Predicting human behaviour from smart-house data is an active and challenging area of research. Applications include improving quality of life and personal healthcare, e.g. smart thermostats and detecting falls. Smart-house technology is becoming increasingly popular and in many cases making a house smarter is as simple as installing off-the-shelf devices. In this paper we focus on predicting the future location of a person in a simulated smart-house environment. We consider three different occupant types who exhibit various working patterns. We develop a versatile model capable of adjusting to significant changes in a person's behaviour without the need of model retraining. To this end, we build a simple event calculus framework based on the Aleph Inductive Logic Programming system. Event calculus helps to handle time and persisting sensor states. Background knowledge encodes important information about the smart-house that is otherwise difficult to learn; it also facilitates transferability of the model to different house layouts. Moreover, rule models are white-box, hence human-readable. Finally, we show that a versatile model performs significantly better than other models that do not explicitly account for the context.
We consider the problem of controlling a heating system in a living room based on
behaviour and location of a resident. We want to predict a resident’s location
half-anhour in advance – the time needed to preheat the room. The majority of off-the-shelf
thermostats have a one-day resolution, with only two modes available: working day and
free day; where each setting allows two different temperature change points: present
and absent from the house. Companies such as Nest have built thermostats that “learn”
daily routines from repetitive, manual temperature adjustments. However, such systems
perform poorly on households with unstructured and irregular working patterns, which
are increasingly common these days. Hence there is a need for smart thermostats [
In most cases, smart-house data appears in the form of a time series consisting of
sensor activations. The events are usually unevenly spaced through time, as they are
caused by a change in sensor state. This property of time in our data causes
representational difficulties well-known in logic. To overcome this issue we use Simple Event
Calculus [
In this paper we consider a simple scenario of a house with two rooms, referred to as
the ‘toy example’. We focus on predicting not being in a selected room, living_room,
during the next time block (as this would allow temporarily switching off the heating).
To this end, we build vanilla and versatile rule-based models and show that the
latter achieves top-ranked performance regardless of context of operation (working
pattern) [
The remaining part of this work has the following structure. In Section 2 we present related work. Section 3 gives mathematical definition of the problem. In Section 4 we describe the data that we use, together with their generation, preprocessing and feature construction steps. Section 5 presents trained models and discusses their performance. Finally, Section 6 summaries our work and explores possibilities for future research. 2
Developing models that recognise Activities of Daily Living in a smart-house setting is
a well studied subject. [
To summarise, most work done in the area of rule-based system applications share one feature: the systems are hand-crafted. Moreover, none of them take context of operation under consideration; this may result in poor performance during deployment, if the problem setting has changed after the training data was collected. In this work we build a solution taking the best of both worlds: it uses the richness of background knowledge formulated by an expert (otherwise difficult to learn); and creates a universal model using context awareness to get top-performing location prediction. 3
We assume that a smart-house fitted with n motion sensors at each time point t provides a feed of boolean (on/off) data in the form of a binary vector xt = (xt1; : : : ; xtn), where xti 2 f0; 1g represents the state of a sensor i at time t. These observable events xt for t 2 [1; T ] create a sequence [x1; : : : ; xt ] 2 X – a smart-house state over time.
Furthermore, this sequence can be divided into a series of consecutive non-observable blocks by a series of time points [m; : : : ; z]: B = [B1m; : : : ; BzT ] for 1 < m < z < T ; where a block Bab is defined as Bab = [xa; : : : ; xb] for 1 < a < b < T . Each block can be characterised by some unique label Lab = L(Bab) from a finite set of labels L . In the toy example L = fsleep; work; leisureg.
Additionally, a sub-sequence of events [xr; : : : ; xs] for some 1 r < s T occurs in an implicit, non-observable context Crs = C([xr; : : : ; xs]). We assume that every complete sequence [x1; : : : ; xT ] is a mixture of several contexts. In our example, possible contexts are C = fworking_day; working_night; working_morning; working_afternoon; free_dayg.
Due to the above property of our data, a na¨ıvely fitted model would implicitly
depend on the sequence of contexts. Such a model is therefore ineffective, if in
deployment the context is not as expected. To remedy this, we propose to use a versatile model
that can adapt to constantly changing contexts, therefore providing accurate predictions
throughout [
Finally, we define the binary target variable to be yt 2 f0; 1g – where [y1; : : : ; yT ] 2 Y ; and yt indicates not being in a selected room (living_room) in the next t + d time block, for d > 0. In the toy example we fix d = 1. With the input space X as defined above, our data are represented as D X Y and we want to learn a function f : X ! Y describing these data.
In the smart-house scenario presented above the versatile model output yt+1 = f ([x1; : : : ; xt ]) = versatile model(Ctt ; [x1; : : : ; xt ]), which is a function of partially observed data sequence [x1; : : : ; xt ] and the current context Ctt . As we observe larger parts of this sequence, our predictions should improve given that we have correctly identified the context. This model requires two predictions: the current context Ctt , dependent on the block structure in the data; and the label yt+1. As the latter is dependent on the former it has to be learnt first, as a separate task. Once the context predicate is in place, it is used together with the partial observations [x1; : : : ; xt ] to predict the label yt+1. The two learning tasks are separate: they access the same information (background knowledge and features), but different examples are provided for each task: the first one uses the day type, the latter requires the future location of a subject.
