I have tried to build a probability model of user's events using Markov process. It is a simple model to calculate the probability of the next events that would occur in the next time step, based on the historical data. It uses the Markov property in which the next state depends only on the current state and not on the sequence of events that preceded it. It assumes the current state has all information from all previous state. This model can generate some results, however I don't think it generates a great result in our problem scenario.
As the labels can be dependent, therefore calculating the next state might require the information of some previous states, not just the current state. For example, we have an event sequence for using Washing Machine (WM). I assume the current state is today, which the WM is used, and we want to calculate the chance that the user will use the WM tomorrow. By applying Markov property, to estimate the probability of using WM tomorrow, we only need the information of the current state, which is the probability of using WM today. This probability is calculated from the historical data.
In a real scenario, using WM at the next state can be dependent on some previous use of WM in the past. Therefore, using Markov process in our model will not give a good result in prediction. However, we can use the model with Markov property as a bench mark to compare with other models, which I will research and implement.
I have read a paper of "A Model for Temporal Dependencies in Event Streams". They try to solve a very similar problem that I am trying to solve. They introduce the Piecewise-Constant Conditional Intensity Model (PCIM) to model the types and timing of events and capture the dependencies of each type of event on events in the past through a set of piecewise-constant conditional intensity functions. The model is very complicated, but I want to implement this model to FigureEnergy data. They apply Bayesian Network Learning in their model, so I will try to read and understand this area more.
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