Polarity detection is a research topic of major interest, with many applications including detecting the polarity of product reviews. However, in some cases, the polarity of the product reviews might not be available while the polarity of the product itself might be, prohibiting the use of any form of fully supervised learning technique. This scenario, while different, is close to that of multiple instance learning (MIL). In this work we propose two new adaptations of support vector machines (SVM) for MIL, θ-MIL, to suit this new scenario, and infer the polarity of products and product reviews. We perform experiments on the proposed methods using the IMDb movie review corpus, and compare the performance of the proposed methods to the traditional SVM for MIL approach. Although we make weaker assumptions about the data, the proposed methods achieve a comparable performance to the SVM for MIL in accurately detecting the polarity of movies and movie reviews.