Maximum a posteriori estimation

About: Maximum a posteriori estimation is a research topic. Over the lifetime, 7486 publications have been published within this topic receiving 222291 citations. The topic is also known as: Maximum a posteriori, MAP & maximum a posteriori probability.

Preconditioned Alternating Projection Algorithms for Maximum a Posteriori ECT Reconstruction

Abstract: We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constrain involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the preconditioned alternating projection algorithm. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality.

An Entropic Estimator for Structure Discovery

Abstract: We introduce a novel framework for simultaneous structure and parameter learning in hidden-variable conditional probability models, based on an entropic prior and a solution for its maximum a posteriori (MAP) estimator The MAP estimate minimizes uncertainty in all respects: cross-entropy between model and data; entropy of the model; entropy of the data's descriptive statistics Iterative estimation extinguishes weakly supported parameters, compressing and sparsifying the model Trimming operators accelerate this process by removing excess parameters and, unlike most pruning schemes, guarantee an increase in posterior probability Entropic estimation takes a overcomplete random model and simplifies it, inducing the structure of relations between hidden and observed variables Applied to hidden Markov models (HMMs), it finds a concise finite-state machine representing the hidden structure of a signal We entropically model music, handwriting, and video time-series, and show that the resulting models are highly concise, structured, predictive, and interpretable: Surviving states tend to be highly correlated with meaningful partitions of the data, while surviving transitions provide a low-perplexity model of the signal dynamics

Improved Quasi-Maximum Likelihood Estimation for Stochastic Volatility Models

Abstract: Jacquier, Poison and Rossi (1994, Journal of Business and Economic Statistics) have proposed a Bayesian hierarchical model and Markov Chain Monte Carlo methodology for parameter estimation and smoothing in a stochastic volatility model, where the logarithm of the conditional variance follows an autoregressive process. In sampling experiments, their estimators perform particularly well relative to a quasi-maximum likelihood approach, in which the nonlinear stochastic volatility model is linearized via a logarithmic transformation and the resulting linear state-space model is treated as Gaussian. In this paper, we explore a simple modification to the treatment of inlier observations which reduces the excess kurtosis in the distribution of the observation disturbances and improves the performance of the quasi-maximum likelihood procedure. The method we propose can be carried out with commercial software.

Document Ink Bleed-Through Removal with Two Hidden Markov Random Fields and a Single Observation Field

Abstract: We present a new method for blind document bleed-through removal based on separate Markov random field (MRF) regularization for the recto and for the verso side, where separate priors are derived from the full graph. The segmentation algorithm is based on Bayesian maximum a posteriori (MAP) estimation. The advantages of this separate approach are the adaptation of the prior to the contents creation process (e.g., superimposing two handwritten pages), and the improvement of the estimation of the recto pixels through an estimation of the verso pixels covered by recto pixels; moreover, the formulation as a binary labeling problem with two hidden labels per pixels naturally leads to an efficient optimization method based on the minimum cut/maximum flow in a graph. The proposed method is evaluated on scanned document images from the 18th century, showing an improvement of character recognition results compared to other restoration methods.