1. A computer implemented method for modeling a class posterior probability of context dependent phonemes in a Hidden Markov Model based speech recognition system, the computer implemented method comprising: receiving a N-dimensional feature vector x 1 , x 2 , . . . , x N with a respective M-dimensional class label vector b 1 , b 2 , . . . , b M , where (x,b) represents the x th feature and its label; assigning a feature to each node of an input layer of a representation network comprising an input layer of N nodes and G≥2 intermediate layers of nodes with each intermediate layer having N g nodes, where g ∈(1, G), all edges of all nodes of the input layer being connected to all nodes of a first intermediate layer, all edges of all nodes of each intermediate layer being connected to all nodes of a next successive intermediate layer; computing, for all nodes of each intermediate layer, discriminative features based on features of nodes in a preceding layer; discretizing features of last intermediate layer Z G into E-intervals to obtain a discretized layer {circumflex over (Z)}, where E≥2; generating a feature vector Q=(q 1 , q 2 , . . . , q V ) by randomly selecting V ∈(1, N G ) features from discretized layer {circumflex over (Z)}; for f=1 to F, hashing Q into Q f =(q 1 f , q 2 f , . . . , q V f ), where Q f is obtained from the f th hashing, where F≥2; determining an equivalent scalar representation for each Q f ; for f=1 to F, determining a posterior probability P f for each (x, b) pair based on the determined respective equivalent scalar representation; use the posterior probabilities to improve classification accuracy in the Hidden Markov Model based speech recognition system; and use the Hidden Markov Model based speech recognition system to recognize speech.
1. A computer implemented method for modeling a class posterior probability of context dependent phonemes in a Hidden Markov Model based speech recognition system, the computer implemented method comprising: receiving a N-dimensional feature vector x 1 , x 2 , . . . , x N with a respective M-dimensional class label vector b 1 , b 2 , . . . , b M , where (x,b) represents the x th feature and its label; assigning a feature to each node of an input layer of a representation network comprising an input layer of N nodes and G≥2 intermediate layers of nodes with each intermediate layer having N g nodes, where g ∈(1, G), all edges of all nodes of the input layer being connected to all nodes of a first intermediate layer, all edges of all nodes of each intermediate layer being connected to all nodes of a next successive intermediate layer; computing, for all nodes of each intermediate layer, discriminative features based on features of nodes in a preceding layer; discretizing features of last intermediate layer Z G into E-intervals to obtain a discretized layer {circumflex over (Z)}, where E≥2; generating a feature vector Q=(q 1 , q 2 , . . . , q V ) by randomly selecting V ∈(1, N G ) features from discretized layer {circumflex over (Z)}; for f=1 to F, hashing Q into Q f =(q 1 f , q 2 f , . . . , q V f ), where Q f is obtained from the f th hashing, where F≥2; determining an equivalent scalar representation for each Q f ; for f=1 to F, determining a posterior probability P f for each (x, b) pair based on the determined respective equivalent scalar representation; use the posterior probabilities to improve classification accuracy in the Hidden Markov Model based speech recognition system; and use the Hidden Markov Model based speech recognition system to recognize speech. 4. The computer implemented method of claim 1 , further comprising: for f=1 to F, set all locations in an array U f [E V ][M] equal to 0; and for f=1 to F, set array location U f [r f (x)][b] equal to 1, for each (x, b) pair.