We propose a new self-organizing hierarchical softmax formulation for neural-network-based language models over large vocabularies. Instead of using a predefined hierarchical structure, our approach is capable of learning word clusters with clear syntactical and semantic meaning during the language model training process. We provide experiments on standard benchmarks for language modeling and sentence compression tasks. We find that this approach is as fast as other efficient softmax approximations, while achieving comparable or even better performance relative to similar full softmax models.
Noise Contrastive Estimation (NCE) is proposed in @cite_18 @cite_24 as a more stable sampling method than IS. NCE does not try to estimate the probability of a word directly. Instead, it uses an auxiliary loss that works to distinguish the original distribution from a noisy one. @cite_4 showed that good performance can be achieved even without computing the softmax normalization.
@cite_24 @cite_18 @cite_4
284754667 1991108537 2125031621 2529545010 2155723880 2045105614 2586584460 2044893557 2171125155 2754272008 2128859735 2124213909 2036723249 2099984896 2120861206 2950797609 2339667469 2152790380 2604243686 2150415460
Two recently introduced criteria for estimation of generative models are both based on a reduction to binary classification. Noise-contrastive estimation (NCE) is an estimation procedure in which a generative model is trained to be able to distinguish data samples from noise samples. Generative adversarial networks (GANs) are pairs of generator and discriminator networks, with the generator network learning to generate samples by attempting to fool the discriminator network into believing its samples are real data. Both estimation procedures use the same function to drive learning, which naturally raises questions about how they are related to each other, as well as whether this function is related to maximum likelihood estimation (MLE). NCE corresponds to training an internal data model belonging to the discriminator network but using a fixed generator network. We show that a variant of NCE, with a dynamic generator network, is equivalent to maximum likelihood estimation. Since pairing a learned discriminator with an appropriate dynamically selected generator recovers MLE, one might expect the reverse to hold for pairing a learned generator with a certain discriminator. However, we show that recovering MLE for a learned generator requires departing from the distinguishability game. Specifically: (i) The expected gradient of the NCE discriminator can be made to match the expected gradient of MLE, if one is allowed to use a non-stationary noise distribution for NCE, (ii) No choice of discriminator network can make the expected gradient for the GAN generator match that of MLE, and (iii) The existing theory does not guarantee that GANs will converge in the non-convex case. This suggests that the key next step in GAN research is to determine whether GANs converge, and if not, to modify their training algorithm to force convergence. An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density y, with the mixing weight chosen by marginal maximum likelihood, in the hope of adapting between sparse and dense sequences. If estimation is then carried out using the posterior median, this is a random thresholding procedure. Other thresholding rules employing the same threshold can also be used. Probability bounds on the threshold chosen by the marginal maximum likelihood approach lead to overall risk bounds over classes of signal sequences of length n, allowing for sparsity of various kinds and degrees. The signal classes considered are nearly black sequences where only a proportion η is allowed to be nonzero, and sequences with normalized p norm bounded by η, for η > 0 and 0 1. Simulations show excellent performance. For appropriately chosen functions y, the method is computationally tractable and software is available. The extension to a modified thresholding method relevant to the estimation of very sparse sequences is also considered. We analyze skip-gram with negative-sampling (SGNS), a word embedding method introduced by , and show that it is implicitly factorizing a word-context matrix, whose cells are the pointwise mutual information (PMI) of the respective word and context pairs, shifted by a global constant. We find that another embedding method, NCE, is implicitly factorizing a similar matrix, where each cell is the (shifted) log conditional probability of a word given its context. We show that using a sparse Shifted Positive PMI word-context matrix to represent words improves results on two word similarity tasks and one of two analogy tasks. When dense low-dimensional vectors are preferred, exact factorization with SVD can achieve solutions that are at least as good as SGNS's solutions for word similarity tasks. On analogy questions SGNS remains superior to SVD. We conjecture that this stems from the weighted nature of SGNS's factorization. Many speech processing algorithms and applications rely on the explicit knowledge of signal-to-noise ratio (SNR) in their design and implementation. Estimating the SNR of a signal can enhance the performance of such technologies. We propose a novel method for estimating the long-term SNR of speech signals based on features, from which we can approximately detect regions of speech presence in a noisy signal. By measuring the energy in these regions, we create sets of energy ratios, from which we train regression models for different types of noise. If the type of noise that corrupts a signal is known, we use the corresponding regression model to estimate the SNR. When the noise is unknown, we use a deep neural network to find the “closest” regression model to estimate the SNR. Evaluations were done based on the TIMIT speech corpus, using noises from the NOISEX-92 noise database. Furthermore, we performed