Throughout the last decade, random forests have established themselves as among the most accurate and popular supervised learning methods. While their black-box nature has made their mathematical analysis difficult, recent work has established important statistical properties like consistency and asymptotic normality by considering subsampling in lieu of bootstrapping. Though such results open the door to traditional inference procedures, all formal methods suggested thus far place severe restrictions on the testing framework and their computational overhead precludes their practical scientific use. Here we propose a permutation-style testing approach to formally assess feature significance. We establish asymptotic validity of the test via exchangeability arguments and show that the test maintains high power with orders of magnitude fewer computations. As importantly, the procedure scales easily to big data settings where large training and testing sets may be employed without the need to construct additional models. Simulations and applications to ecological data where random forests have recently shown promise are provided.

The traditional social recommendation algorithm ignores the following fact: the preferences of users with trust relationships are not necessarily similar, and the consideration of user preference similarity should be limited to specific areas. A social trust and preference segmentation-based matrix factorization (SPMF) recommendation system is proposed to solve the above-mentioned problems. Experimental results based on the Ciao and Epinions datasets show that the accuracy of the SPMF algorithm is significantly higher than that of some state-of-the-art recommendation algorithms. The proposed SPMF algorithm is a more accurate and effective recommendation algorithm based on distinguishing the difference of trust relations and preference domain, which can support commercial activities such as product marketing.

Training generative adversarial networks (GANs) often suffers from cyclic behaviors of iterates. Based on a simple intuition that the direction of centripetal acceleration of an object moving in uniform circular motion is toward the center of the circle, we present the Simultaneous Centripetal Acceleration (SCA) method and the Alternating Centripetal Acceleration (ACA) method to alleviate the cyclic behaviors. Under suitable conditions, gradient descent methods with either SCA or ACA are shown to be linearly convergent for bilinear games. Numerical experiments are conducted by applying ACA to existing gradient-based algorithms in a GAN setup scenario, which demonstrate the superiority of ACA.

Although sentiment analysis has attracted a lot of research, little work has been done on social media data compared to product and movie reviews. This is due to the low accuracy that results from the more informal writing seen in social media data. Currently, most of sentiment analysis tools on social media choose the lexicon-based approach instead of the machine learning approach because the latter requires the huge challenge of obtaining enough human-labeled training data for extremely large-scale and diverse social opinion data. The lexicon-based approach requires a sentiment dictionary to determine opinion polarity. This dictionary can also provide useful features for any supervised learning method of the machine learning approach. However, many benchmark sentiment dictionaries do not cover the many informal and spoken words used in social media. In addition, they are not able to update frequently to include newly generated words online. In this paper, we present an automatic sentiment dictionary generation method, called Constrained Symmetric Nonnegative Matrix Factorization (CSNMF) algorithm, to assign polarity scores to each word in the dictionary, on a large social media corpus — digg.com. Moreover, we will demonstrate our study of Amazon Mechanical Turk (AMT) on social media word polarity, using both the human-labeled dictionaries from AMT and the General Inquirer Lexicon to compare our generated dictionary with. In our experiment, we show that combining links from both WordNet and the corpus to generate sentiment dictionaries does outperform using only one of them, and the words with higher sentiment scores yield better precision. Finally, we conducted a lexicon-based sentiment analysis on human-labeled social comments using our generated sentiment dictionary to show the effectiveness of our method.