In this paper we address the problem of modeling relational data, which appear in many applications such as social network analysis, recommender systems and bioinformatics. Previous studies either consider latent feature based models but disregarding local structure in the network, or focus exclusively on capturing local structure of objects based on latent blockmodels without coupling with latent characteristics of objects. To combine the benefits of the previous work, we propose a novel model that can simultaneously incorporate the effect of latent features and covariates if any, as well as the effect of latent structure that may exist in the data. To achieve this, we model the relation graph as a function of both latent feature factors and latent cluster memberships of objects to collectively discover globally predictive intrinsic properties of objects and capture latent block structure in the network to improve prediction performance. We also develop an optimization transfer algorithm based on the generalized EM-style strategy to learn the latent factors. We prove the efficacy of our proposed model through the link prediction task and cluster analysis task, and extensive experiments on the synthetic data and several real world datasets suggest that our proposed LFBM model outperforms the other state of the art approaches in the evaluated tasks.
: Latent Feature Models are based on matrix or tensor factorization, which learn a distributed representation for each object and each relation, and then make predictions by taking appropriate inner products. Their strength lies in the relative ease of their continuous optimization, and in their excellent predictive performance. The representative model is the Multiplicative Latent Factor Model (MLFM) @cite_1 and the Generalized Latent Factor Model (GLFM) @cite_5 . For example, MLFM includes both the latent class model and the latent distance model as special cases, can somewhat capture both homophily and stochastic equivalence in networks. However, this kinds of latent factor models are often hard to understand and to analyze the learned latent structure. There is a log-linear model with latent features for dyadic prediction in relational data @cite_16 .
@cite_5 @cite_16 @cite_1
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Homophily and stochastic equivalence are two primary features of interest in social networks. Recently, the multiplicative latent factor model (MLFM) is proposed to model social networks with directed links. Although MLFM can capture stochastic equivalence, it cannot model well homophily in networks. However, many real-world networks exhibit homophily or both homophily and stochastic equivalence, and hence the network structure of these networks cannot be modeled well by MLFM. In this paper, we propose a novel model, called generalized latent factor model (GLFM), for social network analysis by enhancing homophily modeling in MLFM. We devise a minorization-maximization (MM) algorithm with linear-time complexity and convergence guarantee to learn the model parameters. Extensive experiments on some real-world networks show that GLFM can effectively model homophily to dramatically outperform state-of-the-art methods. We describe a latent variable model for supervised dimensionality reduction and distance metric learning. The model discovers linear projections of high dimensional data that shrink the distance between similarly labeled inputs and expand the distance between differently labeled ones. The model's continuous latent variables locate pairs of examples in a latent space of lower dimensionality. The model differs significantly from classical factor analysis in that the posterior distribution over these latent variables is not always multivariate Gaussian. Nevertheless we show that inference is completely tractable and derive an Expectation-Maximization (EM) algorithm for parameter estimation. We also compare the model to other approaches in distance metric learning. The model's main advantage is its simplicity: at each iteration of the EM algorithm, the distance metric is re-estimated by solving an unconstrained least-squares problem. Experiments show that these simple updates are highly effective. We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country @math took action @math toward country @math at time @math "---known as dyadic events---in order to form and test theories of international relations. We represent these event data as a tensor of counts and develop Bayesian Poisson tensor factorization to infer a low-dimensional, interpretable representation of their salient patterns. We demonstrate that our model's predictive performance is better than that of standard non-negative tensor factorization methods. We also provide a comparison of our variational updates to their maximum likelihood counterparts. In doing so, we identify a better way to form point estimates of the latent factors than that typically used in Bayesian Poisson matrix factorization. Finally, we showcase our model as an exploratory analysis tool for political scientists. We show that the inferred latent factor matrices capture interpretable multilateral relations that both conform to and inform our knowledge of international affairs. Recommender problems with large and dynamic item pools are ubiquitous in web applications like content optimization, online advertising and web search. Despite the availability of rich item meta-data, excess heterogeneity at the item level often requires inclusion of item-specific "factors" (or weights) in the model. However, since estimating item factors is computationally intensive, it poses a challenge for time-sensitive recommender problems where it is important to rapidly learn factors for new items (e.g., news articles, event updates, tweets) in an online fashion. In this paper, we propose a novel method called FOBFM (Fast Online Bilinear Factor Model) to learn item-specific factors quickly through online regression. The online regression for each item can be performed independently and hence the procedure is fast, scalable and easily parallelizable. However, the convergence of these independent regressions can be slow due to high dimensionality. The central idea of our approach is to use a large amount of historical data to initialize the online models based on offline features and learn linear projections that can effectively reduce the dimensionality. We estimate the rank of our linear projections by taking recourse to online model selection based on optimizing predictive likelihood. Through extensive experiments, we show that our method significantly and uniformly outperforms other competitive methods and obtains relative lifts that are in the range of 10-15 in terms of predictive log-likelihood, 200-300 for a rank correlation metric on a proprietary My Yahoo! dataset; it obtains 9 reduction in root mean squared error over the previously best method on a benchmark MovieLens dataset using a time-based train test data split.