The PredictorMV trait provides a framwork for multiple predictive analytics techniques, e.g., Multi-variate Regression and Neural Netoworks. x is multi-dimensional [1, x_1, ... x_k] and so is y. Fit the NetParam parameters bb in for example the regression equation y = f(bb dot x) + e bb is an array of NetParam where each component is a weight matrix and a bias vector.
Value parameters
- fname
-
the feature/variable names (if null, use x_j's)
- hparam
-
the hyper-parameters for the model/network
- x
-
the input/data m-by-n matrix (augment with a first column of ones to include intercept in model or use bias)
- y
-
the response/output m-by-ny matrix
Attributes
- See also
-
NetParam - Companion
- object
- Graph
-
- Supertypes
- Known subtypes
-
class CNN_1Dclass NeuralNet_2Lclass NeuralNet_3Lclass NeuralNet_XLclass NeuralNet_XLTclass RegressionMVclass RidgeRegressionMVShow all
Members list
Value members
Abstract methods
Build a sub-model that is restricted to the given columns of the data matrix. Override for models that support feature section.
Build a sub-model that is restricted to the given columns of the data matrix. Override for models that support feature section.
Value parameters
- fname2
-
the variable/feature names for the new model (defaults to null)
- x_cols
-
the columns that the new model is restricted to
Attributes
Predict the value of y = f(z) by evaluating the formula y = b dot z, e.g., (b_0, b_1, b_2) dot (1, z_1, z_2). Must override when using transformations, e.g., ExpRegression.
Predict the value of y = f(z) by evaluating the formula y = b dot z, e.g., (b_0, b_1, b_2) dot (1, z_1, z_2). Must override when using transformations, e.g., ExpRegression.
Value parameters
- z
-
the new vector to predict
Attributes
Test the predictive model y_ = f(x_) + e and return its predictions and QoF matrix. Each variable predictions and QoF values are returned in columns of respective matrices. Testing may be in-sample (on the full dataset) or out-of-sample (on the testing set) as determined by the parameters passed in. Note: must call train before test.
Test the predictive model y_ = f(x_) + e and return its predictions and QoF matrix. Each variable predictions and QoF values are returned in columns of respective matrices. Testing may be in-sample (on the full dataset) or out-of-sample (on the testing set) as determined by the parameters passed in. Note: must call train before test.
Value parameters
- x_
-
the testing/full data/input matrix (defaults to full x)
- y_
-
the testing/full response/output matrix (defaults to full y)
Attributes
Train a predictive model y_ = f(x_) + e where x_ is the data/input matrix and y_ is the response/output matrix. These arguments default to the full dataset x and y, but may be restricted to a training dataset. Training involves estimating the model parameters bb.
Train a predictive model y_ = f(x_) + e where x_ is the data/input matrix and y_ is the response/output matrix. These arguments default to the full dataset x and y, but may be restricted to a training dataset. Training involves estimating the model parameters bb.
Value parameters
- x_
-
the training/full data/input matrix (defaults to full x)
- y_
-
the training/full response/output matrix (defaults to full y)
Attributes
Concrete methods
Perform backward elimination to find the least predictive variable to remove from the existing model, returning the variable to eliminate, the new parameter matrix and the new Quality of Fit (QoF). May be called repeatedly.
Perform backward elimination to find the least predictive variable to remove from the existing model, returning the variable to eliminate, the new parameter matrix and the new Quality of Fit (QoF). May be called repeatedly.
Value parameters
- cols
-
the columns of matrix x currently included in the existing model
- first
-
first variable to consider for elimination (default (1) assume intercept x_0 will be in any model)
- qk
-
index of Quality of Fit (QoF) to use for comparing quality
Attributes
- See also
-
Fitfor index of QoF measures.
Perform BACKWARD ELIMINATION to find the LEAST predictive variables to remove from the full model, returning the variables left and the new Quality of Fit (QoF) measures for all steps.
Perform BACKWARD ELIMINATION to find the LEAST predictive variables to remove from the full model, returning the variables left and the new Quality of Fit (QoF) measures for all steps.
Value parameters
- cross
-
indicator to include the cross-validation/validation QoF measure (defaults to "many")
- first
-
first variable to consider for elimination
- qk
-
index of Quality of Fit (QoF) to use for comparing quality
Attributes
- See also
-
Fitfor index of QoF measures.