cross-corpora experiments by training on TIMIT and NOISEX-92 and testing on the Wall Street Journal speech corpus and DEMAND noise database. Our results show that our system provides accurate SNR estimations across different noise types, corpora, and that it outperforms other SNR estimation methods. The paper studies average consensus with random topologies (intermittent links) and noisy channels. Consensus with noise in the network links leads to the bias-variance dilemma-running consensus for long reduces the bias of the final average estimate but increases its variance. We present two different compromises to this tradeoff: the A-ND algorithm modifies conventional consensus by forcing the weights to satisfy a persistence condition (slowly decaying to zero;) and the A-NC algorithm where the weights are constant but consensus is run for a fixed number of iterations [^(iota)], then it is restarted and rerun for a total of [^(p)] runs, and at the end averages the final states of the [^(p)] runs (Monte Carlo averaging). We use controlled Markov processes and stochastic approximation arguments to prove almost sure convergence of A-ND to a finite consensus limit and compute explicitly the mean square error (mse) (variance) of the consensus limit. We show that A-ND represents the best of both worlds-zero bias and low variance-at the cost of a slow convergence rate; rescaling the weights balances the variance versus the rate of bias reduction (convergence rate). In contrast, A-NC, because of its constant weights, converges fast but presents a different bias-variance tradeoff. For the same number of iterations [^(iota)][^(p)] , shorter runs (smaller [^(iota)] ) lead to high bias but smaller variance (larger number [^(p)] of runs to average over.) For a static nonrandom network with Gaussian noise, we compute the optimal gain for A-NC to reach in the shortest number of iterations [^(iota)][^(p)] , with high probability (1-delta), (epsiv, delta)-consensus (epsiv residual bias). Our results hold under fairly general assumptions on the random link failures and communication noise. In this paper, a new object-based method to estimate noise in magnitude MR images is proposed. The main advantage of this object-based method is its robustness to background artefacts such as ghosting. The proposed method is based on the adaptation of the Median Absolute Deviation (MAD) estimator in the wavelet domain for Rician noise. The MAD is a robust and efficient estimator initially proposed to estimate Gaussian noise. In this work, the adaptation of MAD operator for Rician noise is performed by using only the wavelet coefficients corresponding to the object and by correcting the estimation with an iterative scheme based on the SNR of the image. During the evaluation, a comparison of the proposed method with several state-of-the-art methods is performed. A quantitative validation on synthetic phantom with and without artefacts is presented. A new validation framework is proposed to perform quantitative validation on real data. The impact of the accuracy of noise estimation on the performance of a denoising filter is also studied. The results obtained on synthetic images show the accuracy and the robustness of the proposed method. Within the validation on real data, the proposed method obtained very competitive results compared to the methods under study. This paper considers acoustic beamforming for noise robust automatic speech recognition. A beamformer attenuates background noise by enhancing sound components coming from a direction specified by a steering vector. Hence, accurate steering vector estimation is paramount for successful noise reduction. Recently, time-frequency masking has been proposed to estimate the steering vectors that are used for a beamformer. In particular, we have developed a new form of this approach, which uses a speech spectral model based on a complex Gaussian mixture model CGMM to estimate the time-frequency masks needed for steering vector estimation, and extended the CGMM-based beamformer to an online speech enhancement scenario. Our previous experiments showed that the proposed CGMM-based approach outperforms a recently proposed mask estimator based on a Watson mixture model and the baseline speech enhancement system of the CHiME-3 challenge. This paper provides additional experimental results for our online processing, which achieves performance comparable to that of batch processing with a suitable block-batch size. This online version reduces the CHiME-3 word error rate WER on the evaluation set from 8.37 to 8.06 . Moreover, in this paper, we introduce a probabilistic prior distribution for a spatial correlation matrix a CGMM parameter, which enables more stable steering vector estimation in the presence of interfering speakers. In practice, the performance of the proposed online beamformer degrades with observations that contain only noise or and interference because of the failure of the CGMM parameter estimation. The introduced spatial prior enables the target speaker's parameter to avoid overfitting to noise or and interference. Experimental results show that the spatial prior reduces the WER from 38.4 to 29.2 in a conversation recognition task compared with the CGMM-based approach without the prior, and outperforms a conventional online speech enhancement approach. In contrast to the conventional minimum mean square error (MMSE)-based noise reduction techniques, we propose a supervised method to enhance speech by means of finding a mapping function between noisy and clean speech signals based on deep neural networks (DNNs). In order to be able to handle a wide range of additive noises in real-world situations, a large training set that encompasses many possible combinations of speech and noise types, is first designed. A DNN architecture is then employed as a nonlinear regression function to ensure a powerful modeling