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Siukui Au - One of the best experts on this subject based on the ideXlab platform.
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fast bayesian approach for modal identification using free vibration data part ii posterior uncertainty and application
Mechanical Systems and Signal Processing, 2016Co-Authors: Yanchun Ni, Fengliang Zhang, Siukui AuAbstract:Abstract A Bayesian statistical framework has been developed for modal identification using free vibration data in the companion paper (Zhang et al., Mech. Syst. Sig. Process. (2015)). Efficient strategies have been developed for evaluating the most probable value (MPV) of the modal parameters in both well-separated mode and general multiple mode cases. This paper investigates the posterior uncertainty of the modal parameters in terms of their posterior covariance matrix, which is mathematically equal to the inverse of the Hessian of the Negative Log-Likelihood function (NLLF) evaluated at the MPVs. Computational issues associated with the determination of the posterior covariance matrix are discussed. Analytical expressions are derived for the Hessian so that it can be evaluated accurately and efficiently without resorting to finite difference method. The proposed methods are verified with synthetic data and then applied to field vibration test data.
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fast bayesian ambient modal identification in the frequency domain part ii posterior uncertainty
Mechanical Systems and Signal Processing, 2012Co-Authors: Siukui AuAbstract:Abstract This paper investigates the determination of the posterior covariance matrix of modal parameters within the framework of a Bayesian FFT approach for modal identification using ambient vibration data. The posterior covariance matrix is approximated by the inverse of the Hessian of the Negative Log-Likelihood function (NLLF) with respect to the modal parameters. To suppress the growth of computational effort with the number of measured dofs, a condensed form of the NLLF is derived that only involves matrix computation of dimension equal to the number of modes. Issues associated with the singularity of the Hessian due to mode shape scaling are discussed and a strategy is presented to properly evaluate its inverse. The theory described in Parts I and II of this work is applied to modal identification using synthetic and field data with a moderate to large number of measured dofs. It is demonstrated that using the proposed method Bayesian modal identification can be performed in a matter of seconds in typical cases, which is otherwise prohibitive based on the original formulation.
Thanh Minh Nguyen - One of the best experts on this subject based on the ideXlab platform.
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Bounded generalized Gaussian mixture model
Pattern Recognition, 2014Co-Authors: Thanh Minh Nguyen, Hui ZhangAbstract:Abstract The generalized Gaussian mixture model (GGMM) provides a flexible and suitable tool for many computer vision and pattern recognition problems. However, generalized Gaussian distribution is unbounded. In many applications, the observed data are digitalized and have bounded support. A new bounded generalized Gaussian mixture model (BGGMM), which includes the Gaussian mixture model (GMM), Laplace mixture model (LMM), and GGMM as special cases, is presented in this paper. We propose an extension of the generalized Gaussian distribution in this paper. This new distribution has a flexibility to fit different shapes of observed data such as non-Gaussian and bounded support data. In order to estimate the model parameters, we propose an alternate approach to minimize the higher bound on the data Negative Log-Likelihood function. We quantify the performance of the BGGMM with simulations and real data.
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gaussian mixture model based spatial neighborhood relationships for pixel labeling problem
Systems Man and Cybernetics, 2012Co-Authors: Thanh Minh NguyenAbstract:In this paper, we present a new algorithm for pixel labeling and image segmentation based on the standard Gaussian mixture model (GMM). Unlike the standard GMM where pixels themselves are considered independent of each other and the spatial relationship between neighboring pixels is not taken into account, the proposed method incorporates this spatial relationship into the standard GMM. Moreover, the proposed model requires fewer parameters compared with the models based on Markov random fields. In order to estimate model parameters from observations, instead of utilizing an expectation-maximization algorithm, we employ gradient method to minimize a higher bound on the data Negative Log-Likelihood. The performance of the proposed model is compared with methods based on both standard GMM and Markov random fields, demonstrating the robustness, accuracy, and effectiveness of our method.
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robust student s t mixture model with spatial constraints and its application in medical image segmentation
IEEE Transactions on Medical Imaging, 2012Co-Authors: Thanh Minh NguyenAbstract:Finite mixture model based on the Student's-t distribution, which is heavily tailed and more robust than Gaussian, has recently received great attention for image segmentation. A new finite Student's-t mixture model (SMM) is proposed in this paper. Existing models do not explicitly incorporate the spatial relationships between pixels. First, our model exploits Dirichlet distribution and Dirichlet law to incorporate the local spatial constrains in an image. Secondly, we directly deal with the Student's-t distribution in order to estimate the model parameters, whereas, the Student's-t distributions in previous models are represented as an infinite mixture of scaled Gaussians that lead to an increase in complexity. Finally, instead of using expectation maximization (EM) algorithm, the proposed method adopts the gradient method to minimize the higher bound on the data Negative Log-Likelihood and to optimize the parameters. The proposed model is successfully compared to the state-of-the-art finite mixture models. Numerical experiments are presented where the proposed model is tested on various simulated and real medical images.
