Packages

class SimpleLogisticRegression extends ClassifierReal

The SimpleLogisticRegression class supports (binomial) logistic regression. In this case, 'x' is two-dimensional '[1, x_1]'. Fit the parameter vector 'b' in the logistic regression equation

logit (p_y) = b dot x + e = b_0 + b_1 * x_1 + e

where 'e' represents the residuals (the part not explained by the model) and 'y' is now binary.

See also

see.stanford.edu/materials/lsoeldsee263/05-ls.pdf

Linear Supertypes
ClassifierReal, Error, Classifier, AnyRef, Any
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Instance Constructors

  1. new SimpleLogisticRegression(x: MatriD, y: VectoI, fn: Array[String] = Array ("one", "x1"), cn: Array[String] = Array ("no", "yes"))

    x

    the input/design matrix augmented with a first column of ones

    y

    the binary response vector, y_i in {0, 1}

    fn

    the names for all features/variables

    cn

    the names for both classes

Value Members

  1. def calcCorrelation: MatriD

    Calculate the correlation matrix for the feature vectors 'fea'.

    Calculate the correlation matrix for the feature vectors 'fea'. If the correlations are too high, the independence assumption may be dubious.

    Definition Classes
    ClassifierReal
  2. def calcCorrelation2(zrg: Range, xrg: Range): MatriD

    Calculate the correlation matrix for the feature vectors of Z (Level 3) and those of X (level 2).

    Calculate the correlation matrix for the feature vectors of Z (Level 3) and those of X (level 2). If the correlations are too high, the independence assumption may be dubious.

    zrg

    the range of Z-columns

    xrg

    the range of X-columns

    Definition Classes
    ClassifierReal
  3. def classify(z: VectoD): (Int, String, Double)

    Classify the value of 'y = f(z)' by evaluating the formula 'y = sigmoid (b dot z)'.

    Classify the value of 'y = f(z)' by evaluating the formula 'y = sigmoid (b dot z)'. Return the best class, its name and quality metric

    z

    the new vector to classify

    Definition Classes
    SimpleLogisticRegressionClassifier
  4. def classify(xx: MatriD): VectoI

    Classify all of the row vectors in matrix 'xx'.

    Classify all of the row vectors in matrix 'xx'.

    xx

    the row vectors to classify

    Definition Classes
    ClassifierReal
  5. def classify(z: VectoI): (Int, String, Double)

    Given a new discrete (integer-valued) data vector 'z', determine which class it belongs to, by first converting it to a vector of doubles.

    Given a new discrete (integer-valued) data vector 'z', determine which class it belongs to, by first converting it to a vector of doubles. Return the best class, its name and its relative probability

    z

    the vector to classify

    Definition Classes
    ClassifierRealClassifier
  6. def coefficient: VectoD

    Return the vector of coefficient/parameter values.

  7. def crossValidate(nx: Int = 10, show: Boolean = false): Double

    Test the accuracy of the classified results by cross-validation, returning the accuracy.

    Test the accuracy of the classified results by cross-validation, returning the accuracy. The "test data" starts at 'testStart' and ends at 'testEnd', the rest of the data is "training data'. FIX - should return a StatVector

    nx

    the number of crosses and cross-validations (defaults to 10x).

    show

    the show flag (show result from each iteration)

    Definition Classes
    Classifier
  8. def crossValidateRand(nx: Int = 10, show: Boolean = false): Double

    Test the accuracy of the classified results by cross-validation, returning the accuracy.

    Test the accuracy of the classified results by cross-validation, returning the accuracy. This version of cross-validation relies on "subtracting" frequencies from the previously stored global data to achieve efficiency. FIX - are the comments correct? FIX - should return a StatVector

    nx

    number of crosses and cross-validations (defaults to 10x).

    show

    the show flag (show result from each iteration)

    Definition Classes
    Classifier
  9. def featureSelection(TOL: Double = 0.01): Unit

    Perform feature selection on the classifier.

    Perform feature selection on the classifier. Use backward elimination technique, that is, remove the least significant feature, in terms of cross- validation accuracy, in each round.

    TOL

    tolerance indicating negligible accuracy loss when removing features

    Definition Classes
    ClassifierReal
  10. def fit(y: VectoI, yp: VectoI, k: Int = 2): VectoD

    Return the quality of fit.

    Return the quality of fit. Assumes both 'train_null' and 'train' have already been called.

    y

    the actual class labels

    yp

    the predicted class labels

    k

    the number of class labels

    Definition Classes
    SimpleLogisticRegressionClassifier
  11. def fitLabel: Seq[String]

    Return the labels for the fit.

    Return the labels for the fit. Override when necessary.

