Estimating latent feature-feature interactions in large feature-rich graphs

Real-world complex networks describe connections between objects; in reality, those objects are often endowed with some kind of features. How does the presence or absence of such features interplay with the network link structure? Although the situation here described is truly ubiquitous, there is a limited body of research dealing with large graphs of this kind. Many previous works considered homophily as the only possible transmission mechanism translating node features into links. Other authors, instead, developed more sophisticated models, that are able to handle complex feature interactions, but are unfit to scale to very large networks. We expand on the MGJ model, where interactions between pairs of features can foster or discourage link formation. In this work, we will investigate how to estimate the latent feature-feature interactions in this model. We shall propose two solutions: the first one assumes feature independence and it is essentially based on Naive Bayes; the second one, which relaxes the independence assumption assumption, is based on perceptrons. In fact, we show it is possible to cast the model equation in order to see it as the prediction rule of a perceptron. We analyze how classical results for the perceptrons can be interpreted in this context; then, we define a fast and simple perceptron-like algorithm for this task, which can process 108108 links in minutes. We then compare these two techniques, first with synthetic datasets that follows our model, gaining evidence that the Naive independence assumptions are detrimental in practice. Secondly, we consider a real, large-scale citation network where each node (i.e., paper) can be described by different types of characteristics; there, our algorithm can assess how well each set of features can explain the links, and thus finding meaningful latent feature-feature interactions

Non-parametric Bayesian modeling of complex networks

Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to non-parametric Bayesian modeling of complex networks: Using an infinite mixture model as running example we go through the steps of deriving the model as an infinite limit of a finite parametric model, inferring the model parameters by Markov chain Monte Carlo, and checking the model's fit and predictive performance. We explain how advanced non-parametric models for complex networks can be derived and point out relevant literature

Holographic Embeddings of Knowledge Graphs

Learning embeddings of entities and relations is an efficient and versatile method to perform machine learning on relational data such as knowledge graphs. In this work, we propose holographic embeddings (HolE) to learn compositional vector space representations of entire knowledge graphs. The proposed method is related to holographic models of associative memory in that it employs circular correlation to create compositional representations. By using correlation as the compositional operator HolE can capture rich interactions but simultaneously remains efficient to compute, easy to train, and scalable to very large datasets. In extensive experiments we show that holographic embeddings are able to outperform state-of-the-art methods for link prediction in knowledge graphs and relational learning benchmark datasets.Comment: To appear in AAAI-1

Multi-Target Prediction: A Unifying View on Problems and Methods

Multi-target prediction (MTP) is concerned with the simultaneous prediction of multiple target variables of diverse type. Due to its enormous application potential, it has developed into an active and rapidly expanding research field that combines several subfields of machine learning, including multivariate regression, multi-label classification, multi-task learning, dyadic prediction, zero-shot learning, network inference, and matrix completion. In this paper, we present a unifying view on MTP problems and methods. First, we formally discuss commonalities and differences between existing MTP problems. To this end, we introduce a general framework that covers the above subfields as special cases. As a second contribution, we provide a structured overview of MTP methods. This is accomplished by identifying a number of key properties, which distinguish such methods and determine their suitability for different types of problems. Finally, we also discuss a few challenges for future research