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Traditional recommender systems aim to estimate a user's rating to an item based on observed ratings from the population. As with all observational studies, hidden confounders, which are factors that affect both item exposures and user ratings, lead to a systematic bias in the estimation. Consequently, a new trend in recommender system research is to negate the influence of confounders from a causal perspective. Observing that confounders in recommendations are usually shared among items and are therefore multi-cause confounders, we model the recommendation as a multi-cause multi-outcome (MCMO) inference problem. Specifically, to remedy confounding bias, we estimate user-specific latent variables that render the item exposures independent Bernoulli trials. The generative distribution is parameterized by a DNN with factorized logistic likelihood and the intractable posteriors are estimated by variational inference. Controlling these factors as substitute confounders, under mild assumptions, can eliminate the bias incurred by multi-cause confounders. Furthermore, we show that MCMO modeling may lead to high variance due to scarce observations associated with the high-dimensional causal space. Fortunately, we theoretically demonstrate that introducing user features as pre-treatment variables can substantially improve sample efficiency and alleviate overfitting. Empirical studies on simulated and real-world datasets show that the proposed deep causal recommender shows more robustness to unobserved confounders than state-of-the-art causal recommenders. Codes and datasets are released at https://github.com/yaochenzhu/deep-deconf.