Participatory regression modeling is a cost-efficient mechanism to establish the relationships among multiple dimensions of sensory data collected from volunteers. Getting an accurate model estimate is challenging for two main reasons. First, with the concern of confidentiality of individual private data, the original data are nearly unavailable; second, low quality data with outliers are inherently embedded in the collected data. In this paper, we propose an innovative scheme, PURE, which can accurately estimate the global regression model without the need for knowing local private data (referred to as blind regression modeling) even when there is a large portion of outliers embedded. The wisdom of PURE is to let individual participants peer judge and further improve the global estimate via negotiations. Meanwhile, during the whole process, all information is exchanged in an aggregated way. By design, PURE is secure and can well protect individual privacy. Furthermore, PURE is a lightweight protocol suitable for mobile devices. Extensive trace-driven simulation results show that PURE can achieve an outstanding accuracy gain of two orders of magnitude even with random outliers near a ratio of 50 percent compared with the state-of-the-art least square estimator.

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