New Perspectives on the Evaluation of Link Prediction Algorithms for Dynamic Graphs

There is a fast-growing body of research on predicting future links in dynamic networks, with many new algorithms. Some benchmark data exists, and performance evaluations commonly rely on comparing the scores of observed network events (positives) with those of randomly generated ones (negatives). These evaluation measures depend on both the predictive ability of the model and, crucially, the type of negative samples used. Besides, as generally the case with temporal data, prediction quality may vary over time. This creates a complex evaluation space. In this work, we catalog the possibilities for negative sampling and introduce novel visualization methods that can yield insight into prediction performance and the dynamics of temporal networks. We leverage these visualization tools to investigate the effect of negative sampling on the predictive performance, at the node and edge level. We validate empirically, on datasets extracted from recent benchmarks that the error is typically not evenly distributed across different data segments. Finally, we argue that such visualization tools can serve as powerful guides to evaluate dynamic link prediction methods at different levels.

FEIR: Quantifying and Reducing Envy and Inferiority for Fair Recommendation of Limited Resources

In settings such as e-recruitment and online dating, recommendation involves distributing limited opportunities, calling for novel approaches to quantify and enforce fairness. We introduce \emph{inferiority}, a novel (un)fairness measure quantifying a user's competitive disadvantage for their recommended items. Inferiority complements \emph{envy}, a fairness notion measuring preference for others' recommendations. We combine inferiority and envy with \emph{utility}, an accuracy-related measure of aggregated relevancy scores. Since these measures are non-differentiable, we reformulate them using a probabilistic interpretation of recommender systems, yielding differentiable versions. We combine these loss functions in a multi-objective optimization problem called \texttt{FEIR} (Fairness through Envy and Inferiority Reduction), applied as post-processing for standard recommender systems. Experiments on synthetic and real-world data demonstrate that our approach improves trade-offs between inferiority, envy, and utility compared to naive recommendations and the baseline methods.

ReCon: Reducing Congestion in Job Recommendation using Optimal Transport

Recommender systems may suffer from congestion, meaning that there is an unequal distribution of the items in how often they are recommended. Some items may be recommended much more than others. Recommenders are increasingly used in domains where items have limited availability, such as the job market, where congestion is especially problematic: Recommending a vacancy -- for which typically only one person will be hired -- to a large number of job seekers may lead to frustration for job seekers, as they may be applying for jobs where they are not hired. This may also leave vacancies unfilled and result in job market inefficiency. We propose a novel approach to job recommendation called ReCon, accounting for the congestion problem. Our approach is to use an optimal transport component to ensure a more equal spread of vacancies over job seekers, combined with a job recommendation model in a multi-objective optimization problem. We evaluated our approach on two real-world job market datasets. The evaluation results show that ReCon has good performance on both congestion-related (e.g., Congestion) and desirability (e.g., NDCG) measures.

Revised Conditional t-SNE: Looking Beyond the Nearest Neighbors

Conditional t-SNE (ct-SNE) is a recent extension to t-SNE that allows removal of known cluster information from the embedding, to obtain a visualization revealing structure beyond label information. This is useful, for example, when one wants to factor out unwanted differences between a set of classes. We show that ct-SNE fails in many realistic settings, namely if the data is well clustered over the labels in the original high-dimensional space. We introduce a revised method by conditioning the high-dimensional similarities instead of the low-dimensional similarities and storing within- and across-label nearest neighbors separately. This also enables the use of recently proposed speedups for t-SNE, improving the scalability. From experiments on synthetic data, we find that our proposed method resolves the considered problems and improves the embedding quality. On real data containing batch effects, the expected improvement is not always there. We argue revised ct-SNE is preferable overall, given its improved scalability. The results also highlight new open questions, such as how to handle distance variations between clusters.

Topologically Regularized Data Embeddings

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster structure or the fact that the data is known to lie along a tree- or graph-structured topology. However, generic methods to ensure such structure is salient in the low-dimensional representations are lacking. This negatively impacts the interpretability of low-dimensional embeddings, and plausibly downstream learning tasks. To address this issue, we introduce topological regularization: a generic approach based on algebraic topology to incorporate topological prior knowledge into low-dimensional embeddings. We introduce a class of topological loss functions, and show that jointly optimizing an embedding loss with such a topological loss function as a regularizer yields embeddings that reflect not only local proximities but also the desired topological structure. We include a self-contained overview of the required foundational concepts in algebraic topology, and provide intuitive guidance on how to design topological loss functions for a variety of shapes, such as clusters, cycles, and bifurcations. We empirically evaluate the proposed approach on computational efficiency, robustness, and versatility in combination with linear and non-linear dimensionality reduction and graph embedding methods.

