dtFall -- Decision-Theoretic Framework to Report Unseen Falls

Automated systems to report falls have long been sought. However, it is very difficult to train classifiers for falls as these are rare events that are difficult to gather training data for. Further, the costs associated with false alarms and missed alarms are not very well known or understood. In this paper, we present a decision-theoretic framework to fall detection (dtFall) that aims to tackle the core problem of when to report a fall, given an arbitrary amount (possibly zero) of training data for falls, and given little or no information about the costs associated with falls. We derive equations for the expected regret (for not using a decision-theoretic approach), and present a novel method to parameterize unseen falls, such that we can accommodate training situations with no fall data. We identify problems with theoretical thresholding to identify falls using decision-theoretic modeling when training data for fall data is absent, and present a modified empirical thresholding technique to handle imperfect models for falls and non-falls. We present results on two activity recognition datasets and show that knowing the difference in the cost between a reported fall and a false alarm is useful, as the cost of false alarm gets bigger this becomes more significant. The results also show that the difference in the cost of between a reported and non-reported fall is not that useful.