The HiddenMarkov classes provides Hidden Markov Models (HMM). An HMM model consists of a probability vector pi and probability matrices a and b. The discrete-time system is characterized by a hidden state x(t) and an observed symbol/value y(t) at time t, which may be viewed as a time series. pi(i) = P(x(t) = i) a(i, j) = P(x(t+1) = j | x(t) = i) b(i, k) = P(y(t) = k | x(t) = i) model (pi, a, b)
Value parameters
- a
-
the state transition probability matrix (n-by-n)
- b
-
the observation probability matrix (n-by-m)
- cname_
-
the class names for the states, e.g., ("Hot", "Cold")
- hparam
-
the hyper-parameters
- m
-
the number of observation symbols/values {0, 1, ... m-1}
- n
-
the number of (hidden) states in the model
- pi
-
the probabilty vector for the initial state
- y
-
the observation vector/observed discrete-valued time series
Attributes
- Companion
- object
- Graph
-
- Supertypes
Members list
Type members
Inherited classlikes
The BestStep is used to record the best improvement step found so far.
The BestStep is used to record the best improvement step found so far.
Value parameters
- col
-
the column/variable to ADD/REMOVE for this step
- mod
-
the model including selected features/variables for this step
- qof
-
the Quality of Fit (QoF) for this step
Attributes
- Inherited from:
- Classifier
- Supertypes
-
trait Serializabletrait Producttrait Equalsclass Objecttrait Matchableclass AnyShow all
Value members
Concrete methods
The beta-pass: a backward pass from time t = tt-1 to 0 that computes beta bet with scaling. Requires: alp the scaled alpha matrix c the vector of scaling factors
The beta-pass: a backward pass from time t = tt-1 to 0 that computes beta bet with scaling. Requires: alp the scaled alpha matrix c the vector of scaling factors
Attributes
The beta-pass: a backward pass from time t = tt-1 to 0 that computes beta bet.
The beta-pass: a backward pass from time t = tt-1 to 0 that computes beta bet.
Attributes
The alpha-pass: a forward pass from time t = 0 to tt-1 that computes alpha alp with scaling.
The alpha-pass: a forward pass from time t = 0 to tt-1 that computes alpha alp with scaling.
Attributes
The alpha-pass: a forward pass from time t = 0 to tt-1 that computes alpha alp.
The alpha-pass: a forward pass from time t = 0 to tt-1 that computes alpha alp.
Attributes
The gamma-pass: a forward pass from time t = 0 to tt-2 that computes gamma gam. Given the observation vector y, find the most probable sequence of states. Requires: alp the unscaled alpha matrix bet the unscaled beta matrix
The gamma-pass: a forward pass from time t = 0 to tt-2 that computes gamma gam. Given the observation vector y, find the most probable sequence of states. Requires: alp the unscaled alpha matrix bet the unscaled beta matrix
Attributes
Return the vector of scaling factors c.
Return the vector of scaling factors c.
Attributes
Compute the joint probability P(x, y).
Compute the joint probability P(x, y).
Value parameters
- x
-
the state vector
Attributes
Return the parameter vector pi.
Return the parameter matrices a and b.
Return the parameter matrices a and b.
Attributes
Given a new discrete data vector z, determine which class it belongs to, returning the best class, its name and its relative probability.
Given a new discrete data vector z, determine which class it belongs to, returning the best class, its name and its relative probability.
Value parameters
- z
-
the observation vector/time series to classify
Attributes
- Definition Classes
Re-estimate the probability vector pi and the probability matrices a and b. Requires: gam the gamma matrix gat the gamma tensor
Re-estimate the probability vector pi and the probability matrices a and b. Requires: gam the gamma matrix gat the gamma tensor
Attributes
Return the size of the (hidden) state space.
Return the size of the (hidden) state space.
Attributes
Test the predictive model y_ = f(x_) + e and return its predictions and QoF vector. 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 vector. 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 (ignored)
- y_
-
the testing/full response/output vector (defaults to full y)
Attributes
Train the Hidden Markov Model using the observation vector y to determine the model pi, a and b.