For the problem defined above we want to show that a vanilla model performs quite well on the data whenever the implicit context does not change. However, once it changes the vanilla model’s performance drops significantly, while a versatile model performance is resistant to such variations. 4
In this work, we build and evaluate our models using artificially generated data. This
choice is motivated by a wide range of issues – not directly related to the variable
context time series completion – that we experienced while working on real-life data
sets collected by the CASAS group [
To generate the datasets necessary for this study, we implemented a highly
customisable, stochastic smart-house simulator. The simulator takes house layout, sensors
location and configuration, and high-level description of actions for the simulated agent
as an input. This design guarantees each simulation to produce unique data for a strictly
defined smart-house setting [
The toy example house has two rooms: living_room and bedroom, each one fitted with a single motion sensor. Moreover, rather than using 24-hour day we discretise each one into 12 distinctive time blocks. Then a week of data is generated for each of the three working patterns. The data described here are simple to interpret and small enough to facilitate quick model construction and evaluation, yet they exhibit all the necessary characteristics of the variable context time sequence completion problem.
Spatio-temporal data generated by a smart-house pose representation issues, mainly
due to the time variable being unbounded and sensor events occurring in a single time
point, but causing a change persisting through time. These properties lead naturally to
the use of Simple Event Calculus, which addresses all of the above issues [
Rules extracting features from the raw sensor state data are the most important building block of any rule-based system. Most of our features are location-based: either current or one of the previous locations, e.g. being present or absent in a room, visiting a room in a fixed length sliding time window or a sequence of visited rooms. Time-based features extract useful information from a UNIX timestamp e.g. date, time, time of the day, day of the week and season of the year.
Finally, we use five different contexts: working_day, working_night, working_morning, working_afternoon and free_day. They indicate different types of a day, mixture of which creates one of the three different working patterns. In the normal (full-time) pattern a typical working day consists of basic morning activities, 8 hours of work, followed by a leisure time and 8 hours of sleep. A typical free day consists mainly of leisure activities and having a night out. In the part-time pattern the free days are exactly the same as above, but working days are either working mornings or working afternoons where the work period is reduced to 4 hours and the remaining 4 hours are allocated with leisure activities. In the shifts pattern the free days are again the same as above, however they can appear during the weekdays. Additionally, there are two types of work patterns: working days which are exactly the same as in the normal working schedule and working nights – mirror image of working days. 5
The main goal of our work is to show the importance of versatile models in complex scenarios like smart-house location and activity prediction. Non-versatile models learn and use implicit information about the house layout, number of residents and lifestyle patterns. A model performing well on one person’s house is not guaranteed to have similar performance on a different house. A versatile model can handle multiple contexts without retraining – features in such models need to generalise well by using markers specific to given routines rather than fixed time points.
A major advantage of ILP rule-based systems is the white-box nature of the produced model. This gives the user a chance to understand his behaviour by simply inspecting the model, or tweak it whenever necessary by changing the background knowledge. If a person moves from one house to another and does not change living habits, a model once learnt can be reused in the new environment by simply changing sensors bindings in the background knowledge file. Additionally, background knowledge can be used to “inform” the model about the learning problem properties, which with any other learning system would have to be inferred first.
Below we present two model types: vanilla and versatile; we also compare and contrast them against majority class classification. For comparison, we use data for all 3 working patterns as well as merged: 3-weeks long data where each week comes from a different working pattern. Additionally, we use 3-weeks long data where number of days from every context is the same as in merged data but the order is shuffled – we call it shuffled. Results for the toy example are presented in Table 1; they give accuracies (in %) averaged over 3 different realisations of given working pattern under the same distribution (the agent script and the house layout).
A vanilla (non-versatile) model does not use latent contextual information encoded in the data. Each of Normal, Shift and Part models were trained on a single context data; Merged rule list was train with the data containing all 3 contexts (see merged data description).
Given our features, the most basic vanilla model learnt by Aleph is highly dependent on the time structure of the series (Example 1). Due to the repetitive patterns in the data, the model memorises what happened during each day of the week at given time of the day therefore performing well on the data from the same working pattern distribution. However, this model does not perform equally well when working patterns change e.g. Monday for the normal working person is no longer a working day but it is a free day.
not_visiting_room_in_the_next_time_block(living_room,A):holdsAt(day_number(1),A), holdsAt(time_block(3),A), holdsAt(in_room(bedroom),A).
A versatile model identifies patterns and parametrises them based on the context. Most of the patterns in our data are variations in time structure of the same events. Therefore, such model learns structure of sequences in given context, rather than its detailed dependence on time. The versatile model always outperforms self-learnt rules for each of the 3 working patterns. Additionally, it performs very close to the Vanilla model on merged data and it does not suffer significant loss in accuracy for the shuffled data. This 7% drop in performance is mostly caused by the context rule not always correctly recognising the type of the day from the partial data it gets.
not_visiting_room_in_the_next_time_block(living_room,A):context(working_day,A), holdsAt(time_block(6),A), holdsAt(not_in_room(living_room),A).
Wilcoxon signed-rank test comparing the versatile with merged and self-learnt models for the toy dataset shows that the versatile model significantly outperforms the other two. The test rejects the null-hypothesis that the results come from the same distribution with p-values 10 18 for versatile vs. merged, and 10 52 for versatile vs. self-learnt. 6
The work presented in this paper shows the importance of (often implicit) context in which our data is collected. Moreover, we showed that context is not always a monolithic object: it can usually be divided into smaller entities. Furthermore, we demonstrated the utility of the event calculus framework in logic when handling spatio-temporal data, and that it can be implemented in Aleph. We also presented the design of a simple versatile model. Finally, we showed that by recognising context, the model does not suffer significant loss in performance when the operating context changes, therefore avoiding time and resources expensive retraining phase.
In future work we plan to study the variable context time sequence completion problem in more detail using real-life datasets. While working with real data we aim to address the issues identified and described in Section 4. This will enable us to evaluate both vanilla and versatile models on these large scale datasets and further investigate the advantages of our approach. Last but not least, we will compare our rule-based approach with any state-of-the-art propositional learner.