gradDesc_fixed_df: Gradient Descent with a fixed number of constant pieces...
In UMR: Unmatched Monotone Regression

Gradient Descent with a fixed number of constant pieces (degrees of freedom)

gradDesc_fixed_df(
  yy,
  grad,
  init = stats::median(yy),
  counts = length(yy),
  stepsize,
  MM,
  tol = 1e-07,
  printevery = Inf,
  filename
)

`yy`	Y (response) observation vector (numeric)
`grad`	a function(yy, mm) where mm may be shorter length than yy and is the previous iterate value (i.e., the estimate vector).
`init`	Initial value of estimate ('mm'). I.e., numeric vector of length <= length(mm). The output will be of length length(init).
`counts`	Vector of length length(init); each entry indicates how many values of yy the corresponding value of init (and output) corresponds to. Alternatively, can think of counts as a vector of weights for each estimator value.
`stepsize`	Gradient descent stepsize. Set carefully!
`MM`	Number of iterations in which "support reduction" (combining of approximately equal values into a region of constancy) is done (see details and paper). Depending on tol, may not use all MM iterations.
`tol`	Tolerance: end algorithm once sum(abs(mm-mmprev)) < tol or you hit MM iterations.
`printevery`	integer value (generally << MM). Every 'printevery' iterations, a count will be printed and the output saved.
`filename`	path1/path2/filename to save output to.

Prefer using UMRgradDesc_fixed_df now; this function deprecated.

xxxx Implements a gradient descent. See paper for details. Right now stepsize is fixed. Right now: init gets sorted in gradDesc_PC so does not need to be sorted on input. Roughly, the difference between this algorithm and gradDesc() (which is just vanilla gradient descent on this problem) is that: if mm is the current value of the output estimate, then gradDesc_PC 'collapses' or combines values of mm that are (roughly, up to tolerance 'eps') equal. Because the solution is generally piecewise constant with a relatively small number of constant regions this enormously speeds up the later stages of the algorithm. Note that once points are combined/collapsed they contribute identically to the objective function, so they will never be "uncombined".

UMR documentation built on Aug. 14, 2021, 9:09 a.m.