Viterbi Beam Search in Microsoft Office Maker datamatrix 2d barcode in Microsoft Office Viterbi Beam Search

Viterbi Beam Search using barcode encoding for microsoft control to generate, create datamatrix image in microsoft applications. Code128 To explain the ti barcode data matrix for None me-synchronous Viterbi beam search in a formal way [31], we first define some quantities: D (t ; st ; w) total cost of the best path up to time t that ends in state st of grammar word state w. h(t ; st ; w) backtrack pointer for the best path up to time t that ends in state st of grammar word state w. Readers should be aware that w in the two quantities above represents a grammar word state in the search space.

It is different from just the word identity since the same word could occur in many different language model states, as in the trigram search space shown in Figure 12.17. There are two types of dynamic programming (DP) transition rules [30], namely intraword and inter-word transition.

The intra-word transition is just like the Viterbi rule for HMMs and can be expressed as follows: D (t ; st ; w) = min {d (xt , st . st 1 ; w) + D(t 1; st 1 ; w)}. st 1 (12.17) (12.18).

h(t ; st ; w) = h Microsoft Data Matrix 2d barcode (t 1, bmin (t ; st ; w); w). where d (xt , st st 1 ; w) is th Microsoft Office gs1 datamatrix barcode e cost associated with taking the transition from state st 1 to state st while generating output observation xt , and bmin (t ; st ; w) is the optimal predecessor state of cell D(t ; st ; w) . To be specific, they can be expressed as follows: d (xt , st . st 1 ; w) = log P( st st 1 ; w) log P (xt st ; w) (12.19). bmin (t ; st ; w) = arg min {d (xt , st st 1 ; w) + D ( t 1; st 1 ; w)}. st 1 (12.20). Stack decoding (A* Search). The inter-word tr ansition is basically a null transition without consuming any observation. However, it needs to deal with creating a new history node for the backtracking pointer. Let s define F ( w) as the final state of word HMM w and I ( w) as the initial state of word HMM w.

Moreover, state is denoted as the pseudo initial state. The inter-word transition can then be expressed as follows:. D (t ; ; w) = min {log P( w v ) + D (t ; F (v); v)}. (12.21) (12.22).

h(t ; ; w) = vmi n , t :: h(t , F (vmin ); vmin ). where vmin = arg min {log P( w v) + D (t ; F (v); v)} and :: is a link appending operator. The time-synchron Microsoft Office DataMatrix ous Viterbi beam search algorithm assumes that all the intra-word transitions are evaluated before inter-word null transitions take place. The same time index is used intentionally for inter-word transition since the null language model state transition does not consume an observation vector. Since the initial state I ( w) for word HMM w could have a self-transition, the cell D (t ; I ( w); w) might already have active path.

Therefore, we need to perform the following check to advance the inter-word transitions. if D (t ; ; w) < D (t ; I ( w); w) D (t ; I ( w); w) = D (t ; ; w) and h(t ; I ( w); w) = h(t ; ; w) (12.23).

The time-synchron ous Viterbi beam search can be summarized as in Algorithm 12.6. For large-vocabulary speech recognition, the experimental results shows that only a small percentage of the entire search space (the beam) needs to be kept for each time interval t without increasing error rates.

Empirically, the beam size has typically been found to be between 5% and 10% of the entire search space. In 13 we describe strategies of using different level of beams for more effectively pruning..

STACK DECODING (A* SEARCH). If some reliable heuristics are available to guide the decoding, the search can be done in a depth-first fashion around the best path early on, instead of wasting efforts on unpromising paths via the time-synchronous beam search. Stack decoding represents the best attempt to use A* search instead of time-synchronous beam search for continuous speech recognition. Unfortunately, as we will discover in this section, such a heuristic function h( ) (defined in Section 12.

1.3) is very difficult to attain in continuous speech recognition, so search algorithms based on A* search are in general less efficient than time-synchronous beam search. Stack decoding is a variant of the heuristic A* search based on the forward algorithm, where the evaluation function is based on the forward probability.

It is a tree search algorithm, which takes a slightly different viewpoint than the time-synchronous Viterbi search. Time-synchronous beam search is basically a breadth-first search, so it is crucial to control.
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