capability. Several techniques have also been proposed to improve the DNN-based speech enhancement system, including global variance equalization to alleviate the over-smoothing problem of the regression model, and the dropout and noise-aware training strategies to further improve the generalization capability of DNNs to unseen noise conditions. Experimental results demonstrate that the proposed framework can achieve significant improvements in both objective and subjective measures over the conventional MMSE based technique. It is also interesting to observe that the proposed DNN approach can well suppress highly nonstationary noise, which is tough to handle in general. Furthermore, the resulting DNN model, trained with artificial synthesized data, is also effective in dealing with noisy speech data recorded in real-world scenarios without the generation of the annoying musical artifact commonly observed in conventional enhancement methods. Across the field of inverse problems in image and video processing, nearly all algorithms have various parameters which need to be set in order to yield good results. In practice, usually the choice of such parameters is made empirically with trial and error if no “ground-truth” reference is available. Some analytical methods such as cross-validation and Stein's unbiased risk estimate (SURE) have been successfully used to set such parameters. However, these methods tend to be strongly reliant on restrictive assumptions on the noise, and also computationally heavy. In this paper, we propose a no-reference metric Q which is based upon singular value decomposition of local image gradient matrix, and provides a quantitative measure of true image content (i.e., sharpness and contrast as manifested in visually salient geometric features such as edges,) in the presence of noise and other disturbances. This measure 1) is easy to compute, 2) reacts reasonably to both blur and random noise, and 3) works well even when the noise is not Gaussian. The proposed measure is used to automatically and effectively set the parameters of two leading image denoising algorithms. Ample simulated and real data experiments support our claims. Furthermore, tests using the TID2008 database show that this measure correlates well with subjective quality evaluations for both blur and noise distortions. An accurate quantitative noise estimate is required in many image video processing applications like denoising, computer vision, pattern recognition and tracking. But blind and accurate estimation of noise in an unknown image is a challenging task and hence is an open area of research. We propose the first elegant and novel blind noise estimation method based on random image tile selection and statistical sampling theory for estimating standard deviation of zero mean Gaussian and speckle noise in digital images. Randomly selected samples, i.e., pixels with (3 3 ) neighborhood, are checked for availability of edges in the tile. If there is an edge in the tile at more than one neighboring pixel, the tile is excluded. Only non-edge tiles are used for estimation of noise in the tile and subsequently in the image using the concepts of statistical sampling theory. Finally, we propose a supervised curve fitting approach using the proposed noise estimation model for more accurate estimation of standard deviation of the two types of noise. The proposed technique is computationally efficient as it is a selective random sample-based spatial domain technique. Benchmarking with other contemporary techniques published so far shows that the proposed technique clearly outperforms the others by at least 5 improved noise estimates, over a very wide range of noise. We present a new method for clustering based on compression. The method does not use subject-specific features or background knowledge, and works as follows: First, we determine a parameter-free, universal, similarity distance, the normalized compression distance or NCD, computed from the lengths of compressed data files (singly and in pairwise concatenation). Second, we apply a hierarchical clustering method. The NCD is not restricted to a specific application area, and works across application area boundaries. A theoretical precursor, the normalized information distance, co-developed by one of the authors, is provably optimal. However, the optimality comes at the price of using the noncomputable notion of Kolmogorov complexity. We propose axioms to capture the real-world setting, and show that the NCD approximates optimality. To extract a hierarchy of clusters from the distance matrix, we determine a dendrogram (ternary tree) by a new quartet method and a fast heuristic to implement it. The method is implemented and available as public software, and is robust under choice of different compressors. To substantiate our claims of universality and robustness, we report evidence of successful application in areas as diverse as genomics, virology, languages, literature, music, handwritten digits, astronomy, and combinations of objects from completely different domains, using statistical, dictionary, and block sorting compressors. In genomics, we presented new evidence for major questions in Mammalian evolution, based on whole-mitochondrial genomic analysis: the Eutherian orders and the Marsupionta hypothesis against the Theria hypothesis. In this paper, we propose an MMSE a priori SNR estimator for speech enhancement. This estimator has similar benefits to the well-known decision-directed approach, but does not require an ad-hoc weighting factor to balance the past a priori SNR and current ML SNR estimate with smoothing across frames. Performance is evaluated in terms of estimation error and segmental SNR using the standard logSTSA speech enhancement method. Experimental results show that, in contrast with the decision-directed estimator and ML estimator, the proposed SNR estimator can help enhancement