    Definition Classes
    SimpleLogisticRegressionClassifier
  12. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  13. val index_prSq: Int
  14. def ll(b: VectoD): Double

    For a given parameter vector 'b', compute '-2 * Log-Likelihood (-2l)'.

    For a given parameter vector 'b', compute '-2 * Log-Likelihood (-2l)'. '-2l' is the standard measure that follows a Chi-Square distribution.

    b

    the parameters to fit

    See also

    www.statisticalhorizons.com/wp-content/uploads/Allison.StatComp.pdf

    www.stat.cmu.edu/~cshalizi/350/lectures/26/lecture-26.pdf

  15. def ll_null(b: VectoD): Double

    For a given parameter vector 'b = [b(0)]', compute '-2 * Log-Likelihood (-2l)'.

    For a given parameter vector 'b = [b(0)]', compute '-2 * Log-Likelihood (-2l)'. '-2l' is the standard measure that follows a Chi-Square distribution.

    b

    the parameters to fit

    See also

    www.statisticalhorizons.com/wp-content/uploads/Allison.StatComp.pdf

    www.stat.cmu.edu/~cshalizi/350/lectures/26/lecture-26.pdf

  16. def reset(): Unit

    Reset or re-initialize the frequency tables and the probability tables.

    Reset or re-initialize the frequency tables and the probability tables.

    Definition Classes
    SimpleLogisticRegressionClassifier
  17. def size: Int

    Return the number of data vectors in training/test-set (# rows).

    Return the number of data vectors in training/test-set (# rows).

    Definition Classes
    ClassifierRealClassifier
  18. def test(xx: MatriD, yy: VectoI): Double

    Test the quality of the training with a test-set and return the fraction of correct classifications.

    Test the quality of the training with a test-set and return the fraction of correct classifications.

    xx

    the real-valued test vectors stored as rows of a matrix

    yy

    the test classification vector, where 'yy_i = class for row i of xx'

    Definition Classes
    ClassifierReal
  19. def test(itest: IndexedSeq[Int]): Double

    Test the quality of the training with a test-set and return the fraction of correct classifications.

    Test the quality of the training with a test-set and return the fraction of correct classifications.

    itest

    indices of the instances considered test data

    Definition Classes
    ClassifierRealClassifier
  20. def test(testStart: Int, testEnd: Int): Double

    Test the quality of the training with a test dataset and return the fraction of correct classifications.

    Test the quality of the training with a test dataset and return the fraction of correct classifications. Can be used when the dataset is randomized so that the testing/training part of a dataset corresponds to simple slices of vectors and matrices.

    testStart

    the beginning of test region (inclusive).

    testEnd

    the end of test region (exclusive).

    Definition Classes
    Classifier
  21. def train(itest: IndexedSeq[Int]): SimpleLogisticRegression

    For the full model, train the classifier by fitting the parameter vector (b-vector) in the logistic regression equation using maximum likelihood.

    For the full model, train the classifier by fitting the parameter vector (b-vector) in the logistic regression equation using maximum likelihood. Do this by minimizing '-2l'. FIX: Use improved BFGS implementation or IRWLS

    itest

    the indices of test data

    Definition Classes
    SimpleLogisticRegressionClassifier
    See also

    en.wikipedia.org/wiki/Iteratively_reweighted_least_squares

    stats.stackexchange.com/questions/81000/calculate-coefficients-in-a-logistic-regression-with-r

  22. def train(): Classifier

    Train the classifier by computing the probabilities from a training dataset of data vectors and their classifications.

    Train the classifier by computing the probabilities from a training dataset of data vectors and their classifications. Must be implemented in any extending class. Can be used when the whole dataset is used for training.

    Definition Classes
    Classifier
  23. def train(testStart: Int, testEnd: Int): Classifier

    Train the classifier by computing the probabilities from a training dataset of data vectors and their classifications.

    Train the classifier by computing the probabilities from a training dataset of data vectors and their classifications. Must be implemented in any extending class. Can be used when the dataset is randomized so that the training part of a dataset corresponds to simple slices of vectors and matrices.

    testStart

    starting index of test region (inclusive) used in cross-validation

    testEnd

    ending index of test region (exclusive) used in cross-validation

    Definition Classes
    Classifier
  24. def train_null(): Unit

    For the null model, train the classifier by fitting the parameter vector (b-vector) in the logistic regression equation using maximum likelihood.

    For the null model, train the classifier by fitting the parameter vector (b-vector) in the logistic regression equation using maximum likelihood. Do this by minimizing -2l.

  25. def vc_default: Array[Int]

    Return default values for binary input data (value count 'vc' set to 2).

    Return default values for binary input data (value count 'vc' set to 2). Also may be used for binning into two categories.

    Definition Classes
    ClassifierReal