Large Vocabulary Continuous Speech Recognition - Berlin Chen

TC: Decomposition of Search History (1/3)If only the latest m-1 word history is instead kept:hGt t( w;τ , t) = max p( x , s w)tτ + 1s= conditiona l prob. that word w produces xnnt t n( w ; t) = P( w ) max p( x , s w )11= joint prob. of observingt1sτ + 1τ + 1If the whole word history is kept:G11x1t1andnn−1n−1( w1; t) = max{ P( wnw1) G( w1; τ ) h( w;τ , t)}τn−1n−1= P( w w ) ⋅ max{ G( w ; τ ) h( w;τ , t)}n1τ1wn1tτ + 1ending at tGHnm( w1; t) ≈ H ( v2; t)m( v ; t)= max⎧Pn n m⎨1w1: w n − m + 2 = v2⎩(with DP recursion )= maxv21nt t n( w ) ⋅ max p( x , s w )t1sm−1m−1{ P( vmv1) ⋅ max{ H ( v1; τ ) h( w;τ , t)}τ111⎫⎬⎭Speech – Berlin Chen 32