class LogisticRegression extends ClassifierReal
The LogisticRegression
class supports (binomial) logistic regression. In this
case, 'x' may be multi-dimensional '[1, x_1, ... x_k]'. Fit the parameter
vector 'b' in the logistic regression equation
logit (p_y) = b dot x + e = b_0 + b_1 * x_1 + ... b_k * x_k + 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
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- LogisticRegression
- ClassifierReal
- Classifier
- Model
- ConfusionFit
- Error
- QoF
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Instance Constructors
- new LogisticRegression(x: MatriD, y: VectoI, fn_: Strings = null, cn_: Strings = null, hparam: HyperParameter = Classifier.hp)
- 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
- hparam
the hyper-parameters
Value Members
- final def !=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- final def ##: Int
- Definition Classes
- AnyRef → Any
- final def ==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- def accuracy: Double
Compute the accuracy of the classification, i.e., the fraction of correct classifications.
Compute the accuracy of the classification, i.e., the fraction of correct classifications. Note, the correct classifications 'tp_i' are in the main diagonal of the confusion matrix.
- Definition Classes
- ConfusionFit
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- def backwardElim(cols: Set[Int], adjusted: Boolean = true): (Int, VectoD, VectoD)
Perform backward elimination to remove the least predictive variable from the existing model, returning the variable to eliminate, the new parameter vector and the new quality of fit.
Perform backward elimination to remove the least predictive variable from the existing model, returning the variable to eliminate, the new parameter vector and the new quality of fit. May be called repeatedly. FIX - use cols parameter
- cols
the columns of matrix x included in the existing model
- 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
- 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
- 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
- LogisticRegression → Classifier
- def classify(xx: MatriD = x): 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 (defaults to x)
- Definition Classes
- ClassifierReal
- 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
- ClassifierReal → Classifier
- def clearConfusion(): Unit
Clear the total cummulative confusion matrix.
Clear the total cummulative confusion matrix.
- Definition Classes
- ConfusionFit
- def clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
- var cn: Strings
- Attributes
- protected
- Definition Classes
- ClassifierReal
- def confusion(yp: VectoI, yy: VectoI = y): MatriI
Compare the actual class 'y' vector versus the predicted class 'yp' vector, returning the confusion matrix 'cmat', which for 'k = 2' is
Compare the actual class 'y' vector versus the predicted class 'yp' vector, returning the confusion matrix 'cmat', which for 'k = 2' is
yp 0 1 ---------- y 0 | tn fp | 1 | fn tp | ----------
Note: ScalaTion's confusion matrix is Actual × Predicted, but to swap the position of actual 'y' (rows) with predicted 'yp' (columns) simply use 'cmat.t', the transpose of 'cmat'.
- yp
the precicted class values/labels
- yy
the actual class values/labels for full (y) or test (y_e) dataset
- Definition Classes
- ConfusionFit
- See also
www.dataschool.io/simple-guide-to-confusion-matrix-terminology
- def contrast(yp: VectoI, yy: VectoI = y): Unit
Contract the actual class 'yy' vector versus the predicted class 'yp' vector.
Contract the actual class 'yy' vector versus the predicted class 'yp' vector.
- yp
the predicted class values/labels
- yy
the actual class values/labels for full (y) or test (y_e) dataset
- Definition Classes
- ConfusionFit
- def crossValidate(nx: Int = 10, show: Boolean = false): Array[Statistic]
Test the accuracy of the classified results by cross-validation, returning the Quality of Fit (QoF) measures such as accuracy.
Test the accuracy of the classified results by cross-validation, returning the Quality of Fit (QoF) measures such as accuracy. This method slices out instances/rows to form the test dataset.
- nx
number of folds/crosses and cross-validations (defaults to 10x).
- show
the show flag (show result from each iteration)
- Definition Classes
- ClassifierReal → Classifier
- def crossValidateRand(nx: Int = 10, show: Boolean = false): Array[Statistic]
Test the accuracy of the classified results by cross-validation, returning the Quality of Fit (QoF) measures such as accuracy.
Test the accuracy of the classified results by cross-validation, returning the Quality of Fit (QoF) measures such as accuracy. This method randomizes the instances/rows selected for the test dataset.
- nx
number of folds/crosses and cross-validations (defaults to 10x).
- show
the show flag (show result from each iteration)
- Definition Classes
- ClassifierReal → Classifier
- def diagnose(e: VectoD, yy: VectoD, yp: VectoD, w: VectoD = null, ym: Double = noDouble): Unit
Diagnose the health of the model by computing the Quality of Fit (QoF) measures, from the error/residual vector and the predicted & actual responses.
Diagnose the health of the model by computing the Quality of Fit (QoF) measures, from the error/residual vector and the predicted & actual responses. For some models the instances may be weighted.
