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.

The Generalized Area Theorem and Some of its Consequences

Abstract: There is a fundamental relationship between belief propagation (BP) and maximum a posteriori decoding. The case of transmission over the binary erasure channel was investigated in detail in a companion paper (C. MEacuteasson, A. Montanari, and R. Urbanke, "Maxwell's construction: The hidden bridge between iterative and maximum a posteriori decoding," IEEE Transactions on Information Theory, submitted for publication). This paper investigates the extension to general memoryless channels (paying special attention to the binary case). An area theorem for transmission over general memoryless channels is introduced and some of its many consequences are discussed. We show that this area theorem gives rise to an upper bound on the maximum a posteriori threshold for sparse graph codes. In situations where this bound is tight, the extrinsic soft bit estimates delivered by the BP decoder coincide with the correct a posteriori probabilities above the maximum a posteriori threshold. More generally, it is conjectured that the fundamental relationship between the maximum a posteriori probability (MAP) and the BP decoder which was observed for transmission over the binary erasure channel carries over to the general case. We finally demonstrate that in order for the design rate of an ensemble to approach the capacity under BP decoding the component codes have to be perfectly matched, a statement which is well known for the special case of transmission over the binary erasure channel.

Nonlocal Prior Bayesian Tomographic Reconstruction

Abstract: Bayesian approaches, or maximum a posteriori (MAP) methods, are effective in providing solutions to ill-posed problems in image reconstruction. Based on Bayesian theory, prior information of the target image is imposed on image reconstruction to suppress noise. Conventionally, the information in most of prior models comes from weighted differences between pixel intensities within a small local neighborhood. In this paper, we propose a novel nonlocal prior such that differences are computed over a broader neighborhoods of each pixel with weights depending on its similarity with respect to the other pixels. In such a way connectivity and continuity of the image is exploited. A two-step reconstruction algorithm using the nonlocal prior is developed. The proposed nonlocal prior Bayesian reconstruction algorithm has been applied to emission tomographic reconstructions using both computer simulated data and patient SPECT data. Compared to several existing reconstruction methods, our approach shows better performance in both lowering the noise and preserving the edges.

Probabilistic Common Spatial Patterns for Multichannel EEG Analysis

Abstract: Common spatial patterns (CSP) is a well-known spatial filtering algorithm for multichannel electroencephalogram (EEG) analysis. In this paper, we cast the CSP algorithm in a probabilistic modeling setting. Specifically, probabilistic CSP (P-CSP) is proposed as a generic EEG spatio-temporal modeling framework that subsumes the CSP and regularized CSP algorithms. The proposed framework enables us to resolve the overfitting issue of CSP in a principled manner. We derive statistical inference algorithms that can alleviate the issue of local optima. In particular, an efficient algorithm based on eigendecomposition is developed for maximum a posteriori (MAP) estimation in the case of isotropic noise. For more general cases, a variational algorithm is developed for group-wise sparse Bayesian learning for the P-CSP model and for automatically determining the model size. The two proposed algorithms are validated on a simulated data set. Their practical efficacy is also demonstrated by successful applications to single-trial classifications of three motor imagery EEG data sets and by the spatio-temporal pattern analysis of one EEG data set recorded in a Stroop color naming task.

Enhancement of log Mel power spectra of speech using a phase-sensitive model of the acoustic environment and sequential estimation of the corrupting noise

Abstract: This paper presents a novel speech feature enhancement technique based on a probabilistic, nonlinear acoustic environment model that effectively incorporates the phase relationship (hence phase sensitive) between the clean speech and the corrupting noise in the acoustic distortion process. The core of the enhancement algorithm is the MMSE (minimum mean square error) estimator for the log Mel power spectra of clean speech based on the phase-sensitive environment model, using highly efficient single-point, second-order Taylor series expansion to approximate the joint probability of clean and noisy speech modeled as a multivariate Gaussian. Since a noise estimate is required by the MMSE estimator, a high-quality, sequential noise estimation algorithm is also developed and presented. Both the noise estimation and speech feature enhancement algorithms are evaluated on the Aurora2 task of connected digit recognition. Noise-robust speech recognition results demonstrate that the new acoustic environment model which takes into account the relative phase in speech and noise mixing is superior to the earlier environment model which discards the phase under otherwise identical experimental conditions. The results also show that the sequential MAP (maximum a posteriori) learning for noise estimation is better than the sequential ML (maximum likelihood) learning, both evaluated under the identical phase-sensitive MMSE enhancement condition.