Train the Hidden Markov Model using the observation vector y to determine the model pi, a and b.
Value parameters
- x_
-
the training/full data/input matrix (ignored)
- y_
-
the training/full response/output vector (defaults to full y)
Attributes
- Definition Classes
The gamma-pass: a forward pass from time t = 0 to tt-2 that computes gamma gam and gat. Given the observation vector y, find the most probable sequence of states. Note: gat is computed as a side-effect. Requires: alp the scaled alpha matrix bet the scaled beta matrix
The gamma-pass: a forward pass from time t = 0 to tt-2 that computes gamma gam and gat. Given the observation vector y, find the most probable sequence of states. Note: gat is computed as a side-effect. Requires: alp the scaled alpha matrix bet the scaled beta matrix
Attributes
Inherited methods
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.
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.
Attributes
- Inherited from:
- FitC
Perform backward elimination to find the least predictive variable to remove from the existing model, returning the variable to eliminate, the new parameter vector 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 vector 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)
- idx_q
-
index of Quality of Fit (QoF) to use for comparing quality
Attributes
- See also
-
Fitfor index of QoF measures. - Inherited from:
- Classifier
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
-
whether to include the cross-validation QoF measure
- first
-
first variable to consider for elimination
- idx_q
-
index of Quality of Fit (QoF) to use for comparing quality
Attributes
- See also
-
Fitfor index of QoF measures. - Inherited from:
- Classifier
Build a sub-model that is restricted to the given columns of the data matrix. Override for models that support feature selection.
Build a sub-model that is restricted to the given columns of the data matrix. Override for models that support feature selection.
Value parameters
- x_cols
-
the columns that the new model is restricted to
Attributes
- Inherited from:
- Classifier
Given a continuous data vector z, classify it returning the class number (0, ..., k-1) with the highest relative posterior probability. Return the best class, its name and its relative probability.
Given a continuous data vector z, classify it returning the class number (0, ..., k-1) with the highest relative posterior probability. Return the best class, its name and its relative probability.
Value parameters
- z
-
the data vector to classify
Attributes
- Inherited from:
- Classifier
Given a discrete data vector z, classify it returning the class number (0, ..., k-1) with the highest relative posterior probability. Return the best class, its name and its relative probability.
Given a discrete data vector z, classify it returning the class number (0, ..., k-1) with the highest relative posterior probability. Return the best class, its name and its relative probability.
Value parameters
- z
-
the data vector to classify
Attributes
- Inherited from:
- Classifier
Clear the total cummulative confusion matrix.
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.transpose, the transpose of cmat.
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.transpose, the transpose of cmat.
Value parameters
- y_
-
the actual class values/labels for full (y) or test (y_e) dataset
- yp
-
the predicted class values/labels
Attributes
- See also
- Inherited from:
- FitC
Contract the actual class y_ vector versus the predicted class yp vector.
Contract the actual class y_ vector versus the predicted class yp vector.
Value parameters
- y_
-
the actual class values/labels for full (y) or test (y_e) dataset
- yp
-
the predicted class values/labels
Attributes
- Inherited from:
- FitC
Attributes
- Inherited from:
- Classifier
Diagnose the health of the model by computing the Quality of Fit (QoF) measures, from the error/residual vector and the predicted & actual responses. Requires the actual and predicted responses to be non-negative integers. Must override when there negative 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. Requires the actual and predicted responses to be non-negative integers. Must override when there negative responses.
Value parameters
- y_
-
the actual response/output vector to use (test/full)
- yp
-
the predicted response/output vector (test/full)
Attributes
- Inherited from:
- FitC
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.
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.
Value parameters
- w
-
the weights on the instances (defaults to null)
- y_
-
the actual response/output vector to use (test/full)
- yp
-
the predicted response/output vector (test/full)
Attributes
- Definition Classes
- Inherited from:
- FitC
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.
Value parameters
- p
-
the precision
- r
-
the recall
Attributes
- Inherited from:
- FitC
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.
