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A new paradigm for wireless sensor networks (WSN) information gathering, called Collaborative Sampling is proposed in this paper. Collaborative Sampling is a distributed active sampling regime that requires that each sensor to coordinate the tasks of data sampling and dissemination through succinct collaboration with neighboring sensor nodes. This is made possible by exploiting the inherent correlation among neighboring sensor measurements. The goal is to minimize energy wasted on transmitting redundant information through wireless channels while ensuring the quality of collected data. Collaborative Sampling entails two parts of key operations: at individual sensor nodes, a model of sensor measurements as a function of space time coordinates are computed based on local sensor measurements and those obtained by overhearing neighboring sensor nodes wireless broadcasting. Sensor nodes collaborate by announcing its local measurements to its neighbors to help build a global function approximation of the sensor measurements over the entire sensor field. To reduce redundant information being broadcast, each sensor node will determine whether announcing its own reading to its neighbors will contribute most to achieve the global goal of function approximation. A probabilistic competitive mechanism, based on the medium access control (MAC) layer carrier sensing multiple access (CSMA) protocol, is developed to allow the sensor nodes that offers most contribution to report their value earlier and thereby speedup the convergence to a solution. Theoretical analysis and simulation results showing that the new algorithm performs as well as the best possible greedy result are provided.