Dima Kuzmin - One of the best experts on this subject based on the ideXlab platform.
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bayesian generalized probability calculus for density matrices escholarship
2010Co-Authors: Manfred K Warmuth, Dima KuzminAbstract:One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be diagonal. We develop a probability calculus based on these more general distributions that includes definitions of joints, conditionals and formulas that relate these, including anaLogs of the Theorem of Total Probability and various Bayes rules for the calculation of posterior density matrices. The resulting calculus parallels the familiar “conventional” probability calculus and always retains the latter as a special case when all matrices are diagonal. We motivate both the conventional and the generalized Bayes rule with a minimum relative entropy principle, where the Kullbach-Leibler version gives the conventional Bayes rule and Umegaki’s quantum relative entropy the new Bayes rule for density matrices. Whereas the conventional Bayesian methods maintain uncertainty about which model has the highest data Likelihood, the generalization maintains uncertainty about which unit direction has the largest variance. Surprisingly the bounds also generalize: as in the conventional setting we upper bound the Negative Log Likelihood of the data by the Negative Log Likelihood of the MAP estimator.
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a bayesian probability calculus for density matrices
Uncertainty in Artificial Intelligence, 2006Co-Authors: Manfred K Warmuth, Dima KuzminAbstract:One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be diagonal. We develop a probability calculus based on these more general distributions that includes definitions of joints, conditionals and formulas that relate these, including anaLogs of the Theorem of Total Probability and various Bayes rules for the calculation of posterior density matrices. The resulting calculus parallels the familiar "conventional" probability calculus and always retains the latter as a special case when all matrices are diagonal. Whereas the conventional Bayesian methods maintain uncertainty about which model has the highest data Likelihood, the generalization maintains uncertainty about which unit direction has the largest variance. Surprisingly the bounds also generalize: as in the conventional setting we upper bound the Negative Log Likelihood of the data by the Negative Log Likelihood of the MAP estimator.
Taylor Bergkirkpatrick - One of the best experts on this subject based on the ideXlab platform.
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unsupervised text style transfer using language models as discriminators
Neural Information Processing Systems, 2018Co-Authors: Zichao Yang, Eric Po Xing, Zhiting Hu, Chris Dyer, Taylor BergkirkpatrickAbstract:Binary classifiers are employed as discriminators in GAN-based unsupervised style transfer models to ensure that transferred sentences are similar to sentences in the target domain. One difficulty with the binary discriminator is that error signal is sometimes insufficient to train the model to produce rich-structured language. In this paper, we propose a technique of using a target domain language model as the discriminator to provide richer, token-level feedback during the learning process. Because our language model scores sentences directly using a product of locally normalized probabilities, it offers more stable and more useful training signal to the generator. We train the generator to minimize the Negative Log Likelihood (NLL) of generated sentences evaluated by a language model. By using continuous approximation of the discrete samples, our model can be trained using back-propagation in an end-to-end way. Moreover, we find empirically with a language model as a structured discriminator, it is possible to eliminate the adversarial training steps using Negative samples, thus making training more stable. We compare our model with previous work using convolutional neural networks (CNNs) as discriminators and show our model outperforms them significantly in three tasks including word substitution decipherment, sentiment modification and related language translation.
Stefano Ermon - One of the best experts on this subject based on the ideXlab platform.
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maximum Likelihood training of score based diffusion models
arXiv: Machine Learning, 2021Co-Authors: Yang Song, Conor Durkan, Iain Murray, Stefano ErmonAbstract:Score-based diffusion models synthesize samples by reversing a stochastic process that diffuses data to noise, and are trained by minimizing a weighted combination of score matching losses. The Log-Likelihood of score-based models can be tractably computed through a connection to continuous normalizing flows, but Log-Likelihood is not directly optimized by the weighted combination of score matching losses. We show that for a specific weighting scheme, the objective upper bounds the Negative Log-Likelihood, thus enabling approximate maximum Likelihood training of score-based models. We empirically observe that maximum Likelihood training consistently improves the Likelihood of score-based models across multiple datasets, stochastic processes, and model architectures. Our best models achieve Negative Log-Likelihoods of 2.74 and 3.76 bits/dim on CIFAR-10 and ImageNet 32x32, outperforming autoregressive models on these tasks.
