title: Slope Estimation in Noisy Piecewise Linear Functions.
abstract: This paper discusses the development of a slope estimation algorithm called MAPSlope for piecewise linear data that is corrupted by Gaussian noise. The number and locations of slope change points (also known as breakpoints) are assumed to be unknowna priorithough it is assumed that the possible range of slope values lies within known bounds. A stochastic hidden Markov model that is general enough to encompass real world sources of piecewise linear data is used to model the transitions between slope values and the problem of slope estimation is addressed using a Bayesian maximum a posteriori approach. The set of possible slope values is discretized, enabling the design of a dynamic programming algorithm for posterior density maximization. Numerical simulations are used to justify choice of a reasonable number of quantization levels and also to analyze mean squared error performance of the proposed algorithm. An alternating maximization algorithm is proposed for estimation of unknown model parameters and a convergence result for the method is provided. Finally, results using data from political science, finance and medical imaging applications are presented to demonstrate the practical utility of this procedure.
authors.affiliation: Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison WI 53706, USA. ; Department of Medical Physics, University of Wisconsin-Madison, Madison WI 53705, USA.
authors.forename: Atul
authors.initials: A
authors.lastname: Ingle
authors.affiliation: Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison WI 53706, USA.
authors.forename: James
authors.initials: J
authors.lastname: Bucklew
authors.affiliation: Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison WI 53706, USA.
authors.forename: William
authors.initials: W
authors.lastname: Sethares
authors.affiliation: Department of Medical Physics, University of Wisconsin-Madison, Madison WI 53705, USA. ; Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison WI 53706, USA.
authors.forename: Tomy
authors.initials: T
authors.lastname: Varghese
keywords: EM algorithm; MAP estimation; alternating maximization; dynamic programming optimization; piecewise linear function