A set of low-cost sensors is deployed to infer the network topology of a self-organizing wireless network. The sensors operate in a non-invasive fashion, extracting only the timings of data packets and acknowledgment (ACK) packets from all nodes in a network. The meta-data also reports the source node of each packet, but not the destination nodes or the contents of the packets. A central processor collects the meta-data from the sensors, and the goal is for the processor to infer the network topology based solely on such information. Prior work leveraged causality metrics to identify which links are active. If the data timings and ACK timings of two nodes– say node 1 and node 2, respectively– are causally related, this may be taken as evidence that node 1 is communicating to node 2 (which sends back ACK packets to node 1). This paper starts with the observation that packet losses can weaken the causality relationship between data and ACK timing streams. To obviate this problem, a new Expectation Maximization (EM)-based algorithm is introduced– EM-causality discovery algorithm (EM-CDA)– which treats packet losses as latent variables. EM-CDA iterates between the estimation of packet losses and the evaluation of causality metrics. The method is validated through extensive experiments in wireless sensor networks on the NS-3 simulation platform.