Perform BEAM SEARCH SELECTION to find a GOOD COMBINATION of predictive features/variables to have in the model, returning the top k sets of features/variables selected and the new Quality of Fit (QoF) measures/metrics for all steps. At each step, iterate over the models in the beam (top k) and create candidates by adding features (phase 1) and then removing (phase 2). From all the candidates, keep the best k and start a new iteration. Stops when there is no improvement in any of top k (or the maximum number of features is reached.
Perform BEAM SEARCH SELECTION to find a GOOD COMBINATION of predictive features/variables to have in the model, returning the top k sets of features/variables selected and the new Quality of Fit (QoF) measures/metrics for all steps. At each step, iterate over the models in the beam (top k) and create candidates by adding features (phase 1) and then removing (phase 2). From all the candidates, keep the best k and start a new iteration. Stops when there is no improvement in any of top k (or the maximum number of features is reached.
Value parameters
- bk
-
the beam width holding the top k models (defaults to 3)
- cross
-
indicator to include the cross-validation/validation QoF measure (defaults to "many")
- qk
-
index of Quality of Fit (QoF) to use for comparing quality
Attributes
- See also
-
Fitfor index of QoF measures/metrics.
Convert QoF results into an array (of size 1) of Statistic for compatibility with the crossValidate method.
Convert QoF results into an array (of size 1) of Statistic for compatibility with the crossValidate method.
Value parameters
- qof
-
the Quality of Fit (QoF) results def qof2Stat (qof: MatrixD): Array [Statistic] = val stats = Fit.qofStatTable // create table for QoF measures if qof(QoF.sst.ordinal)(0) > 0.0 then // requires variation in test-set for q <- qof.indices do stats(q).tally (qof(q)(0)) // tally these QoF measures stats end qof2Stat
Attributes
Perform forward selection to find the most predictive variable to add the existing model, returning the variable to add and the new model. May be called repeatedly.
Perform forward selection to find the most predictive variable to add the existing model, returning the variable to add and the new model. May be called repeatedly.
Value parameters
- cols
-
the columns of matrix x currently included in the existing model
- qk
-
index of Quality of Fit (QoF) to use for comparing quality
Attributes
- See also
-
Fitfor index of QoF measures.
Perform FORWARD SELECTION to find the MOST predictive variables to have in the model, returning the variables added and the new Quality of Fit (QoF) measures for all steps.
Perform FORWARD SELECTION to find the MOST predictive variables to have in the model, returning the variables added and the new Quality of Fit (QoF) measures for all steps.
Value parameters
- cross
-
indicator to include the cross-validation/validation QoF measure (defaults to "many")
- qk
-
index of Quality of Fit (QoF) to use for comparing quality
Attributes
- See also
-
Fitfor index of QoF measures.
Return the best model found from feature selection.
Return the best model found from feature selection.
Attributes
Return the feature/variable names.
Return the feature/variable names.
Attributes
Return the used data matrix x. Mainly for derived classes where x is expanded from the given columns in x_.
Return the used data matrix x. Mainly for derived classes where x is expanded from the given columns in x_.
Attributes
Return the used response vector y (first colum in matrix).
Return the used response vector y (first colum in matrix).
Attributes
Return the used response matrix y. Mainly for derived classes where y is transformed.
Return the used response matrix y. Mainly for derived classes where y is transformed.
Attributes
- Definition Classes
Return the hyper-parameters.
Return the hyper-parameters.
Attributes
Perform In-Sample Testing, i.e., train and test on the full data set. Return the prediction and the Quality of Fit.
Perform In-Sample Testing, i.e., train and test on the full data set. Return the prediction and the Quality of Fit.
Value parameters
- showYp
-
whether to show the prediction vector
- skip
-
the number of initial data points to skip (due to insufficient information)
Attributes
Make plots for each output/response variable (column of matrix y). Must override if the response matrix is transformed or rescaled.
Make plots for each output/response variable (column of matrix y). Must override if the response matrix is transformed or rescaled.
Value parameters
- yp
-
the testing/full predicted response/output matrix (defaults to full y)
- yy
-
the testing/full actual response/output matrix (defaults to full y)
Attributes
Return the set of columns (numbers) for the features in this model.
Return the set of columns (numbers) for the features in this model.
Attributes
Return the number of terms/parameters in the model, e.g., b_0 + b_1 x_1 + b_2 x_2 has three terms.