- e
the m-dimensional error/residual vector (yy - yp)
- yy
the actual response vector to use (test/full)
- yp
the predicted response vector (test/full)
- w
the weights on the instances (defaults to null)
- ym
the mean of the actual response vector to use (test/full)
- Definition Classes
- ConfusionFit → QoF
- See also
Regression_WLS
- final def eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def equals(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef → Any
- def eval(xx: MatriD, yy: VectoD = null): ClassifierReal
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.
- xx
the integer-valued test vectors stored as rows of a matrix
- yy
the classification vector (impl. classes should ignore or default yy to y)
- Definition Classes
- ClassifierReal → Model
- def f1_measure(p: Double, r: Double): Double
Compute the F1-measure, i.e., the harmonic mean of the precision and recall.
Compute the F1-measure, i.e., the harmonic mean of the precision and recall.
- p
the precision
- r
the recall
- Definition Classes
- ConfusionFit
- def f1v: VectoD
Compute the micro-F1-measure vector, i.e., the harmonic mean of the precision and recall.
Compute the micro-F1-measure vector, i.e., the harmonic mean of the precision and recall.
- Definition Classes
- ConfusionFit
- def f_(z: Double): String
Format a double value.
- 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
- def fit: VectoD
Return the quality of fit.
Return the quality of fit. Assumes both 'train_null' and 'train' have already been called.
- Definition Classes
- LogisticRegression → ConfusionFit → QoF
- def fitLabel: Seq[String]
Return the labels for the fit.
Return the labels for the fit. Override when necessary.
- Definition Classes
- LogisticRegression → ConfusionFit → QoF
- def fitLabel_v: Seq[String]
Return the labels for the Quality of Fit (QoF) measures.
Return the labels for the Quality of Fit (QoF) measures. Override to add additional QoF measures.
- Definition Classes
- ConfusionFit
- def fitMap: Map[String, String]
Build a map of quality of fit measures (use of
LinkedHashMap
makes it ordered).Build a map of quality of fit measures (use of
LinkedHashMap
makes it ordered).- Definition Classes
- QoF
- def fitMicroMap: Map[String, VectoD]
Return the Quality of Fit (QoF) vector micor-measures, i.e., measures for each class.
Return the Quality of Fit (QoF) vector micor-measures, i.e., measures for each class.
- Definition Classes
- ConfusionFit
- final def flaw(method: String, message: String): Unit
- Definition Classes
- Error
- var fn: Strings
- Attributes
- protected
- Definition Classes
- ClassifierReal
- def forwardSel(cols: Set[Int], adjusted: Boolean = true): (Int, VectoD, VectoD)
Perform forward selection to add the most predictive variable to the existing model, returning the variable to add, the new parameter vector and the new quality of fit.
Perform forward selection to add the most predictive variable to the existing model, returning the variable to add, the new parameter vector and the new quality of fit. May be called repeatedly. FIX - implement method
- cols
the columns of matrix x included in the existing model
- val fset: Array[Boolean]
the set of features to turn on or off.
the set of features to turn on or off. All features are on by default. Used for feature selection.
- Attributes
- protected
- Definition Classes
- ClassifierReal
- final def getClass(): Class[_ <: AnyRef]
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- def hashCode(): Int
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- def help: String
Return the help string describing the Quality of Fit (QoF) measues.
Return the help string describing the Quality of Fit (QoF) measues. Override when necessary.
- Definition Classes
- LogisticRegression → ConfusionFit → QoF
- def hparameter: HyperParameter
Return the model hyper-parameters (if none, return null).
Return the model hyper-parameters (if none, return null). Hyper-parameters may be used to regularize parameters or tune the optimizer.
- Definition Classes
- ClassifierReal → Model
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- def kappa: Double
Compute Cohen's 'kappa' coefficient that measures agreement between actual 'y' and predicted 'yp' classifications.
Compute Cohen's 'kappa' coefficient that measures agreement between actual 'y' and predicted 'yp' classifications.
- Definition Classes
- ConfusionFit
- See also
en.wikipedia.org/wiki/Cohen%27s_kappa
- 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.stat.cmu.edu/~cshalizi/350/lectures/26/lecture-26.pdf
www.statisticalhorizons.com/wp-content/uploads/Allison.StatComp.pdf
- 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.stat.cmu.edu/~cshalizi/350/lectures/26/lecture-26.pdf
www.statisticalhorizons.com/wp-content/uploads/Allison.StatComp.pdf
- val m: Int
the number of data vectors in training-set (# rows)
the number of data vectors in training-set (# rows)
- Attributes
- protected
- Definition Classes
- ClassifierReal
- val md: Double
the training-set size as a Double
the training-set size as a Double
- Attributes
- protected
- Definition Classes
- ClassifierReal
- val modelConcept: URI
An optional reference to an ontological concept
An optional reference to an ontological concept
- Definition Classes
- Model
- def modelName: String
An optional name for the model (or modeling technique)
An optional name for the model (or modeling technique)
- Definition Classes
- Model
- val n: Int
the number of features/variables (# columns)
the number of features/variables (# columns)
- Attributes
- protected
- Definition Classes
- ClassifierReal
- val nd: Double
the feature-set size as a Double
the feature-set size as a Double
- Attributes
- protected
- Definition Classes
- ClassifierReal
- final def ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- final def notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- final def notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- def p_r_s(): Unit
Compute the micro-precision, micro-recall and micro-specificity vectors which have elements for each class i in {0, 1, ...
