Automatic speech recognition. A deep learning approach by Dong Yu

By Dong Yu

This e-book offers a entire review of the new development within the box of automated speech popularity with a spotlight on deep studying types together with deep neural networks and plenty of in their variations. this can be the 1st computerized speech popularity publication devoted to the deep studying process. as well as the rigorous mathematical therapy of the topic, the e-book additionally offers insights and theoretical starting place of a chain of hugely profitable deep studying models.

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36. Then we have an equivalent objective function of N Tr Q 1 (μ i , Σ i ) = γt (i) ot − μi T Σ i−1 ot − μi − i=1 t=1 1 log |Σ i |. 43) for i = 1, 2, . . , N . For solving it, we employ the trick of variable transformation: K = Σ −1 (we omit the state index i for simplicity), and we treat Q 1 as a function of K. Then, the derivative of log |K| (a term in Eq. 36) with respect to K’s (l, m)-th entry, klm , is ∂ Q1 = 0 to the (l, m)-th entry of Σ, or σlm . 44) for each entry: l, m = 1, 2, . . , D.

This has been misleading, however, since a mixture of Gaussians each with a diagonal covariance matrix can at least effectively describe the correlations modeled by one Gaussian with a full covariance matrix. 3 Parameter Estimation The Gaussian-mixture distributions we just discussed contain a set of parameters. In the multivariate case of Eq. 8, the parameter set consists of Θ = cm, μm , Σ m . The parameter estimation problem, also called learning, is to determine the values of these parameters from a set of data typically assumed to be drawn from the Gaussianmixture distribution.

To approximate the statistical characteristics of such a source, we often call it a hidden Markov model (HMM). , [1, 12, 17, 46–48, 66, 71, 81, 83, 103, 111, 120, 124, 126, 128]. In these applications, the HMM is used as a powerful model to characterize the temporally nonstationary, spatially variable, but regular, learnable patterns of the speech signal. One key aspect of the HMM as the acoustic model of speech is its sequentially arranged Markov states, which permit the use of piecewise stationarity for approximating the globally nonstationary properties of speech feature sequences.

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