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