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In online advertising, response prediction is the problem of estimating the probability that an advertisement is clicked when displayed on a content publisher's webpage. In this paper, we show how response prediction can be viewed as a problem of matrix completion, and propose to solve it using matrix factorization techniques from collaborative filtering (CF). We point out the two crucial differences between standard CF problems and response prediction, namely the requirement of predicting probabilities rather than scores, and the issue of confidence in matrix entries. We address these issues using a matrix factorization analogue of logistic regression, and by applying a principled confidence-weighting scheme to its objective. We show how this factorization can be seamlessly combined with explicit features or side-information for pages and ads, which let us combine the benefits of both approaches. Finally, we combat the extreme sparsity of response prediction data by incorporating hierarchical information about the pages and ads into our factorization model. Experiments on three very large real-world datasets show that our model outperforms current state-of-the-art methods for response prediction.