-- Logistic regression model from Anglican
-- (https://bitbucket.org/probprog/anglican-white-paper)

module LogReg where

import Control.Monad (replicateM)
import Control.Monad.Bayes.Class
import Numeric.Log

xs :: [Double]
xs = [-10, -5, 2, 6, 10]

labels :: [Bool]
labels = [False, False, True, True, True]

logisticRegression :: (MonadInfer m) => [(Double, Bool)] -> m Double
logisticRegression dat = do
  m <- normal 0 1
  b <- normal 0 1
  sigma <- gamma 1 1
  let y x = normal (m * x + b) sigma
      sigmoid x = y x >>= \t -> return $ 1 / (1 + exp (- t))
      obs x label = do
        p <- sigmoid x
        factor $ (Exp . log) $ if label then p else 1 - p
  mapM_ (uncurry obs) dat
  sigmoid 8

syntheticData :: MonadSample m => Int -> m [(Double, Bool)]
syntheticData n = replicateM n syntheticPoint
  where
    syntheticPoint = do
      x <- uniform (-1) 1
      label <- bernoulli 0.5
      return (x, label)