Factorization machines are a generic framework which allows to mimic many factorization models simply by feature engineering. In this way, they combine the high predictive accuracy of factorization models with the flexibility of feature engineering. Unfortunately, factorization machines involve a non-convex optimization problem and are thus subject to bad local minima. In this paper, we propose a convex formulation of factorization machines based on the nuclear norm. Our formulation imposes fewer restrictions on the learned model and is thus more general than the original formulation. To solve the corresponding optimization problem, we present an efficient globally-convergent two-block coordinate descent algorithm. Empirically, we demonstrate that our approach achieves comparable or better predictive accuracy than the original factorization machines on 4 recommendation tasks and scales to datasets with 10 million samples.

Our findings may provide information to help clinicians make timely interventions to avoid MAs.

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This paper presents a method for designing semi-supervised classifiers trained on labeled and unlabeled samples. We focus on probabilistic semi-supervised classifier design for multi-class and single-labeled classification problems, and propose a hybrid approach that takes advantage of generative and discriminative approaches. In our approach, we first consider a generative model trained by using labeled samples and introduce a bias correction model, where these models belong to the same model family, but have different parameters. Then, we construct a hybrid classifier by combining these models based on the maximum entropy principle. To enable us to apply our hybrid approach to text classification problems, we employed naive Bayes models as the generative and bias correction models. Our experimental results for four text data sets confirmed that the generalization ability of our hybrid classifier was much improved by using a large number of unlabeled samples for training when there were too few labeled samples to obtain good performance. We also confirmed that our hybrid approach significantly outperformed generative and discriminative approaches when the performance of the generative and discriminative approaches was comparable. Moreover, we examined the performance of our hybrid classifier when the labeled and unlabeled data distributions were different.

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