Modelling discussion

 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.

Mathematical model for event prediction

Predicting user's activities is not an easy task. Specifically, the activities themselves are dependent to each other, and the information of activities are given in uncertain ways (i.e., it is hard to get fully correct information of events in reality).

Previously, I have tried Poisson processes to predict user's events, however it has been uncesseful model as the events are independents in Poisson process. Continuing researching for an appropirate model, I have had a good chat with Long about a model, still using Markov process. I think we came with an appealing model, which also works for dependent data. I am implementing the model with the data collected from the FigureEnergy system, however there is not enough information to conclude this model. For further testing, I will test it with a large appropriate data, which are released by MIT. Thanksfully the data can be obtained from Oli. I will try to implement this model asap for further analysis.

Then, I will have to define a scenario in a formal mathematical way, then an existing model will be chosen to implement as a benchmark for future comparison. In addition, the paper of "A model for Temporal Dependencies in Event Streams" will be needed to read and understand as well.

A quick update of my work.

In the last meeting, we discovered that the Poisson process is not  a good model to apply in our scenario. It considers events are independent, while they are dependent in our case. Therefore, I need to switch to another appealing model, which should be done before 01 January 2012.

The strategy is to looking for models which work with dependent data. In addition, I need to gain much knowledge about machine learning and other mathematical models, so I am able to judge and select the right one.

I kick off with the paper of "Unsupervised Disaggregation of Low Frequency Power Measurements", which has been given by Oli. The paper mainly discusses the effectiveness of several unsupervised disaggregation methods using the factorial hidden Markov model on low frequency power measurements collected in real homes. In their model, the states of appliances are the hidden variables, and the aggregate power load is the observation. Therefore, they chose variants of Hidden Markov Model (HMM). More specially, they extend a Conditional Factorial Hidden Semi-Markov Model (CFHSMM), which allows the model to consider the dependencies between appliances and the dependencies on additional features, that I think is quite relevant to our case. Then, they apply machine learning process to estimate the parameters from the observations, and the hidden variables (which is the states of the appliances). Specifically, they use Expectation-Maximization algorithm (EM) to estimate the parameters, then using Maximum Likelihood Estimation (MLE) to estimate the hidden states.

In our case, the events are possibly annotated by users. So, I think Hidden Semi-Markov models could be used. I will check more references paper on CFHSMM to see if there is any relevant existing models.

Furthermore, I have grasped some book to read with the hope to have a better overal view on machine learning models. I will check out this list:

- Chapter 9: Mixture Models and EM (423-455) (book " Pattern Recognition and Machine Learning" - Christopher M. Bishop).

- Chapter 6: Bayesian Learning (154-199) (book: "Machine Learning" - Tom M. Mitchell).

Poisson Process prediction vs the actual data

In this post, I do some comparison between the actual events that used by the given user, and the predictive events using by PPs. I firstly take 14 training days to calculate the mean number of event types. From the given event file, there is only user ecenergy39 that has the maximum historical data of 17 days, therefore I only use this user to generate the results.

As you can see from the above graph, by using 14 days as a training period, TV and Kettle are predicted to occur in the next 24 hours with the probability very high, approximately 80%. The actual results show that TV event has been annotated for 4 times, while "kettle" event has been annotated for 1 times.

Then, we use 15 days as a training period to predict the events occured in the next 24 hours. The result is below:

The process is repeated for the 17th day, with the result as follows:

As we all know that the data of events are collected from the real experiment, where users manually annotated the information of the event. Therefore, the data itself has so much noise. We need to think of the solution of increase the accuracy of the event information. The direction could be automatically recognise the pattern of the events.

User's Average Day Calculation (with more user's data)

I have been given more user's data of energy consumption, therefore I plotted again the average day for some specific users between the weekdays and weekend days. The following graphs show some results:

With more data, the gap of energy consumed between the weekdays and the weekend days has become maller, and look regularly.

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.

Meeting on 25 November 2011.

Pre-meeting notes on 25 Nov 2011.

1 – Tasks have been tackled:

·         Calculated and plotted user consumption in average day again in week days and weekend days. Different users show a different result. Interestingly, there is a correlation of consuming energy between the weekday and weekend days for the same user in average day.

·         Plotted frequency of labels per day for both single users and all users.

·         Have done some reaching on Google scholar about event prediction and faults in machinery. I think I have obtained some nice papers but have not read them all.

·         Have read about Poisson process in the wiki. In addition, I have researched more tutorials and sections talking about Poisson process. I have gone through some examples and have understood some basic principles to apply to our case. Furthermore, I have prepared some calculation in draft to calculate the probability of events to appear at the given time step t. However, I have not yet successfully implemented in Matlab to generate the graph.

·         Have chatted with Rama about the problem that I am trying to tackle. I found it is hard to describe the issue in email, therefore I talked to him instead. The talk was just around events prediction and how to improve the event information as well as the prediction. He suggested some nice things, I summarise a few key things as follows:

·         As each event has its own energy usage. By using FE, the user annotates the event from the past history. By using this way, the information given from the user would have so much noise, and it is hard to tell the exact amount of energy that event would consume. Therefore, we should have a method to improve the certainty of event information. At the time being, I just assume that the events in FE would show the right information, including the time period and the usage of events.

·         Having predicted the events for a day ahead (I suppose this could be done by using Poisson process), how the agent system can improve the event prediction.

·         The optimisation of machine learning will focus on minimise both aggregate demand and events time.

·         Attended the probability course, which has been started intensively for 2 weeks.

2 – Remaining tasks:

·         Detect events based on peaks.

·         Read 1-2 related papers

·         Find existing work or models to apply to our situation.

·         Prepare emails to Steve Reece. (Not sure what I should say in here)

After meeting discussion:

3 – Next tasks:

·         Look, understand and implement Poisson distribution. Particularly, understand likelihood, Bayesian inference and confidence interval.

·         During the meeting, I and Enrico have a discussion about making a prediction of the specific event at the specific time. In my opinion, I think if we can predict the event at the specific time, then we can have an optimisation problem by minimising the carbon intensity based on scheduling the events. After that, this scheduling will be suggested to users. However, it could be impossible to correctly predict the events at the given time as they are controlled by the real human.

An alternative option is to predict the event to be happened in the next 24 hours, then we could make a suggestion to users to run the event at the other time to minimise the carbon intensity. The event with the probability is higher than 80% will be selected to suggest to users. Furthermore, we can calculate the difference between the worst case and the best case to advise users more effectively. However, how to run the optimisation without knowing the time, I am still not clear.