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Randomized experiments are widely used to estimate the causal effects of a proposed treatment in many areas of science, from medicine and healthcare to the physical and biological sciences, from the social sciences to engineering, and from public policy to the technology industry. Here we consider situations where classical methods for estimating the total treatment effect on a target population are considerably biased due to confounding network effects, i.e., the fact that the treatment of an individual may impact its neighbors’ outcomes, an issue referred to as network interference or as nonindividualized treatment response. A key challenge in these situations is that the network is often unknown and difficult or costly to measure. We assume a potential outcomes model with heterogeneous additive network effects, encompassing a broad class of network interference sources, including spillover, peer effects, and contagion. First, we characterize the limitations in estimating the total treatment effect without knowledge of the network that drives interference. By contrast, we subsequently develop a simple estimator and efficient randomized design that outputs an unbiased estimate with low variance in situations where one is given access to average historical baseline measurements prior to the experiment. Our solution does not require knowledge of the underlying network structure, and it comes with statistical guarantees for a broad class of models. Due to their ease of interpretation and implementation, and their theoretical guarantees, we believe our results will have significant impact on the design of randomized experiments. 

We consider sparse matrix estimation where the goal is to estimate an n-by-n matrix from noisy observations of a small subset of its entries. We analyze the estimation error of the popularly used collaborative filtering algorithm for the sparse regime. Specifically, we propose a novel iterative variant of the algorithm, adapted to handle the setting of sparse observations. We establish that as long as the number of entries observed at random scale logarithmically larger than linear in n, the estimation error with respect to the entry-wise max norm decays to zero as n goes to infinity, assuming the underlying matrix of interest has constant rank r. Our result is robust to model misspecification in that if the underlying matrix is approximately rank r, then the estimation error decays to the approximation error with respect to the [Formula: see text]-norm. In the process, we establish the algorithm’s ability to handle arbitrary bounded noise in the observations.