Attributes
- Inherited from:
- FitC
Return the Quality of Fit (QoF) measures corresponding to the labels given above in the fitLabel method.
Return the Quality of Fit (QoF) measures corresponding to the labels given above in the fitLabel method.
Attributes
- Inherited from:
- FitC
Return the labels for the Quality of Fit (QoF) measures. Override to add additional QoF measures.
Return the labels for the Quality of Fit (QoF) measures. Override to add additional QoF measures.
Attributes
- Inherited from:
- FitC
Return the Quality of Fit (QoF) vector micro-measures, i.e., measures for each class.
Return the Quality of Fit (QoF) vector micro-measures, i.e., measures for each class.
Attributes
- Inherited from:
- FitC
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
- idx_q
-
index of Quality of Fit (QoF) to use for comparing quality
Attributes
- See also
-
Fitfor index of QoF measures. - Inherited from:
- Classifier
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
-
whether to include the cross-validation QoF measure
- idx_q
-
index of Quality of Fit (QoF) to use for comparing quality
Attributes
- See also
-
Fitfor index of QoF measures. - Inherited from:
- Classifier
Return the feature/variable names.
Return the used data matrix x. Mainly for derived classes where x is expanded from the given columns in x_, e.g., SymbolicRegression.quadratic adds squared columns.
Return the used data matrix x. Mainly for derived classes where x is expanded from the given columns in x_, e.g., SymbolicRegression.quadratic adds squared columns.
Attributes
- Inherited from:
- Classifier
Return the used response vector y. Mainly for derived classes where y is transformed, e.g., TranRegression, Regression4TS.
Return the used response vector y. Mainly for derived classes where y is transformed, e.g., TranRegression, Regression4TS.
Attributes
- Inherited from:
- Classifier
Return the help string that describes the Quality of Fit (QoF) measures provided by the FitC class. Override to correspond to fitLabel.
Return the help string that describes the Quality of Fit (QoF) measures provided by the FitC class. Override to correspond to fitLabel.
Attributes
- Inherited from:
- FitC
Return the hyper-parameters.
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.
Value parameters
- y_
-
the actual response/output vector to use (test/full)
- yp
-
the predicted response/output vector (test/full)
Attributes
- See also
-
en.wikipedia.org/wiki/Cohen%27s_kappa
- Inherited from:
- FitC
Given a continuous data vector z, classify it returning the class number (0, ..., k-1) with the highest relative posterior probability. Return the best class, its name and its relative log-probability. This method adds "positive log probabilities" to avoids underflow. To recover q relative probability compute 2^(-q) where q is a plog.
Given a continuous data vector z, classify it returning the class number (0, ..., k-1) with the highest relative posterior probability. Return the best class, its name and its relative log-probability. This method adds "positive log probabilities" to avoids underflow. To recover q relative probability compute 2^(-q) where q is a plog.
Value parameters
- z
-
the data vector to classify
Attributes
- Inherited from:
- Classifier
Given a discrete data vector z, classify it returning the class number (0, ..., k-1) with the highest relative posterior probability. Return the best class, its name and its relative log-probability. This method adds "positive log probabilities" to avoids underflow. To recover q relative probability compute 2^(-q) where q is a plog.
Given a discrete data vector z, classify it returning the class number (0, ..., k-1) with the highest relative posterior probability. Return the best class, its name and its relative log-probability. This method adds "positive log probabilities" to avoids underflow. To recover q relative probability compute 2^(-q) where q is a plog.
Value parameters
- z
-
the data vector to classify
Attributes
- Inherited from:
- Classifier
Attributes
- Inherited from:
- Classifier
Predict the integer value of y = f(z) by computing the product of the class probabilities p_y and all the conditional probabilities P(X_j = z_j | y = c) and returning the class with the highest relative probability. This method adds "positive log probabilities" to avoids underflow. To recover q relative probability compute 2^(-q) where q is a plog.
Predict the integer value of y = f(z) by computing the product of the class probabilities p_y and all the conditional probabilities P(X_j = z_j | y = c) and returning the class with the highest relative probability. This method adds "positive log probabilities" to avoids underflow. To recover q relative probability compute 2^(-q) where q is a plog.
