By Dong Yu
This ebook presents a complete assessment of the new development within the box of computerized speech acceptance with a spotlight on deep studying types together with deep neural networks and lots of in their editions. this can be the 1st automated speech popularity e-book devoted to the deep studying process. as well as the rigorous mathematical therapy of the topic, the ebook additionally offers insights and theoretical origin of a chain of hugely winning deep studying models.
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Additional info for Automatic Speech Recognition: A Deep Learning Approach
J. Acoust. Soc. Am. 121, 723–742 (2007) 30. : A functional articulatory dynamic model for speech production. In: Proceedings of International Conference on Acoustics, Speech and Signal Processing (ICASSP), vol. 2, pp. 797–800. Salt Lake City (2001) 31. : The infinite gaussian mixture model. In: Proceedings of Neural Information Processing Systems (NIPS) (1999) 32. : Robust text-independent speaker identification using gaussian mixture speaker models. IEEE Trans. Speech Audio Process. 3(1), 72–83 (1995) 33.
With the use of the precision parameter r, a Gaussian PDF can also be written as p(x) = r r exp − (x − μ)2 . 6) It is a simple exercise to show that for a Gaussian random variable x, E(x) = μ, var (x) = σ 2 = r −1 . The normal random vector x = (x1 , x2 , . . , x D )T , also called multivariate or vector-valued Gaussian random variable, is defined by the following joint PDF: p(x) = 1 (2π ) D/2 |Σ|1/2 1 . 7) An equivalent notation is x ∼ N (μ ∈ R D , Σ ∈ R D×D ). It is also straight forward to show that for a multivariate Gaussian random variable, the expectation and covariance matrix are given by E(x) = μ; E[(x − x)(x − x)T ] = Σ.
In this as well as a few other later chapters, we use the same notations to describe random variables and other concepts as those adopted in . The fundamental characterization of a continuous-valued random variable, x, is its distribution or the probability density function (PDF), denoted generally by p(x). The PDF for a continuous random variable at x = a is defined by P(a − Δa < x ≤ a) . 1) where P(·) denotes the probability of the event. The cumulative distribution function of a continuous random variable x evaluated at x = a is defined by .