algorithms preserve more weak speech information and efficiently suppress musical noise. This paper presents a novel preprocessing method based on mathematical morphology techniques to improve the subsequent thresholding quality of raw degraded word images. The raw degraded word images contain undesirable shapes called critical shadows on the background that cause noise in binary images. This noise constitutes obstacles to posterior segmentation of characters. Direct application of a thresholding method produces inadequate binary versions of these degraded word images. Our preprocessing method called Shadow Location and Lightening (SL*L) adaptively, accurately and without manual fine-tuning of parameters locates these critical shadows on grayscale degraded images using morphological operations, and lightens them before applying eventual thresholding process. In this way, enhanced binary images without unpredictable and inappropriate noise can be provided to subsequent segmentation of characters. Then, adequate binary characters can be segmented and extracted as input data to optical character recognition (OCR) applications saving computational effort and increasing recognition rate. The proposed method is experimentally tested with a set of several raw degraded images extracted from real photos acquired by unsophisticated imaging systems. A qualitative analysis of experimental results led to conclusions that the thresholding result quality was significantly improved with the proposed preprocessing method. Also, a quantitative evaluation using a testing data of 1194 degraded word images showed the essentiality and effectiveness of the proposed preprocessing method to increase segmentation and recognition rates of their characters. Furthermore, an advantage of the proposed method is that Otsu's method as a simple and easily implementable global thresholding technique can be sufficient to reducing computational load. This paper proposes a new robust adaptive beamformer applicable to microphone arrays. The proposed beamformer is a generalized sidelobe canceller (GSC) with a new adaptive blocking matrix using coefficient-constrained adaptive filters (CCAFs) and a multiple-input canceller with norm-constrained adaptive filters (NCAFs). The CCAFs minimize leakage of the target-signal into the interference path of the GSC. Each coefficient of the CCAFs is constrained to avoid mistracking. The input signal to all the CCAFs is the output of a fixed beamformer. In the multiple-input canceller, the NCAFs prevent undesirable target-signal cancellation when the target-signal minimization at the blocking matrix is incomplete. The proposed beamformer is shown to be robust to target-direction errors as large as 200 with almost no degradation in interference-reduction performance, and it can be implemented with several microphones. The maximum allowable target-direction error can be specified by the user. Simulated anechoic experiments demonstrate that the proposed beamformer cancels interference by over 30 dB. Simulation with real acoustic data captured in a room with 0.3-s reverberation time shows that the noise is suppressed by 19 dB. In subjective evaluation, the proposed beamformer obtains 3.8 on a five-point mean opinion score scale, which is 1.0 point higher than the conventional robust beamformer. In spite of their superior performance, neural probabilistic language models (NPLMs) remain far less widely used than n-gram models due to their notoriously long training times, which are measured in weeks even for moderately-sized datasets. Training NPLMs is computationally expensive because they are explicitly normalized, which leads to having to consider all words in the vocabulary when computing the log-likelihood gradients. We propose a fast and simple algorithm for training NPLMs based on noise-contrastive estimation, a newly introduced procedure for estimating unnormalized continuous distributions. We investigate the behaviour of the algorithm on the Penn Treebank corpus and show that it reduces the training times by more than an order of magnitude without affecting the quality of the resulting models. The algorithm is also more efficient and much more stable than importance sampling because it requires far fewer noise samples to perform well. We demonstrate the scalability of the proposed approach by training several neural language models on a 47M-word corpus with a 80K-word vocabulary, obtaining state-of-the-art results on the Microsoft Research Sentence Completion Challenge dataset. In spite of their superior performance, neural probabilistic language models (NPLMs) remain far less widely used than n-gram models due to their notoriously long training times, which are measured in weeks even for moderately-sized datasets. Training NPLMs is computationally expensive because they are explicitly normalized, which leads to having to consider all words in the vocabulary when computing the log-likelihood gradients. We propose a fast and simple algorithm for training NPLMs based on noise-contrastive estimation, a newly introduced procedure for estimating unnormalized continuous distributions. We investigate the behaviour of the algorithm on the Penn Treebank corpus and show that it reduces the training times by more than an order of magnitude without affecting the quality of the resulting models. The algorithm is also more efficient and much more stable than importance sampling because it requires far fewer noise samples to perform well. We demonstrate the scalability of the proposed approach by training several neural language models on a 47M-word corpus with a 80K-word vocabulary, obtaining state-of-the-art results on the Microsoft Research Sentence Completion Challenge dataset. We propose an efficient open-loop channel estimator for a millimeter-wave (mm-wave) hybrid multiple-input multiple-output (MIMO) system consisting of radio-frequency (RF) beamformers