document: Recovering latent time-series from their observed sums : network tomography with particle filters . Hidden variables , evolving over time , appear in multiple settings , where it is valuable to recover them , typically from observed sums . Our driving application is ` network tomography ' , where we need to estimate the origin-destination ( OD ) traffic flows to determine , e.g. , who is communicating with whom in a local area network . This information allows network engineers and managers to solve problems in design , routing , configuration debugging , monitoring and pricing . Unfortunately the direct measurement of the OD traffic is usually difficult , or even impossible ; instead , we can easily measure the loads on every link , that is , sums of desirable OD flows . In this paper we propose i-FILTER , a method to solve this problem , which improves the state-of-the-art by ( a ) introducing explicit time dependence , and by ( b ) using realistic , non-Gaussian marginals in the statistical models for the traffic flows , as never attempted before . We give experiments on real data , where i-FILTER scales linearly with new observations and out-performs the best existing solutions , in a wide variety of settings . Specifically , on real network traffic measured at CMU , and at AT&T , i-FILTER reduced the estimation errors between 15 % and 46 % in all cases .
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