For LDA, this trend is much smaller. In out-of-matrix predictions, since predictions are made on new articles, these frequencies do not have an effect on training the model. We now turn to an exploratory analysis of our results on the CTR model. (In the following, the precision λv = 100.)
Examining User Profiles. One advantage of the CTR model is that it can explain the user latent space using the topics learned from the data. For one user, we can find the top matched topics by ranking the entries of her latent vector ui. Table 1 shows two example users and their top 3 matched topics along with their top 10 preferred articles as predicted by the CTR model. The learned topics serve as a summary of what users might be interested in. For user I, we see that he or she might be a researcher working on machine learning and its applications to texts and images. Although the predicted top 10 articles don’t contain a vision article, we see such articles when more articles are retrieved. For user II, he or she might be a researcher who is interested in user interfaces and collaborative filtering.
Examining the Latent Space of Articles. We can also examine the latent space of articles beyond their topic proportions. Here we inspect the articles with the largest overall offsets j . Table 2 shows the top 10 articles with the largest offsets measured by the distance between vj and θj ,  T j j = (vj − θj ) T (vj − θj ). The last two columns show the average of predicted ratings over those users who actually have that article (avg–like) and those users who do not have that article (avg–dislike). These articles are popular in this data. Among the top 50 articles by this measure, 94% of them have at least 50 appearances. Articles with large offsets enjoy readership from different areas, and their item latent vectors have to diverge from the topic proportions to account for this. For example, Figure 7 illustrates the article that is the main citation for the expectation-maximization algorithm, “Maximum likelihood from incomplete data via the EM algorithm” [9]. Its top topic (found by k = arg maxk θjk), is shown as topic 1. It is about “parameter estimation,” which is the main focus of this Topic −0.1 0.0 0.1 0.2 0.3 0.4 0.5 1 2 3 4 5 6 7 8 9 var theta theta correction topic 1: neurons, responses, neuronal, spike, cortical, stimuli, stimulus article. We can also examine the topics that are offset the most, k = arg maxk |jk| = arg maxk |vjk −θjk|. The maximum offset is for topic 10, a topic about “Bayesian statistics.” Topic 10 has a low value in θj—the EM paper is not a Bayesian paper—but readers of Bayesian statistics typically have this paper in their library. Examining the offset can yield the opposite kind of article. For example, consider the article “Phase-of-firing coding of natural visual stimuli in primary visual cortex” in Figure 8. Its most probable topic is topic 1 (about “Computational Neuroscience”). Taking into account the offset, the most probable topic does not change and nor are new topics brought in. This indicates that the offset j only adjusts vj so that the objective function is well minimized. This article is not as interesting to users outside of Neuroscience.