Journal Article10.1198/106186008X285591
Complexity Penalized M-Estimation
TL;DR: Very fast algorithms for the exact computation of estimators for time series, based on complexity penalized log-likelihood or M-functions, to a wide range of functionals with morphological constraints, in particular to Potts or Blake–Zisserman functionals.
read more
Abstract: We present very fast algorithms for the exact computation of estimators for time series, based on complexity penalized log-likelihood or M-functions. The algorithms apply to a wide range of functionals with morphological constraints, in particular to Potts or Blake–Zisserman functionals. The latter are the discrete versions of the celebrated Mumford–Shah functionals. All such functionals contain model parameters. Our algorithms allow for optimization not only for each separate parameter, but even for all parameters simultaneously. This allows for the examination of the models in the sense of a family approach. The algorithms are accompanied by a series of illustrative examples from molecular biology.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Multiscale change point inference
TL;DR: A new estimator, the simultaneous multiscale change point estimator SMUCE, is introduced, which achieves the optimal detection rate of vanishing signals as n→∞, even for an unbounded number of change points.
423
Consistencies and rates of convergence of jump-penalized least squares estimators
TL;DR: In this paper, the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions are studied and it is shown that these estimators are in an adaptive sense rate optimal over certain classes of "approximation spaces."
Consistencies and rates of convergence of jump-penalized least squares estimators
TL;DR: In this article, the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions are studied, and it is shown that these estimators are in an adaptive sense rate optimal over certain classes of approximate spaces.
147
Jump-Sparse and Sparse Recovery Using Potts Functionals
TL;DR: A new optimization method is proposed which is based on dynamic programming and the alternating direction method of multipliers (ADMM) and yields very satisfactory jump-sparse and sparse reconstructions, respectively.
Joint image reconstruction and segmentation using the Potts model
TL;DR: A new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems is proposed and a suitable splitting into specific subproblems that can all be solved efficiently is derived.
References
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
Stuart Geman,Donald Geman +1 more
TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
•Book
A Distribution-Free Theory of Nonparametric Regression
László Györfi
- 16 Apr 2013
TL;DR: How to Construct Nonparametric Regression Estimates * Lower Bounds * Partitioning Estimates * Kernel Estimates * k-NN Estimates * Splitting the Sample * Cross Validation * Uniform Laws of Large Numbers
2.3K
•Book
Limit theorems in change-point analysis
Miklos Csorgo,Lajos Horváth +1 more
- 01 Jan 1997
TL;DR: The Likelihood Approach as discussed by the authors is a nonparametric method for estimating the likelihood of a given hypothesis in a linear model with respect to a given set of observations, i.e., dependent observations.