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
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.