Compute the micro-precision, micro-recall and micro-specificity vectors which have elements for each class i in {0, 1, ... k-1}. -------------------------------------------------------------------------- Precision is the fraction classified as true that are actually true. Recall (sensitivity) is the fraction of the actually true that are classified as true. Specificity is the fraction of the actually false that are classified as false. -------------------------------------------------------------------------- Note, for 'k = 2', ordinary precision 'p', recall 'r' and specificity 's' will correspond to the last elements in the 'pv', 'rv' and 'sv' micro vectors.
- Definition Classes
- ConfusionFit
- def parameter: VectoD
Return the vector of coefficient/parameter values.
Return the vector of coefficient/parameter values.
- Definition Classes
- LogisticRegression → Model
- def pseudo_rSq: Double
Compute McFaffen's pseudo R-squared.
Compute McFaffen's pseudo R-squared.
- Definition Classes
- LogisticRegression → ConfusionFit
- def report: String
Return a basic report on the trained model.
Return a basic report on the trained model.
- Definition Classes
- ClassifierReal → Model
- 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
- LogisticRegression → Classifier
- def setStream(str: Int = 0): Unit
Set the random number 'stream' to 'str'.
Set the random number 'stream' to 'str'. This is useful for testing purposes, since a fixed stream will follow the same sequence each time.
- str
the new fixed random number stream
- Definition Classes
- Classifier
- 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
- ClassifierReal → Classifier
- val stream: Int
the random number stream {0, 1, ..., 999} to be used
the random number stream {0, 1, ..., 999} to be used
- Attributes
- protected
- Definition Classes
- Classifier
- def summary(b: VectoD = null, show: Boolean = false): String
Produce a summary report with diagnostics and the overall quality of fit.
Produce a summary report with diagnostics and the overall quality of fit.
- b
the parameters of the model
- show
flag indicating whether to print the summary
- Definition Classes
- ConfusionFit
- final def synchronized[T0](arg0: => T0): T0
- Definition Classes
- AnyRef
- 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
- def test(itest: VectorI): 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
- ClassifierReal → Classifier
- 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
- def tn_fp_fn_tp(con: MatriI = cmat): (Double, Double, Double, Double)
Return the confusion matrix for 'k = 2' as a tuple (tn, fp, fn, tp).
Return the confusion matrix for 'k = 2' as a tuple (tn, fp, fn, tp).
- con
the confusion matrix (defaults to cmat)
- Definition Classes
- ConfusionFit
- def toString(): String
- Definition Classes
- AnyRef → Any
- def total_cmat(): MatriI
Return a copy of the total cummulative confusion matrix 'tcmat' and clear 'tcmat'.
Return a copy of the total cummulative confusion matrix 'tcmat' and clear 'tcmat'.
- Definition Classes
- ConfusionFit
- def train(itest: VectorI): LogisticRegression
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 the instances considered as testing data@param itestStart the indices of test test data
- Definition Classes
- LogisticRegression → Classifier
- See also
stats.stackexchange.com/questions/81000/calculate-coefficients-in-a-logistic-regression-with-r
en.wikipedia.org/wiki/Iteratively_reweighted_least_squares
- def train(xx: MatriD = null, yy: VectoD = null): 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.
- xx
the data/input matrix (impl. classes should ignore or default xx to x)
- yy
the response/classification vector (impl. classes should ignore or default yy to y)
- Definition Classes
- Classifier → Model
- 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
- 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.
- 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
- def vif: VectoD
Compute the Variance Inflation Factor (VIF) for each variable to test for multi-collinearity by regressing 'xj' against the rest of the variables.
Compute the Variance Inflation Factor (VIF) for each variable to test for multi-collinearity by regressing 'xj' against the rest of the variables. A VIF over 10 indicates that over 90% of the variance of 'xj' can be predicted from the other variables, so 'xj' is a candidate for removal from the model. FIX or remove
- final def wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
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- final def wait(arg0: Long): Unit
- Definition Classes
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- final def wait(): Unit
- Definition Classes
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Deprecated Value Members
- def finalize(): Unit
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