Learning

Machine learning utilities

A micro library containing the most common machine learning tools. Check also the mltool package https://hackage.haskell.org/package/mltool.

Datasets

data Dataset a b

A dataset representation for supervised learning

Constructors

Dataset

Fields

• _samples :: [a]
• _labels :: [b]
• toList :: [(a, b)]

fromList :: [(a, b)] -> Dataset a b

Create a Dataset from list of samples (first) and labels (second)

Principal components analysis

data PCA

Principal components analysis tools

Constructors

PCA

Fields

• _u :: Matrix Double

  Compression matrix U

• _compress :: Vector Double -> Matrix Double

  Compression function

• _decompress :: Matrix Double -> Vector Double

  Inverse to compression function

pca

Arguments

:: Int

Number of principal components to preserve

-> [Vector Double]

Analyzed data samples

-> PCA

Principal components analysis resulting in PCA tools

pca'

Arguments

:: [Vector Double]

Data samples

-> (Matrix Double, Vector Double)

Compute the covariance matrix sigma and return its eigenvectors u' and eigenvalues s

Supervised learning

type Teacher = Matrix Double

Teacher matrix

0 0 0 0 0
0 0 0 0 0
1 1 1 1 1 <- Desired class index is 2
0 0 0 0 0 <- Number of classes is 4
        ^
  5 repetitions

teacher

Arguments

:: Int

Number of classes (labels)

-> Int

Desired class index (starting from zero)

-> Int

Number of repeated columns in teacher matrix

-> Teacher

Create a binary Teacher matrix with ones row corresponding to the desired class index

newtype Classifier a

Classifier function that maps some network state with measurements as matrix columns and features as rows, into a categorical output.

Constructors

Classifier

Fields

• classify :: Matrix Double -> a

newtype Regressor

Regressor function that maps some feature matrix into a continuous multidimensional output. The feature matrix is expected to have columns corresponding to measurements (data points) and rows, features.

Constructors

Regressor

Fields

• predict :: Matrix Double -> Matrix Double

type Readout = Matrix Double

Linear readout (matrix)

learnClassifier

Arguments

:: (Storable a, Eq a)

=> Vector a

All possible outcomes (classes) list

-> Matrix Double

Network state (nonlinear response) where each matrix column corresponds to a measurement (data point) and each row corresponds to a feature

-> Matrix Double

Horizontally concatenated Teacher matrices where each row corresponds to a desired class

-> Either String (Classifier a)

Perform supervised learning (ridge regression) and create a linear Classifier function. The regression is run with regularization parameter μ = 1e-4.

learnRegressor

Arguments

:: Matrix Double

Feature matrix with data points (measurements) as colums and features as rows

-> Matrix Double

Desired outputs matrix corresponding to data point columns. In case of scalar (one-dimensional) prediction output, it should be a single row matrix.

-> Either String Regressor

Perform supervised learning (ridge regression) and create a linear Regressor function.

learn'

Arguments

:: Matrix Double

Network state (nonlinear response)

-> Matrix Double

Horizontally concatenated Teacher matrices

-> Maybe Readout

Create a linear Readout using the ridge regression. Similar to learnRegressor, but instead of a Regressor function a (already transposed) Readout matrix may be returned.

scores

Arguments

:: Readout

Readout matrix

-> Matrix Double

Network state

-> Vector Double

Evaluate the network state (nonlinear response) according to some Readout matrix. Used by classification strategies such as winnerTakesAll.

winnerTakesAll

Arguments

:: (Storable a, Eq a)

=> Readout

Readout matrix

-> Vector a

Vector of possible classes

-> Classifier a

Classifier

Winner-takes-all classification method

Evaluation

errorRate :: (Eq a, Fractional err) => [a] -> [a] -> err

Error rate in %, an error measure for classification tasks

>>> errorRate [1,2,3,4] [1,2,3,7]
25.0

errors :: Eq a => [(a, a)] -> [(a, a)]

Pairs of misclassified and correct values

>>> errors $ zip ['x','y','z'] ['x','b','a']
[('y','b'),('z','a')]

accuracy :: (Eq a, Fractional acc) => [a] -> [a] -> acc

Accuracy of classification, 100% - errorRate

>>> accuracy [1,2,3,4] [1,2,3,7]
75.0

nrmse

Arguments

:: (Storable a, Floating a)

=> Vector a

Target signal

-> Vector a

Predicted signal

-> a

NRMSE

Normalized root mean square error (NRMSE), one of the most common error measures for regression tasks