Apply Poisson process on FE labels

A Poisson process (PPs) is a collection {N(t), t>=0} of random variables, where N(t) is the number of events that have occured up to time t (starting from time 0). By using PPs, we can calculate the probablity of actual number of events that would be occured in the given period.

In our scenario, we have a list of the data of the events, which annotated by users using the FigureEnergy system. We want to use PPs to calculate the probability that event will be occured in the next time period (typically in daily unit). If the probability of the event to be occured is high (greater than 70%), we can ask the users to confirm the information. Then, we will be able to run the optimisation problem of minimising the carbon intensity, then we can send feedback to users by advising them using the events in the appropriate time.

To do that, firstly we filter all labels of the specific user. Then, we calculate the mean number of events per day. After that, we use PPs to calculate the probability of no labels which would be occureed in the next 24 hours. The results of the few users can be seen as follows:

From the graph above, we can tell the events that will be like occured in the next 24 hours. For example, for user "ecenergy39", the probability of using TV and Kettle in the next 24 hours are very high (greater than 80%).

Next step, I will check the accurate of the PPs prediction on the real FE data.