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
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.
