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.

Compound Gauss-Markov random fields for image estimation

Abstract: Algorithms for obtaining approximations to statistically optimal estimates for images modeled as compound Gauss-Markov random fields are discussed. The authors consider both the maximum a posteriori probability (MAP) estimate and the minimum mean-squared error (MMSE) estimate for image estimation and image restoration. Compound image models consist of several submodels having different characteristics along with an underlying structure model which govern transitions between these image submodels. Two different compound random field models are employed, the doubly stochastic Gaussian (DSG) random field and a compound Gauss-Markov (CGM) random field. The authors present MAP estimators for DSG and CGM random fields using simulated annealing. A fast-converging algorithm called deterministic relaxation, which, however, converges to only a locally optimal MAP estimate, is also presented as an alternative for reducing computational loading on sequential machines. For comparison purposes, the authors include results on the fixed-lag smoothing MMSE estimator for the DSG field and its suboptimal M-algorithm approximation. >

Multiple Choice Learning: Learning to Produce Multiple Structured Outputs

Abstract: We address the problem of generating multiple hypotheses for structured prediction tasks that involve interaction with users or successive components in a cascaded architecture. Given a set of multiple hypotheses, such components/users typically have the ability to retrieve the best (or approximately the best) solution in this set. The standard approach for handling such a scenario is to first learn a single-output model and then produce M-Best Maximum a Posteriori (MAP) hypotheses from this model. In contrast, we learn to produce multiple outputs by formulating this task as a multiple-output structured-output prediction problem with a loss-function that effectively captures the setup of the problem. We present a max-margin formulation that minimizes an upper-bound on this loss-function. Experimental results on image segmentation and protein side-chain prediction show that our method outperforms conventional approaches used for this type of scenario and leads to substantial improvements in prediction accuracy.

Iterative multiuser joint decoding: optimal power allocation and low-complexity implementation

Abstract: We consider a canonical model for coded code-division multiple access (CDMA) with random spreading, where the receiver makes use of iterative belief-propagation (BP) joint decoding. We provide simple density-evolution analysis in the large-system limit (large number of users) of the performance of the BP decoder and of some suboptimal approximations based on interference cancellation (IC). Based on this analysis, we optimize the received user signal-to-noise ratio (SNR) distribution in order to maximize the system spectral efficiency for given user channel codes, channel load (users per chip), and target user bit-error rate (BER). The optimization of the received SNR distribution is obtained by solving a simple linear program and can be easily incorporated into practical power control algorithms. Remarkably, under the optimized SNR assignment, the suboptimal minimum mean-square error (MMSE) IC-based decoder performs almost as well as the more complex BP decoder. Moreover, for a large class of commonly used convolutional codes, we observe that the optimized SNR distribution consists of a finite number of discrete SNR levels. Based on this observation, we provide a low-complexity approximation of the MMSE-IC decoder that suffers from very small performance degradation while attaining considerable savings in complexity. As by-products of this work, we obtain a closed-form expression of the multiuser efficiency (ME) of power-mismatched MMSE filters in the large-system limit, and we extend the analysis of the symbol-by-symbol maximum a posteriori probability (MAP) multiuser detector in the large-system limit to the case of nonconstant user powers and nonuniform symbol prior probabilities.

Problems of inference for Azzalini's skewnormal distribution

Abstract: This paper considers various unresolved inference problems for the skewnormal distribution We give reasons as to why the direct parameterization should not be used as a general basis for estimation, and consider method of moments and maximum likelihood estimation for the distribution's centred parameterization Large sample theory results are given for the method of moments estimators, and numerical approaches for obtaining maximum likelihood estimates are discussed Simulation is used to assess the performance of the two types of estimation We also present procedures for testing for departures from the limiting folded normal distribution Data on the percentage body fat of elite athletes are used to illustrate some of the issues raised

Bayesian wavelet-based image deconvolution: a GEM algorithm exploiting a class of heavy-tailed priors

Abstract: Image deconvolution is formulated in the wavelet domain under the Bayesian framework. The well-known sparsity of the wavelet coefficients of real-world images is modeled by heavy-tailed priors belonging to the Gaussian scale mixture (GSM) class; i.e., priors given by a linear (finite of infinite) combination of Gaussian densities. This class includes, among others, the generalized Gaussian, the Jeffreys , and the Gaussian mixture priors. Necessary and sufficient conditions are stated under which the prior induced by a thresholding/shrinking denoising rule is a GSM. This result is then used to show that the prior induced by the "nonnegative garrote" thresholding/shrinking rule, herein termed the garrote prior, is a GSM. To compute the maximum a posteriori estimate, we propose a new generalized expectation maximization (GEM) algorithm, where the missing variables are the scale factors of the GSM densities. The maximization step of the underlying expectation maximization algorithm is replaced with a linear stationary second-order iterative method. The result is a GEM algorithm of O(NlogN) computational complexity. In a series of benchmark tests, the proposed approach outperforms or performs similarly to state-of-the art methods, demanding comparable (in some cases, much less) computational complexity.