Bayesian Modelling of the Temporal Aspects of Smart Home Activity with Circular Statistics
Typically, when analysing patterns of activity in a smart home environment, the daily patterns of activity are either ignored completely or summarised into a high-level “hour-of-day” feature that is then combined with sensor activities. However, when summ
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Abstract. Typically, when analysing patterns of activity in a smart home environment, the daily patterns of activity are either ignored completely or summarised into a high-level “hour-of-day” feature that is then combined with sensor activities. However, when summarising the temporal nature of an activity into a coarse feature such as this, not only is information lost after discretisation, but also the strength of the periodicity of the action is ignored. We propose to model the temporal nature of activities using circular statistics, and in particular by performing Bayesian inference with Wrapped Normal (WN ) and WN Mixture (WN M) models. We firstly demonstrate the accuracy of inference on toy data using both Gibbs sampling and Expectation Propagation (EP), and then show the results of the inference on publicly available smarthome data. Such models can be useful for analysis or prediction in their own right, or can be readily combined with larger models incorporating multiple modalities of sensor activity.
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Introduction
One of the central hypotheses of a “smart home” is that a number of different sensor technologies may be combined to build accurate models of the Activities of Daily Living (ADL) of its residents. These models can then be used to make informed decisions relating to medical or health-care issues. For example, such models could help by predicting falls, detecting strokes, analysing eating behaviour, tracking whether people are taking prescribed medication, or detecting periods of depression and anxiety. Since 2007, the Centre for Advanced Studies in Adaptive Systems (CASAS) research group has been collecting data from homes with various different sensor layouts and differing numbers of residents (see e.g. [2]). In most of the approaches taken to date [6,7,13], classifiers are learnt which put weights over individual sensors, and then take linear combinations of these weights to produce a decision function for the set of active sensors at any given time. In addition, an extra “hour-of-day” feature is often added, which in some sense attempts to capture the periodic nature of many of the activities under examination. However this can produce undesirable effects, since this is a rather coarse discretisation. This in turn can result in border effects, such as activities that are short-lived but often span an hour boundary. c Springer International Publishing Switzerland 2015 A. Appice et al. (Eds.): ECML PKDD 2015, Part II, LNAI 9285, pp. 279–294, 2015. DOI: 10.1007/978-3-319-23525-7 17
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We propose instead that it is more satisfactory to take a model-based approach, in which the temporally periodic nature of the activities (i.e. circadian or diurnal rhythms) is taken directly into account. A natural framework for this is the area of “circular” statistics [5,9,18], where univariate data is defined on an angular scale, typically the (unit) circle. In addition we suggest that, rather than using frequentist methods to fit circular distributions to the data, a full Bayesian approach wou
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