Application of Piece-wise Regression to Detecting Internal Structure of Signal. Brailovsky, V. L. & Kempner, Y. Pattern Recognition, 25:1361--1370, Elsevier, 1992.
bibtex   
@Article{Brailovsky1992,
  author    = {Brailovsky, V. L. and Kempner, Y.},
  title     = {Application of Piece-wise Regression to Detecting Internal Structure of Signal},
  journal   = {Pattern Recognition},
  year      = {1992},
  volume    = {25},
  pages     = {1361--1370},
  groups    = {Lit Review 2013-09},
  publisher = {Elsevier},
  review    = {Observation is divided up into k regions. Each region is represented by a simple form (constant, linear, quadratic). Want to find k, the length of each region, and the appropriate singal. Given a fixed value for 'k', they use Bellman and Roth's piece-wise regression to calculate the best fit. But the problem is how to select this value k? We can usually guess a upperbound for k (and thus calculate k regressions, and thus getting k error values between the function and the obs), but selecting based on least error will automatically mean the highest possible k value is chosen, so this is not the best movie.

They use 'predictive probabilistic estimate' to select the best subset of regressors.

Set of value response function (SVRF), which is basically the observation plus some normally distrubited noise, and the regression calculated. -> can't really follow this section, but it seems to have nothing to do with the 'k' selection

There is no way this method can be used online...it seems like the solution is to calculate the regression for an array of k, calculate the error, and pick a reasonable one. -> yeah, doesn't look like online k calculations are done


Brailovsky and Kempner \cite{Brailovsky1992} employs piecewise regression, allowing the regression to fit both linear and quadratic equations. The main issue they examine is how to divide up the observation data, noting that simply using a distance error metric is insufficient as it will simply choose the highest number of segments to result in the smallest error, leading to over-fitting. Instead, a normally distributed perturbation is applied to observation data, and the sample estimate of fit (SEF) is calculated. This is performed several times, generating an array of SEFs, and the predictive probabilistic estimate, $PPE = Pr(\Delta_{perturb} \geq \Delta_{non-pertrubed}$ is calculated. The number of regions that results in the largest PPE is considered the best fit.},
  timestamp = {2013.10.06},
}
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