Elastic Functional Regression¶

These functions compute elastic standard, logistic, and m-logistic regression models. This code is experimental and results are not guaranteed

Regression Models and Prediction¶

elastic_regression(f, y, timet; B=None, lambda=0, df=20, max_itr=20, smooth=false)

Calculate elastic regression from function data f, for response y

• f array (M,N) of N functions
• y vector (N) of responses
• timet vector (N) describing time samples
• B matrix describing basis functions (M,N) (default=None generates a B-spline basis
• lambda regularization parameter
• df degree of freedom of basis
• max_itr maximum number of iterations
• smooth smooth data

Returns Dict describing regression:

• alpha intercept
• beta regression function
• fn aligned functions
• qn aligned srsfs
• gamma warping functions
• q original srsfs
• B basis functions
• type type of regression
• b coefficients
• SSE sum of squared error
elastic_logistic(f, y, timet; B=None, df=20, max_itr=20, smooth=false)

Calculate elastic logistic regression from function data f, for response y

• f array (M,N) of N functions
• y vector (N) of responses
• timet vector (N) describing time samples
• B matrix describing basis functions (M,N) (default=None generates a B-spline basis
• df degree of freedom of basis
• max_itr maximum number of iterations
• smooth smooth data

Returns Dict describing regression:

• alpha intercept
• beta regression function
• fn aligned functions
• qn aligned srsfs
• gamma warping functions
• q original srsfs
• B basis functions
• type type of regression
• b coefficients
• LL logistic loss
elastic_mlogistic(f, y, timet; B=None, df=20, max_itr=20, smooth=false)

Calculate elastic m-logistic regression from function data f, for response y

• ``f: array (M,N) of N functions
• ``y: vector (N) of responses
• ``timet: vector (N) describing time samples
• ``B: matrix describing basis functions (M,N) (default=None generates a B-spline basis
• ``df: degree of freedom of basis
• ``max_itr: maximum number of iterations
• ``smooth: smooth data

Returns Dict describing regression:

• alpha intercept
• beta regression function
• fn aligned functions
• qn aligned srsfs
• gamma warping functions
• q original srsfs
• B basis functions
• type type of regression
• b coefficients
• n_classes number of classes
• LL logistic loss
elastic_prediction(f, timet, model; y=None, smooth=false)

Prediction from elastic regression model

• f functions to predict
• timet vector describing time samples
• model calculated model (regression, logistic, mlogistic)
• y true responses (default = None)
• smooth smooth data (default = false)

Returns:

• y_pred predicted value
• y_labels labels of predicted value
• Perf Performance metric if truth is supplied