A Systematic Evaluation of Node Embedding Robustness

Node embedding methods map network nodes to low dimensional vectors that can be subsequently used in a variety of downstream prediction tasks. The popularity of these methods has significantly increased in recent years, yet, their robustness to perturbations of the input data is still poorly understood. In this paper, we assess the empirical robustness of node embedding models to random and adversarial poisoning attacks. Our systematic evaluation covers representative embedding methods based on Skip-Gram, matrix factorization, and deep neural networks. We compare edge addition, deletion and rewiring strategies computed using network properties as well as node labels. We also investigate the effect of label homophily and heterophily on robustness. We report qualitative results via embedding visualization and quantitative results in terms of downstream node classification and network reconstruction performances. We found that node classification suffers from higher performance degradation as opposed to network reconstruction, and that degree-based and label-based attacks are on average the most damaging.

A challenge-based survey of e-recruitment recommendation systems

E-recruitment recommendation systems recommend jobs to job seekers and job seekers to recruiters. The recommendations are generated based on the suitability of the job seekers for the positions as well as the job seekers' and the recruiters' preferences. Therefore, e-recruitment recommendation systems could greatly impact job seekers' careers. Moreover, by affecting the hiring processes of the companies, e-recruitment recommendation systems play an important role in shaping the companies' competitive edge in the market. Hence, the domain of e-recruitment recommendation deserves specific attention. Existing surveys on this topic tend to discuss past studies from the algorithmic perspective, e.g., by categorizing them into collaborative filtering, content based, and hybrid methods. This survey, instead, takes a complementary, challenge-based approach, which we believe might be more practical to developers facing a concrete e-recruitment design task with a specific set of challenges, as well as to researchers looking for impactful research projects in this domain. We first identify the main challenges in the e-recruitment recommendation research. Next, we discuss how those challenges have been studied in the literature. Finally, we provide future research directions that we consider promising in the e-recruitment recommendation domain.

ExClus: Explainable Clustering on Low-dimensional Data Representations

Dimensionality reduction and clustering techniques are frequently used to analyze complex data sets, but their results are often not easy to interpret. We consider how to support users in interpreting apparent cluster structure on scatter plots where the axes are not directly interpretable, such as when the data is projected onto a two-dimensional space using a dimensionality-reduction method. Specifically, we propose a new method to compute an interpretable clustering automatically, where the explanation is in the original high-dimensional space and the clustering is coherent in the low-dimensional projection. It provides a tunable balance between the complexity and the amount of information provided, through the use of information theory. We study the computational complexity of this problem and introduce restrictions on the search space of solutions to arrive at an efficient, tunable, greedy optimization algorithm. This algorithm is furthermore implemented in an interactive tool called ExClus. Experiments on several data sets highlight that ExClus can provide informative and easy-to-understand patterns, and they expose where the algorithm is efficient and where there is room for improvement considering tunability and scalability.

Adversarial Robustness of Probabilistic Network Embedding for Link Prediction

In today's networked society, many real-world problems can be formalized as predicting links in networks, such as Facebook friendship suggestions, e-commerce recommendations, and the prediction of scientific collaborations in citation networks. Increasingly often, link prediction problem is tackled by means of network embedding methods, owing to their state-of-the-art performance. However, these methods lack transparency when compared to simpler baselines, and as a result their robustness against adversarial attacks is a possible point of concern: could one or a few small adversarial modifications to the network have a large impact on the link prediction performance when using a network embedding model? Prior research has already investigated adversarial robustness for network embedding models, focused on classification at the node and graph level. Robustness with respect to the link prediction downstream task, on the other hand, has been explored much less. This paper contributes to filling this gap, by studying adversarial robustness of Conditional Network Embedding (CNE), a state-of-the-art probabilistic network embedding model, for link prediction. More specifically, given CNE and a network, we measure the sensitivity of the link predictions of the model to small adversarial perturbations of the network, namely changes of the link status of a node pair. Thus, our approach allows one to identify the links and non-links in the network that are most vulnerable to such perturbations, for further investigation by an analyst. We analyze the characteristics of the most and least sensitive perturbations, and empirically confirm that our approach not only succeeds in identifying the most vulnerable links and non-links, but also that it does so in a time-efficient manner thanks to an effective approximation.