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Recommender systems are personalized information systems that learn individual preferences from interacting with users. Recommender systems use machine learning techniques to compute suggestions for the users. Supervised machine learning relies on optimizing for a suitable objective function. Suitability means here that the function actually reflects what users and operators consider to be a good system performance. Most of the academic literature on recommendation is about rating prediction. For two reasons, this is not the most practically relevant prediction task in the area of recommender systems: First, the important question is not how much a user will express to like a given item (by the rating), but rather which items a user will like. Second, obtaining explicit preference information like ratings requires additional actions from the side of the user, which always comes at a cost. Implicit feedback in the form of purchases, viewing times, clicks, etc., on the other hand, is abundant anyway. Very often, this implicit feedback is only present in the form of positive expressions of preference. In this work, we primarily consider item recommendation from positive-only feedback. A particular problem is the suggestion of new items -- items that have no interaction data associated with them yet. This is an example of a cold-start scenario in recommender systems. Collaborative models like matrix factorization rely on interaction data to make predictions. We augment a matrix factorization model for item recommendation with a mechanism to estimate the latent factors of new items from their attributes (e.g. descriptive keywords). In particular, we demonstrate that optimizing the latent factor estimation with regard to the overall loss of the item recommendation task is superior to optimizing it with regard to the prediction error on the latent factors. The idea of estimating latent factors from attributes can be extended to other tasks (new users, rating prediction) and prediction models, yielding a general framework to deal with cold-start scenarios. We also adapt the Bayesian Personalized Ranking (BPR) framework, which is state of the art in item recommendation, to a setting where more popular items are more frequently encountered when making predictions. By generalizing even more, we get Weighted Bayesian Personalized Ranking, an extension of BPR that allows importance weights to be placed on specific users and items. All method contributions are supported by experiments using large-scale real-life datasets from various application areas like movie recommendation and music recommendation. The software used for the experiments has been released as part of an efficient and scalable free software package.