Return the number of terms/parameters in the model, e.g., b_0 + b_1 x_1 + b_2 x_2 has three terms.
Attributes
Order vectors y_ and yp_ accroding to the ascending order of y_.
Order vectors y_ and yp_ accroding to the ascending order of y_.
Value parameters
- y_
-
the vector to order by (e.g., true response values)
- yp_
-
the vector to be order by y_ (e.g., predicted response values)
Attributes
Return only the first matrix of parameter/coefficient values.
Return only the first matrix of parameter/coefficient values.
Attributes
Return the array of network parameters (weight matrix, bias vector) bb.
Return the array of network parameters (weight matrix, bias vector) bb.
Attributes
Predict the value of vector y = f(x_, b), e.g., x_ * b for Regression.
Predict the value of vector y = f(x_, b), e.g., x_ * b for Regression.
Value parameters
- x_
-
the matrix to use for making predictions, one for each row
Attributes
Return a basic report on a trained and tested multi-variate model.
Return a basic report on a trained and tested multi-variate model.
Value parameters
- ftMat
-
the matrix of qof values produced by the
Fittrait
Attributes
- Definition Classes
Reset the best-step to default
Reset the best-step to default
Attributes
Return the matrix of residuals/errors.
Return the matrix of residuals/errors.
Attributes
Perform STEPWISE SELECTION to find a GOOD COMBINATION of predictive variables to have in the model, returning the variables selected and the new Quality of Fit (QoF) measures for all steps. At each step it calls 'forwardSel' and 'backwardElim' and takes the best of the two actions. Stops when neither action yields improvement.
Perform STEPWISE SELECTION to find a GOOD COMBINATION of predictive variables to have in the model, returning the variables selected and the new Quality of Fit (QoF) measures for all steps. At each step it calls 'forwardSel' and 'backwardElim' and takes the best of the two actions. Stops when neither action yields improvement.
Value parameters
- cross
-
indicator to include the cross-validation/validation QoF measure (defaults to "many")
- qk
-
index of Quality of Fit (QoF) to use for comparing quality
Attributes
- See also
-
Fitfor index of QoF measures.
Test/evaluate the model's Quality of Fit (QoF) and return the predictions and QoF vectors. This may include the importance of its parameters (e.g., if 0 is in a parameter's confidence interval, it is a candidate for removal from the model). Extending traits and classes should implement various diagnostics for the test and full (training + test) datasets.
Test/evaluate the model's Quality of Fit (QoF) and return the predictions and QoF vectors. This may include the importance of its parameters (e.g., if 0 is in a parameter's confidence interval, it is a candidate for removal from the model). Extending traits and classes should implement various diagnostics for the test and full (training + test) datasets.
Value parameters
- x_
-
the testing/full data/input matrix (impl. classes may default to x)
- y_
-
the testing/full response/output vector (impl. classes may default to y)
Attributes
Return the indices for the test-set.
Return the indices for the test-set.
Value parameters
- n_test
-
the size of test-set
- rando
-
whether to select indices randomly or in blocks
Attributes
- See also
-
scalation.mathstat.TnT_Split
Return the indices for the test-set for (1) RANDONLY or (3) LAST
Return the indices for the test-set for (1) RANDONLY or (3) LAST
Value parameters
- n_test
-
the size of test-set
- n_total
-
the size of full dataset
- rando
-
whether to select indices randomly or in blocks
Attributes
- See also
-
scalation.mathstat.TnT_Split
Train the model 'y_ = f(x_) + e' on a given dataset, by optimizing the model parameters in order to minimize error '||e||' or maximize log-likelihood 'll'.
Train the model 'y_ = f(x_) + e' on a given dataset, by optimizing the model parameters in order to minimize error '||e||' or maximize log-likelihood 'll'.
Value parameters
- x_
-
the training/full data/input matrix (impl. classes may default to x)
- y_
-
the training/full response/output vector (impl. classes may default to y)
Attributes
The train2 method should work like the train method, but should also optimize hyper-parameters (e.g., shrinkage or learning rate). Only implementing classes needing this capability should override this method.
The train2 method should work like the train method, but should also optimize hyper-parameters (e.g., shrinkage or learning rate). Only implementing classes needing this capability should override this method.
