###### Markov model state topology Link to heading

The second piece of coursework for my speech & audio processing & recognition module was focused on the machine learning side of the field. One of the main methods we learnt about were **Hidden Markov Models** and how to train them, this coursework was a test of the theory. My submission achieved 98%.

###### Re-estimated probability density function outputs after training Link to heading

The provided spec for the model included the **entry, exit** and **transition** probabilities, the parameters for each state’s **Gaussian output** function and the observations used for training.

From here, the coursework tested the ability to calculate and analyse various aspects of the model including **forward, backward, occupation** and **transition** likelihoods. A single iteration of **Baum-Welch**-based training was completed resulting in a new set of **transition** probabilities and **output function parameters**.

###### Probability of being in each state at each time step or observation Link to heading

The above graph is presenting the **occupation likelihoods** of each state at each time step or observation. It is the joint probability from the forward and backward likelihoods. From here it looks like the observations were taken from state 2 for 3 time-steps before swapping to state 1 for 4 time-steps and changing back to state 2 for the last one.