We have recently discussed digital watermarking techniques based on modifying the spectral coefficient of an image, and have presented a model of the watermark embedding and extracting processes and a model of waterma...
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ISBN:
(纸本)9781617388767
We have recently discussed digital watermarking techniques based on modifying the spectral coefficient of an image, and have presented a model of the watermark embedding and extracting processes and a model of watermark distortion caused by image processing and attack of watermarked images. In this paper, based on these models, we formulate the watermark detection problem as a kind of blind deconvolution problem. Then, as a solution to this problem, we propose a watermark detection method using Bayesian estimation and EM algorithm.
We consider the problem of learning dictionaries for data compression. Different from ordinary learning methods, the objective is to design a dictionary such that the signal has a low entropy representation in the bas...
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ISBN:
(纸本)9781509041183
We consider the problem of learning dictionaries for data compression. Different from ordinary learning methods, the objective is to design a dictionary such that the signal has a low entropy representation in the basis of the dictionary, rather than giving a sparse or low-energy representation. To achieve this goal, we need to consider the effect of quantization on the rate-distortion curve as well as an estimation of the distributions of the coefficients. Based on this probability estimation, the coefficients are computed, quantized and then entropy-coded. As such, we have developed algorithms for different classes of dictionaries;orthonormal, union of orthonormals and general dictionaries with unit-norm atoms, to iteratively learn the dictionary and the distribution models of the coefficients. A mixture of Gaussians is adopted to estimate the probability and is updated using the expectation maximization algorithm together with the dictionary learning. Simulation results on the real seismic data show the effectiveness of the proposed algorithm compared to ordinary dictionary learning methods.
We consider multi-view classification for the challenging scenario where, for some views, there are no labeled training examples. Several discriminative approaches have been recently proposed for special instances of ...
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ISBN:
(纸本)9781479903573
We consider multi-view classification for the challenging scenario where, for some views, there are no labeled training examples. Several discriminative approaches have been recently proposed for special instances of this problem. Here, alternatively, we propose a generative semi-supervised mixture model across all views which, via marginalization, flexibly performs exact class inference, given any subset of available views. The proposed model is an extension of semi-supervised mixtures to a multi-view setting, as well as a semi-supervised extension of mixtures of factors analyzers (MFA)[1]. A novel EM algorithm with a computationally efficient E-step is derived for learning our multi-view model. Specialization of this formulation to the standard MFA problem also gives a reduced complexity E-step, compared to the original EM algorithm proposed for MFA. Our multi-view method is experimentally demonstrated on digit recognition using audio and lip video views, achieving competitive results with alternative, discriminative approaches.
Mixture modeling is a general technique for making any simple model more expressive through weighted combination. This generality and simplicity in part explains the success of the expectation Maximization (EM) algori...
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ISBN:
(纸本)9781510825024
Mixture modeling is a general technique for making any simple model more expressive through weighted combination. This generality and simplicity in part explains the success of the expectation Maximization (EM) algorithm, in which updates are easy to derive for a wide class of mixture models. However, the likelihood of a mixture model is non-convex, so EM has no known global convergence guarantees. Recently, method of moments approaches offer global guarantees for some mixture models, but they do not extend easily to the range of mixture models that exist. In this work, we present Polymom, an unifying framework based on method of moments in which estimation procedures are easily derivable, just as in EM. Polymom is applicable when the moments of a single mixture component are polynomials of the parameters. Our key observation is that the moments of the mixture model are a mixture of these polynomials, which allows us to cast estimation as a Generalized Moment Problem. We solve its relaxations using semidefinite optimization, and then extract parameters using ideas from computer algebra. This framework allows us to draw insights and apply tools from convex optimization, computer algebra and the theory of moments to study problems in statistical estimation. Simulations show good empirical performance on several models.
This paper presents a novel probabilistic framework for localizing multiple speakers with a microphone array. In this framework, the generalized cross correlation function (GCC) of each microphone pair is interpreted ...
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ISBN:
(纸本)9781479903573
This paper presents a novel probabilistic framework for localizing multiple speakers with a microphone array. In this framework, the generalized cross correlation function (GCC) of each microphone pair is interpreted as a probability distribution of the time difference of arrival (TDOA) and subsequently approximated as a Gaussian mixture. The distribution parameters are estimated with a weighted expectation maximization algorithm. Then, the joint distribution of the TDOA Gaussian mixtures is mapped to a multimodal distribution in the location space, where each mode represents a potential source location. The approach taken here performs the localization by 1) reducing the search space to some regions that are likely to contain a source and then 2) extracting the actual speaker locations with a numerical optimization algorithm. The effectiveness of the proposed approach is shown using the AV16.3 corpus.