Value parameters
- x_
-
the training/full data/input matrix (defaults to full x)
- y_
-
the training/full response/output matrix (defaults to full y)
Attributes
Train and test the predictive model y_ = f(x_) + e and report its QoF and plot its predictions. FIX - currently must override if y is transformed, @see TranRegression
Train and test the predictive model y_ = f(x_) + e and report its QoF and plot its predictions. FIX - currently must override if y is transformed, @see TranRegression
Value parameters
- x_
-
the training/full data/input matrix (defaults to full x)
- xx
-
the testing/full data/input matrix (defaults to full x)
- y_
-
the training/full response/output matrix (defaults to full y)
- yy
-
the testing/full response/output matrix (defaults to full y)
Attributes
Train and test the predictive model y_ = f(x_) + e and report its QoF and plot its predictions. This version does auto-tuning. FIX - currently must override if y is transformed, @see TranRegression
Train and test the predictive model y_ = f(x_) + e and report its QoF and plot its predictions. This version does auto-tuning. FIX - currently must override if y is transformed, @see TranRegression
Value parameters
- x_
-
the training/full data/input matrix (defaults to full x)
- xx
-
the testing/full data/input matrix (defaults to full x)
- y_
-
the training/full response/output matrix (defaults to full y)
- yy
-
the testing/full response/output matrix (defaults to full y)
Attributes
Compute the Variance Inflation Factor (VIF) for each variable to test for multi-collinearity by regressing x_j against the rest of the variables. A VIF over 50 indicates that over 98% of the variance of x_j can be predicted from the other variables, so x_j may be a candidate for removal from the model. Note: override this method to use a superior regression technique.
Compute the Variance Inflation Factor (VIF) for each variable to test for multi-collinearity by regressing x_j against the rest of the variables. A VIF over 50 indicates that over 98% of the variance of x_j can be predicted from the other variables, so x_j may be a candidate for removal from the model. Note: override this method to use a superior regression technique.
Value parameters
- skip
-
the number of columns of x at the beginning to skip in computing VIF
Attributes
Inherited methods
Print the model prediction equation in readable form. Override per model.
Print the model prediction equation in readable form. Override per model.
Attributes
- Inherited from:
- Model
Print the model prediction equation in LaTex form. Override per model.
Print the model prediction equation in LaTex form. Override per model.
Attributes
- Inherited from:
- Model
Return the data matrix x concatenated with response vector y.
Get the model name.
Convert QoF results into an array (of size 1) of Statistic for compatibility with the crossValidate method.
Convert QoF results into an array (of size 1) of Statistic for compatibility with the crossValidate method.
Value parameters
- qof
-
the Quality of Fit (QoF) results
Attributes
- Inherited from:
- Model
Return a basic report on a trained and tested model.
Return a basic report on a trained and tested model.
Value parameters
- ftVec
-
the vector of qof values produced by the
Fittrait
Attributes
- Inherited from:
- Model
Screen the x-columns of matrix xy based on the two thresholds, returning the reduced matrix and the column indices/predictor variables selected.
Screen the x-columns of matrix xy based on the two thresholds, returning the reduced matrix and the column indices/predictor variables selected.
Value parameters
- dep
-
the variable/column dependency measure (defaults to correlation)
- thr1
-
the threshold used to compare the predictor x-columns to the y-column only want variables above some minimal dependency level
- thr2
-
the threshold used to compare the predictor x-columns with each other only want variables below some cut-off dependency/collinearity level
- xy
-
the [ x, y ] combined data-response matrix
Attributes
- Inherited from:
- Model
Perform feature selection to find the most predictive features/variables to have in the model, returning the features/variables added and the new Quality of Fit (QoF) measures/metrics for all steps.
Perform feature selection to find the most predictive features/variables to have in the model, returning the features/variables added and the new Quality of Fit (QoF) measures/metrics for all steps.
Value parameters
- cross
-
indicator to include the cross-validation/validation QoF measure (defaults to "many")
- first
-
first variable to consider for elimination (default (1) assume intercept x_0 will be in any model)
- qk
-
index of Quality of Fit (QoF) to use for comparing quality
- swap
-
whether to allow a swap step (swap out a feature for a new feature in one step)
- tech
-
the feature selection technique to apply
Attributes
- See also
-
Fitfor index of QoF measures/metrics. - Inherited from:
- FeatureSelection
Inherited fields
The optional reference to an ontological concept