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.

Bayesian and regularization methods for hyperparameter estimation in image restoration

Abstract: In this paper, we propose the application of the hierarchical Bayesian paradigm to the image restoration problem. We derive expressions for the iterative evaluation of the two hyperparameters applying the evidence and maximum a posteriori (MAP) analysis within the hierarchical Bayesian paradigm. We show analytically that the analysis provided by the evidence approach is more realistic and appropriate than the MAP approach for the image restoration problem. We furthermore study the relationship between the evidence and an iterative approach resulting from the set theoretic regularization approach for estimating the two hyperparameters, or their ratio, defined as the regularization parameter. Finally the proposed algorithms are tested experimentally.

Comparison of Bayesian predictive methods for model selection

Abstract: The goal of this paper is to compare several widely used Bayesian model selection methods in practical model selection problems, highlight their differences and give recommendations about the preferred approaches. We focus on the variable subset selection for regression and classification and perform several numerical experiments using both simulated and real world data. The results show that the optimization of a utility estimate such as the cross-validation (CV) score is liable to finding overfitted models due to relatively high variance in the utility estimates when the data is scarce. This can also lead to substantial selection induced bias and optimism in the performance evaluation for the selected model. From a predictive viewpoint, best results are obtained by accounting for model uncertainty by forming the full encompassing model, such as the Bayesian model averaging solution over the candidate models. If the encompassing model is too complex, it can be robustly simplified by the projection method, in which the information of the full model is projected onto the submodels. This approach is substantially less prone to overfitting than selection based on CV-score. Overall, the projection method appears to outperform also the maximum a posteriori model and the selection of the most probable variables. The study also demonstrates that the model selection can greatly benefit from using cross-validation outside the searching process both for guiding the model size selection and assessing the predictive performance of the finally selected model.

Audio source separation with a single sensor

Abstract: In this paper, we address the problem of audio source separation with one single sensor, using a statistical model of the sources. The approach is based on a learning step from samples of each source separately, during which we train Gaussian scaled mixture models (GSMM). During the separation step, we derive maximum a posteriori (MAP) and/or posterior mean (PM) estimates of the sources, given the observed audio mixture (Bayesian framework). From the experimental point of view, we test and evaluate the method on real audio examples.

Iterative multiuser detection for coded CDMA signals in AWGN and fading channels

Abstract: A new iterative receiver for joint detection and decoding of code division multiple access (CDMA) signals is presented. The new scheme is based on a combination of the minimum mean square error (MMSE) criterion and the turbo processing principle by Hagenauer (see Proc. Int. Symp. Turbo Codes and Related Topics, Brest, France, p.1-9, 1997). The complexity of the new scheme is of polynomial order in the number of users. The new scheme is applicable to two situations: (a) when the receiver is capable of decoding the signals from all users and (b) when the receiver is only capable of decoding the signals from a subset of users. In the first scenario, we establish that the proposed receiver achieves superior performance to the iterative soft interference cancellation technique under certain conditions. On the other hand, in the second scenario, we argue that the proposed receiver outperforms both the iterative soft interference canceler and the iterative maximum a posteriori (MAP) receiver because of its superior near-far resistance. For operation over fading channels, the estimation of the complex fading parameters for all users becomes an important ingredient in any multiuser detector. In our scheme, the soft information provided by the decoders is used to enhance this estimation process. Two iterative soft-input channel estimation algorithms are presented: the first is based on the MMSE criterion, and the second is a lower-complexity approximation of the first. The proposed multiuser detection algorithm(s) are suitable for both terrestrial and satellite applications of CDMA.