draw an initial state q_1 from the initial state distribution \pi For each state q_{i}… Drew observe something o_{t} according to the action distribution of state q_{i} Use transition probability a_{i,j} to draw a next state q_{j} Isolated recognition: train a family of HMMs, one for each word or something. Then, given new data, perform scoring of the HMM onto the features. components of HMMs scoring Given an observation o_1, …, o_{T} and a model, we compute P(O | λ)—the probability of a sequence given a model \lambda “forward and backward algorithm” decoding Given observations, find the state sequence q1, …, q_{T} most likely to have generated its dijisktra: for every block, label each edge in the trellis with distance to the recieved code. then we dijistra to find the shorted path based on those edge distances. training Given observations O, find the model parameters \lambda that maximize P(O|\lambda), the . continuous-density HMM There are some HMMs that blend the discrete timestamps into s. continuous speech Scoring becomes hard because you have to go through and calculate every freaking word. THerefore:

Therefore, we really desire: