v1.0 of code to infer departures from routine in daily life mobility.

Runs EM algorithm to infer latent variables indicating: (0) user is in routine, or (1) user is departing from routine. Since we use a probabilistic approach, the inferred state of the user at each time step can take any value [0,1] indicating different degrees of departure.

What the code does:

0. generates synthetic data

1. runs the Baum-Welch EM algorithm and plots the convergence properties

2. re-runs 2 times more, to check for other possible maxima on the data log-likelihood surface

3. plots the inferred latent variables indicating departure (blue crosses) and the ground truth (red dots). Also plots the inferred trajectory using the Viterbi algorithm (green vertical dashes)

4. calculates a threshold corresponding to the upper quartile of inferred latent values. Could be fairly easily extended to consider the utility value of false positives, true positives, false negatives, and true negatives. At the moment, we are favouring TP, at the cost of a fair number of FP, with the motivating scenario of prefering to catch more cases of departing from routine than missing them. This results in a fairly high recall (70+ %) at the cost of a lower precision.