Topic
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.
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Papers
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TL;DR: This paper discusses a set of possible estimation procedures that are based on the Prony and the Pencil methods, relate them one to the other, and compare them through simulations, and presents an improvement over these methodsbased on the direct use of the maximum-likelihood estimator, exploiting the above methods as initialization.
Abstract: This paper discusses the problem of recovering a planar polygon from its measured complex moments These moments correspond to an indicator function defined over the polygon's support Previous work on this problem gave necessary and sufficient conditions for such successful recovery process and focused mainly on the case of exact measurements being given In this paper, we extend these results and treat the same problem in the case where a longer than necessary series of noise corrupted moments is given Similar to methods found in array processing, system identification, and signal processing, we discuss a set of possible estimation procedures that are based on the Prony and the Pencil methods, relate them one to the other, and compare them through simulations We then present an improvement over these methods based on the direct use of the maximum-likelihood estimator, exploiting the above methods as initialization Finally, we show how regularization and, thus, maximum a posteriori probability estimator could be applied to reflect prior knowledge about the recovered polygon
120 citations
TL;DR: Experimental studies show that the RiIG MAP filter has excellent filtering performance in the sense that it smooths homogeneous regions, and at the same time preserves details.
Abstract: In this paper, a new statistical model for representing the amplitude statistics of ultrasonic images is presented. The model is called the Rician inverse Gaussian (RiIG) distribution, due to the fact that it is constructed as a mixture of the Rice distribution and the Inverse Gaussian distribution. The probability density function (pdf) of the RiIG model is given in closed form as a function of three parameters. Some theoretical background on this new model is discussed, and an iterative algorithm for estimating its parameters from data is given. Then, the appropriateness of the RiIG distribution as a model for the amplitude statistics of medical ultrasound images is experimentally studied. It is shown that the new distribution can fit to the various shapes of local histograms of linearly scaled ultrasound data better than existing models. A log-likelihood cross-validation comparison of the predictive performance of the RiIG, the K, and the generalized Nakagami models turns out in favor of the new model. Furthermore, a maximum a posteriori (MAP) filter is developed based on the RiIG distribution. Experimental studies show that the RiIG MAP filter has excellent filtering performance in the sense that it smooths homogeneous regions, and at the same time preserves details.
120 citations
TL;DR: A Bayesian approach to regularize the RNN-LM and apply it for continuous speech recognition by compensating for the uncertainty of the estimated model parameters, which is represented by a Gaussian prior.
Abstract: A language model (LM) is calculated as the probability of a word sequence that provides the solution to word prediction for a variety of information systems. A recurrent neural network (RNN) is powerful to learn the large-span dynamics of a word sequence in the continuous space. However, the training of the RNN-LM is an ill-posed problem because of too many parameters from a large dictionary size and a high-dimensional hidden layer. This paper presents a Bayesian approach to regularize the RNN-LM and apply it for continuous speech recognition. We aim to penalize the too complicated RNN-LM by compensating for the uncertainty of the estimated model parameters, which is represented by a Gaussian prior. The objective function in a Bayesian classification network is formed as the regularized cross-entropy error function. The regularized model is constructed not only by calculating the regularized parameters according to the maximum a posteriori criterion but also by estimating the Gaussian hyperparameter by maximizing the marginal likelihood. A rapid approximation to a Hessian matrix is developed to implement the Bayesian RNN-LM (BRNN-LM) by selecting a small set of salient outer-products. The proposed BRNN-LM achieves a sparser model than the RNN-LM. Experiments on different corpora show the robustness of system performance by applying the rapid BRNN-LM under different conditions.
119 citations
119 citations
TL;DR: The 3-D pose tracking task is formulated in a Bayesian framework which fuses feature correspondence information from both previous frame and some selected key-frames into the posterior distribution of pose and the maximum a posteriori estimation of pose is obtained via stochastic sampling to achieve stable and drift-free tracking.
Abstract: In this paper, we propose a novel approach for real-time 3-D tracking of object pose from a single camera. We formulate the 3-D pose tracking task in a Bayesian framework which fuses feature correspondence information from both previous frame and some selected key-frames into the posterior distribution of pose. We also developed an inter-frame motion inference algorithm which can get reliable inter-frame feature correspondences and relative pose. Finally, the maximum a posteriori estimation of pose is obtained via stochastic sampling to achieve stable and drift-free tracking. Experiments show significant improvement of our algorithm over existing algorithms especially in the cases of tracking agile motion, severe occlusion, drastic illumination change, and large object scale change
119 citations