Efficient estimation of AUC in a sliding window

In many applications, monitoring area under the ROC curve (AUC) in a sliding window over a data stream is a natural way of detecting changes in the system. The drawback is that computing AUC in a sliding window is expensive, especially if the window size is large and the data flow is significant. In this paper we propose a scheme for maintaining an approximate AUC in a sliding window of length $k$. More specifically, we propose an algorithm that, given $\epsilon$, estimates AUC within $\epsilon / 2$, and can maintain this estimate in $O((\log k) / \epsilon)$ time, per update, as the window slides. This provides a speed-up over the exact computation of AUC, which requires $O(k)$ time, per update. The speed-up becomes more significant as the size of the window increases. Our estimate is based on grouping the data points together, and using these groups to calculate AUC. The grouping is designed carefully such that ($i$) the groups are small enough, so that the error stays small, ($ii$) the number of groups is small, so that enumerating them is not expensive, and ($iii$) the definition is flexible enough so that we can maintain the groups efficiently. Our experimental evaluation demonstrates that the average approximation error in practice is much smaller than the approximation guarantee $\epsilon / 2$, and that we can achieve significant speed-ups with only a modest sacrifice in accuracy

Hidden salt in breads of Blantyre (Malawi) and labelling practices: A national wake-up call

A study was carried out to the determine amount of salt in breads sold in five major retail shops in Blantyre (Malawi). Determined salt concentrations were compared with declared values on labels. In addition, the study also assessed labelling practices among bread manufacturers to check compliance with labelling regulations in Malawi. Six brands of breads were sampled from the five major retail shops. Twelve samples were collected for each of the six brands of bread herein designated as bread 1, bread 2, bread 3, bread 4, bread 5 and bread 6. The study found that average concentration of sodium in the breads ranged from 1.7 g/100 g to 2.6 g/100 g. Significant differences of sodium content were observed in four brands of bread; bread 1, bread 2, bread 4 and bread 5 (p<0.05). No significant difference was observed between bread 3 and bread 6 (p>0.05). None of the sampled breads had declared sodium content. All the breads complied with Malawi requirements for general labelling of breads. However, all the breads did not comply with nutrition labelling guidelines. The study reveals policy gap, in Malawi, on salt reduction in foods. The study also reveals regulation and regulation enforcement gaps that need to be urgently addressed to improve the current situation. Considering the results in this study, the authors recommend that Malawi should develop policies to support reduction of salt in food products such as bread to minimise risks associated with high salt intake. The authors also recommend enforcement of Malawi standard for nutrition labelling by the relevant authorities and a complete national survey to assess understanding of nutrition labelling among manufactures. Furthermore, the authors recommend urgent revision of 1985 Malawi standard for common bread, currently in use, to include sodium content limits as one way of initiating a reduction of sodium content in breads being sold on the market.Keywords: salt reduction, bread, labelling, standard, Malawi, hypertension, sodium, consume