as a column lifts the fit from mediocre to exact — still a formula you can read:

interactions = D.fromNamedColumns
    [ ("a", D.fromList as)
    , ("b", D.fromList bs)
    , ("y", D.fromList (zipWith (*) as bs))
    ]
  where
    as = [-1, -1, 1, 1, -2, 2, -2, 2] :: [Double]
    bs = [-1, 1, -1, 1, -2, -2, 2, 2] :: [Double]

rawModel = fit defaultLinearConfig (D.col @Double "y") interactions
feature  = fit defaultSynthesisConfig (D.col @Double "y") interactions
withFeat = D.derive "synth" (predict feature) interactions
fitModel =
    fit defaultLinearConfig (D.col @Double "y")
        (D.select ["synth", "y"] withFeat)

putStr (unlines
    [ "discovered feature: " ++ D.prettyPrint (predict feature)
    , "raw linear R^2:     " ++ show (evaluate r2 (predict rawModel) (D.col @Double "y") interactions)
    , "with synth feature: " ++ show (evaluate r2 (predict fitModel) (D.col @Double "y") withFeat)
    ])

discovered feature: a * b raw linear R^2: 0.0 with synth feature: 1.0

predict feature is the single best expression; sfFeatures feature is the whole ranked, deduplicated bank, ready to derive as a batch of candidate columns.