Value parameters
- z
-
the new vector to predict
Attributes
- Inherited from:
- Classifier
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
- Inherited from:
- Classifier
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.
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.
Attributes
- Inherited from:
- FitC
Predict the value of y = f(z) by evaluating the model equation. Single output models return Double, while multi-output models return VectorD.
Predict the value of y = f(z) by evaluating the model equation. Single output models return Double, while multi-output models return VectorD.
Value parameters
- z
-
the new vector to predict
Attributes
- Inherited from:
- Classifier
Predict the value of vector y = f(x_) using matrix x_
Predict the value of vector y = f(x_) using matrix x_
Value parameters
- x_
-
the matrix to use for making predictions, one for each row
Attributes
- Inherited from:
- Classifier
Compute the Efron's pseudo R-squared value. Override to McFadden's, etc.
Compute the Efron's pseudo R-squared value. Override to McFadden's, etc.
Value parameters
- p1
-
the first parameter
- p2
-
the second parameter
Attributes
- Inherited from:
- FitC
Return the coefficient of determination (R^2). Must call diagnose first.
Return the coefficient of determination (R^2). Must call diagnose first.
Attributes
- Inherited from:
- FitM
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
FitCtrait
Attributes
- Definition Classes
-
Classifier -> Model
- Inherited from:
- Classifier
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
- Inherited from:
- Model
Return the vector of residuals/errors.
Perform feature 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 feature 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
-
whether to include the cross-validation QoF measure
- idx_q
-
index of Quality of Fit (QoF) to use for comparing quality
- tech
-
the feature selection technique to apply
Attributes
- See also
-
Fitfor index of QoF measures. - Inherited from:
- Classifier
Return the sum of the squares for error (sse). Must call diagnose first.
Return the sum of the squares for error (sse). Must call diagnose first.
Attributes
- Inherited from:
- FitM
Perform stepwise regression to find the most predictive variables to have in the model, returning the variables left 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 regression to find the most predictive variables to have in the model, returning the variables left 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
-
whether to include the cross-validation QoF measure
- idx_q
-
index of Quality of Fit (QoF) to use for comparing quality
Attributes
- See also
-
Fitfor index of QoF measures. - Inherited from:
- Classifier
Produce a summary report with diagnostics and the overall Quality of Fit (QoF). Classifier should override this method.
Produce a summary report with diagnostics and the overall Quality of Fit (QoF). Classifier should override this method.
Value parameters
- b
-
the parameters/pmf for the model
- fname
-
the array of feature/variable names
- vifs
-
the Variance Inflation Factors (VIFs)
- x_
-
the testing/full data/input matrix
Attributes
- Inherited from:
- FitC
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 classess 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 classess should implement various diagnostics for the test and full (training + test) datasets.
Value parameters
- x_
-
the testiing/full data/input matrix (impl. classes may default to x)
- y_
-
the testiing/full response/output vector (impl. classes may default to y)
Attributes
- Inherited from:
- Classifier
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 - Inherited from:
- Classifier
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).
Value parameters
- con
-
the confusion matrix (defaults to cmat)
Attributes
- Inherited from:
- FitC
Return a copy of the total cumulative confusion matrix tcmat and clear tcmat.
Return a copy of the total cumulative confusion matrix tcmat and clear tcmat.
Attributes
- Inherited from:
- FitC
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
- Inherited from:
- Classifier
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 vector (defaults to full y)
Attributes
- Inherited from:
- Classifier
Train and test the predictive model y_ = f(x_) + e and report its QoF and plot its predictions.
Train and test the predictive model y_ = f(x_) + e and report its QoF and plot its predictions.
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 vector (defaults to full y)
- yy
-
the testing/full response/output vector (defaults to full y)
Attributes
- Inherited from:
- Classifier
Attributes
- Inherited from:
- Classifier
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 from:
- Classifier
Inherited fields
The optional reference to an ontological concept