with large antenna arrays followed by a baseband MIMO processor. A sparse signal recovery problem exploiting the sparse nature of mm-wave channels is formulated for channel estimation based on the parametric channel model with quantized angles of departures arrivals (AoDs AoAs), called the angle grids. The problem is solved by the orthogonal matching pursuit (OMP) algorithm employing a redundant dictionary consisting of array response vectors with finely quantized angle grids. We suggest the use of non-uniformly quantized angle grids and show that such grids reduce the coherence of the redundant dictionary. The lower and upper bounds of the sum-of-squared errors of the proposed OMP-based estimator are derived analytically: the lower bound is derived by considering the oracle estimator that assumes the knowledge of AoDs AoAs, and the upper bound is derived based on the results of the OMP performance guarantees. The design of training vectors (or sensing matrix) is particularly important in hybrid MIMO systems, because the RF beamformer prevents the use of independent and identically distributed random training vectors, which are popular in compressed sensing. We design training vectors so that the total coherence of the equivalent sensing matrix is minimized for a given RF beamforming matrix, which is assumed to be unitary. It is observed that the estimation accuracy can be improved significantly by randomly permuting the columns of the RF beamforming matrix. The simulation results demonstrate the advantage of the proposed OMP with a redundant dictionary over the existing methods such as the least squares method and the OMP based on the virtual channel model. We present a new estimation principle for parameterized statistical models. The idea is to perform nonlinear logistic regression to discriminate between the observed data and some artificially generated noise, using the model log-density function in the regression nonlinearity. We show that this leads to a consistent (convergent) estimator of the parameters, and analyze the asymptotic variance. In particular, the method is shown to directly work for unnormalized models, i.e. models where the density function does not integrate to one. The normalization constant can be estimated just like any other parameter. For a tractable ICA model, we compare the method with other estimation methods that can be used to learn unnormalized models, including score matching, contrastive divergence, and maximum-likelihood where the normalization constant is estimated with importance sampling. Simulations show that noise-contrastive estimation offers the best trade-off between computational and statistical efficiency. The method is then applied to the modeling of natural images: We show that the method can successfully estimate a large-scale two-layer model and a Markov random field. Detecting incidental scene text is a challenging task because of multi-orientation, perspective distortion, and variation of text size, color and scale. Retrospective research has only focused on using rectangular bounding box or horizontal sliding window to localize text, which may result in redundant background noise, unnecessary overlap or even information loss. To address these issues, we propose a new Convolutional Neural Networks (CNNs) based method, named Deep Matching Prior Network (DMPNet), to detect text with tighter quadrangle. First, we use quadrilateral sliding windows in several specific intermediate convolutional layers to roughly recall the text with higher overlapping area and then a shared Monte-Carlo method is proposed for fast and accurate computing of the polygonal areas. After that, we designed a sequential protocol for relative regression which can exactly predict text with compact quadrangle. Moreover, a auxiliary smooth Ln loss is also proposed for further regressing the position of text, which has better overall performance than L2 loss and smooth L1 loss in terms of robustness and stability. The effectiveness of our approach is evaluated on a public word-level, multi-oriented scene text database, ICDAR 2015 Robust Reading Competition Challenge 4 Incidental scene text localization. The performance of our method is evaluated by using F-measure and found to be 70.64 , outperforming the existing state-of-the-art method with F-measure 63.76 . An unsupervised learning algorithm for the separation of sound sources in one-channel music signals is presented. The algorithm is based on factorizing the magnitude spectrogram of an input signal into a sum of components, each of which has a fixed magnitude spectrum and a time-varying gain. Each sound source, in turn, is modeled as a sum of one or more components. The parameters of the components are estimated by minimizing the reconstruction error between the input spectrogram and the model, while restricting the component spectrograms to be nonnegative and favoring components whose gains are slowly varying and sparse. Temporal continuity is favored by using a cost term which is the sum of squared differences between the gains in adjacent frames, and sparseness is favored by penalizing nonzero gains. The proposed iterative estimation algorithm is initialized with random values, and the gains and the spectra are then alternatively updated using multiplicative update rules until the values converge. Simulation experiments were carried out using generated mixtures of pitched musical instrument samples and drum sounds. The performance of the proposed method was compared with independent subspace analysis and basic nonnegative matrix factorization, which are based on the same linear model. According to these simulations, the proposed method enables a better separation quality than the previous algorithms. Especially, the temporal continuity criterion improved the detection of pitched musical sounds. The sparseness criterion did not produce significant improvements