An original pattern recognition approach for the diagnosis of switch mechanisms driven by an electric motor is presented in this paper. Its main advantage is that it does not require a physical model of the system and...
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An original pattern recognition approach for the diagnosis of switch mechanisms driven by an electric motor is presented in this paper. Its main advantage is that it does not require a physical model of the system and can easily be adapted to other complex systems. The available data for this task are the signals of the electrical power consumption during the switch actuation period and the proposed method consists of two steps: the feature extraction from the signals and the recognition of different operating states (class without defect, class with minor defect and class with critical defect) using mixture discriminant analysis (MDA). This method assumes the classes to be represented by a Gaussian mixture distribution whose parameters are estimated by the maximum likelihood method, using the expectation-maximization (EM) algorithm. An experimental study performed on real measured signals covering a wide range of defects reveals some good performances of the proposed approach compared to others classification methods such as K-Nearest-Neighbors, Neural Networks and the classical Bayesian discriminant approach (with one Gaussian distribution per class).
In this paper, we consider the problem of dictionary learning for sparse representations. Several algorithms dealing with this problem can be found in the literature. One of them, introduced by Sezer et al. in [1] opt...
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ISBN:
(纸本)9781424442959
In this paper, we consider the problem of dictionary learning for sparse representations. Several algorithms dealing with this problem can be found in the literature. One of them, introduced by Sezer et al. in [1] optimizes a dictionary made up of the union of orthonormal bases. In this paper, we propose a probabilistic interpretation of Sezer's algorithm and suggest a novel optimization procedure based on the EM algorithm. Comparisons of the performance in terms of missed detection rate show a clear superiority of the proposed approach.
Remarkably easy implementation and guaranteed convergence has made the EM algorithm one of the most used algorithms for mixture modeling. On the downside, the E-step is linear in both the sample size and the number of...
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ISBN:
(纸本)9781617823800
Remarkably easy implementation and guaranteed convergence has made the EM algorithm one of the most used algorithms for mixture modeling. On the downside, the E-step is linear in both the sample size and the number of mixture components, making it impractical for large-scale data. Based on the variational EM framework, we propose a fast alternative that uses component-specific data partitions to obtain a sub-linear E-step in sample size, while the algorithm still maintains provable convergence. Our approach builds on previous work, but is significantly faster and scales much better in the number of mixture components. We demonstrate this speedup by experiments on large-scale synthetic and real data.
Runtime predictive analysis of quantitative models can support software reliability in various application scenarios. The spread of logging technologies promotes approaches where such models are learned from observed ...
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ISBN:
(纸本)9781728149837
Runtime predictive analysis of quantitative models can support software reliability in various application scenarios. The spread of logging technologies promotes approaches where such models are learned from observed events. We consider a system visiting transient states of a hidden process until reaching a final state and producing observations with stochastic arrival times and types conditioned by visited states, and we abstract it as a marked Markov modulated Poisson Process (MMMPP) with left-to right structure. We present an expectation-Maximization (EM) algorithm that learns the MMMPP parameters from observation sequences acquired in repeated execution of the transient behavior, and we use the model at runtime to infer the current state of the process from actual observed events and to dynamically evaluate the remaining time to the final state. The approach is illustrated using synthetic datasets generated from a stochastic attack tree of the literature enriched with an observation model associating each state with an expected statistics of observation types and arrival times. Accuracy of prediction is evaluated under different variability of hidden states sojourn durations and of the observations arrival process, and compared against previous literature that mainly exploits either the timing or the types of observed events.
We propose a dynamic Bayesian model for motifs in biopolymer sequences which captures rich biological prior knowledge and positional dependencies in motif structure in a principled way. Our model posits that the posit...
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ISBN:
(纸本)0262025507
We propose a dynamic Bayesian model for motifs in biopolymer sequences which captures rich biological prior knowledge and positional dependencies in motif structure in a principled way. Our model posits that the position-specific multinomial parameters for monomer distribution are distributed as a latent Dirichlet-mixture random variable, and the position-specific Dirichlet component is determined by a hidden Markov process. Model parameters can be fit on training motifs using a vari-ational EM algorithm within an empirical Bayesian framework. Varia-tional inference is also used for detecting hidden motifs. Our model improves over previous models that ignore biological priors and positional dependence. It has much higher sensitivity to motifs during detection and a notable ability to distinguish genuine motifs from false recurring patterns.
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