Alisa reviews HMM, EM, and shows us how to combine them.
The EM version treats the transition probabilities (exchanging coins) and emission probabilities (chance of heads/tails under each coin) as unknowns. Make a guess, calculate the blue line from before. This can be used to calculate a new guess that will hill climb to the locally optimum solution (EM).
New guess for the transition probability is:
\[ A_{lk} = \frac{f_i b_i a_{lk} e_k(x_{i+1}) }{P(x)} \]
New guess for the emission probability is just:
\[ \frac{\sum f_i b_i}{P(x)}\]
(example code coming)
Future Topics
Sweave/literate programming, Github – Carl
Large Scale spatial analysis – Yaniv
Bayesian CP analysis – Alisa
Dirchelet process
machine learning: GA/SVM/NN – Dave
Optimal Control/Lagrangian
EC2 / HPC
debug/profile/unit tests/code optimization