Xi Chen HMM Modified Based on Amr s Recitation 1 Factorization Short hand of Paramters Initial State K 1 Transition K K 1 Emission K M 1 2 Inference known parameters MAP Veterbi Learning learn parameters Fully Observed Data Count and Normalize Partially Observed Data EM 3 Find 4 Trick add a variable and marginalize over it to enable the recursion 5 6 Compute 7 8 Find the globally maximal posterior sequence Goal Maximal Probability of ending in state k at time t where we maximize over 9 Scaling Keeping track of i 10 Hidden State 11 Inference known parameters MAP Veterbi Learning learn parameters Fully Observed Model count and normalize No Observed Hidden State EM 12 Fully Observed Data Initial State Transition Emission 13 14 15 All parameters are decoupled Take the gradient w r t each parameter and set it to zero Simple count and normalization 16 EM E Step 17 Forward Backward Algorithm 18 19 EM M Step Solve MLE as in fully observed case 20 21 Output o x n f w0 wi xi i 1 n net w0 wi xi i 1 o x f net 22 Linear activation Sigmoid activation f net f net net 1 1 e net 1 0 Hyperbolic tangent activation Threshold activation 1 f net sign net 1 if if net 0 net 0 f net tanh net 1 e 2 net 1 e 2 net 1 1 0 1 z 1 23 24 Forward Propagation 25 26
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