Text.PhonotacticLearner.Util.Probability

Data structures and functions for counting and probability.

Counting

newtype Multicount

Monoid holding a list of integer counters which are summed independently

Constructors

MC

Fields

• unMC :: Vector Int

Instances

Eq Multicount

Methods

(==) :: Multicount -> Multicount -> Bool

(/=) :: Multicount -> Multicount -> Bool

Show Multicount

Methods

showsPrec :: Int -> Multicount -> ShowS

show :: Multicount -> String

showList :: [Multicount] -> ShowS

Monoid Multicount

Methods

mempty :: Multicount

mappend :: Multicount -> Multicount -> Multicount

mconcat :: [Multicount] -> Multicount

NFData Multicount

Methods

rnf :: Multicount -> ()

PackedDFA MulticountDFST Multicount

Methods

numStates :: Ix sigma => MulticountDFST sigma -> Int

psegBounds :: Ix sigma => MulticountDFST sigma -> (sigma, sigma)

unpackDFA :: Ix sigma => MulticountDFST sigma -> DFST Int sigma Multicount

packDFA :: Ix sigma => Int16 -> Int16 -> (sigma, sigma) -> ((Int16, sigma) -> Int16) -> ((Int16, sigma) -> Multicount) -> (Int16 -> Multicount) -> MulticountDFST sigma

getCounts :: Multicount -> [Int]

Return the counts as a list of Ints

consMC :: Sum Int -> Multicount -> Multicount

Add a new count to the head of the list

singleMC :: Sum Int -> Multicount

Use a single coutner as a Multicount.

fromMC :: Multicount -> Vec

Convert the counts to coordinates

Expectations

data Expectation v

Expectation semiring as described by Eisner.

Represents an events contribution to the total expectation of a vector-valued variable. Addition takes the union of mutually exclusive events and multiplication either takes the intersection fo independent events or applies a conditional probability.

As a simple example, the expectation of the total value from rolling a 2 on a 6 sided die would be Exp (16) (26).

Constructors

Exp

Fields

• prob :: !Double

  Probability of event occuring.

• exps :: !v

  Event's contribution to expectation of the variable

Instances

PackedDFA ExpDoubleDFST (Expectation Double)

Methods

numStates :: Ix sigma => ExpDoubleDFST sigma -> Int

psegBounds :: Ix sigma => ExpDoubleDFST sigma -> (sigma, sigma)

unpackDFA :: Ix sigma => ExpDoubleDFST sigma -> DFST Int sigma (Expectation Double)

packDFA :: Ix sigma => Int16 -> Int16 -> (sigma, sigma) -> ((Int16, sigma) -> Int16) -> ((Int16, sigma) -> Expectation Double) -> (Int16 -> Expectation Double) -> ExpDoubleDFST sigma

PackedDFA ExpVecDFST (Expectation Vec)

Methods

numStates :: Ix sigma => ExpVecDFST sigma -> Int

psegBounds :: Ix sigma => ExpVecDFST sigma -> (sigma, sigma)

unpackDFA :: Ix sigma => ExpVecDFST sigma -> DFST Int sigma (Expectation Vec)

packDFA :: Ix sigma => Int16 -> Int16 -> (sigma, sigma) -> ((Int16, sigma) -> Int16) -> ((Int16, sigma) -> Expectation Vec) -> (Int16 -> Expectation Vec) -> ExpVecDFST sigma

Eq v => Eq (Expectation v)

Methods

(==) :: Expectation v -> Expectation v -> Bool

(/=) :: Expectation v -> Expectation v -> Bool

Show v => Show (Expectation v)

Methods

showsPrec :: Int -> Expectation v -> ShowS

show :: Expectation v -> String

showList :: [Expectation v] -> ShowS

RingModule Double v => Semiring (Expectation v)

Methods

one :: Expectation v

(⊗) :: Expectation v -> Expectation v -> Expectation v

RingModule Double v => Additive (Expectation v)

Methods

zero :: Expectation v

(⊕) :: Expectation v -> Expectation v -> Expectation v

normalizeExp :: RingModule Double v => Expectation v -> v

Get the expectation conditional on the event actually occurring.

Sampling and Distributions

data Cdf a

Cumulative distribution table that can be sampled easily.

Instances

Show a => Show (Cdf a)

Methods

showsPrec :: Int -> Cdf a -> ShowS

show :: Cdf a -> String

showList :: [Cdf a] -> ShowS

massToCdf :: [(a, Double)] -> Cdf a

Generate a CDF which from a list of outcomes and their relative probabilities (their sum will eb normalized and does not have to be 1).

sampleCdf :: (RandomGen g, MonadState g m) => Cdf a -> m a

Sample a random variable according to a Cdf, gets the random generator state from the monad.

uniformSample :: Cdf a -> Int -> [(a, Int)]

Deterministically sample n points spaced throughout the distribution. Used when the number of samples greatly outnumbers the number of outcomes.

upperConfidenceOE :: Double -> Double -> Double

Get the upper confidence bound of Observed/Expected