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Download Statistical Methods for Speech Recognition by Frederick Jelinek PDF

By Frederick Jelinek

This ebook displays a long time of vital learn at the mathematical foundations of speech popularity. It specializes in underlying statistical ideas comparable to hidden Markov versions, determination bushes, the expectation-maximization set of rules, info theoretic goodness standards, greatest entropy likelihood estimation, parameter and knowledge clustering, and smoothing of likelihood distributions. The author's aim is to provide those ideas truly within the easiest environment, to teach the benefits of self-organization from genuine information, and to let the reader to use the techniques.

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Repeat if Fe< Fd then set ak+l = ak, bk+l = dk, dk+l = ck ck+l = ak+l + {1 ~r) (bk+l -ak+l) else Fd =Fe, Fe= F(ck+d set ak+l = ck, bk+l = bk, ck+l = dk dk+l = bk+l ~ (l~r)(bk+l-ak+d Fe= Fd, Fd =F(dk+d end end until bk+l - ak+l < tol Comments The iterations terminate when the interval of uncertainty has fallen below tol. 1. This is achieved in the same number of iterations for this particular example with a slightly larger final interval. 2. 4 Bisection When the first derivative of the objective function is available at the extreme points of an interval of uncertainty, it is necessary to evaluate function information at only one interior point in order to reduce this interval.

Detailed proofs of convergence are omitted from this book, We shall imply convergence where possible by establishing that a sufficient reduction in function value can be obtained at each iteration until the solution is found. 2 Rate of convergence Given that a method is stable, it is important to have a theoretical indication of the rate of convergence to a solution since this may be so slow as to render the method of little practical value. While it is obviously important that an algorithm should arrive in the vicinity of a minimum in as few iterations as possible, quantifiable theoretical predictions of convergence rate are confined to this region.

The details of the former algorithm are as follows. 6: Interval location by Davidon 's method 2 3 4 5 input a1, ~ax• Fx set Fa= Fb =F(ad,Ka =Kb =g(ad,ao =bo ifga 0 or Fa Fb Comments The function decreases with increasing x. The function decreases with decreasing x. 5 HYBRID MEmODS It has been noted that function comparison methods for interval reduction have a first-order rate of convergence while polynomial interpolation methods have a rate that is better than superlinear.

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