Diverse Weighted Bipartite b-Matching

Bipartite matching, where agents on one side of a market are matched to agents or items on the other, is a classical problem in computer science and economics, with widespread application in healthcare, education, advertising, and general resource allocation. A practitioner's goal is typically to maximize a matching market's economic efficiency, possibly subject to some fairness requirements that promote equal access to resources. A natural balancing act exists between fairness and efficiency in matching markets, and has been the subject of much research. In this paper, we study a complementary goal---balancing diversity and efficiency---in a generalization of bipartite matching where agents on one side of the market can be matched to sets of agents on the other. Adapting a classical definition of the diversity of a set, we propose a quadratic programming-based approach to solving a supermodular minimization problem that balances diversity and total weight of the solution. We also provide a scalable greedy algorithm with theoretical performance bounds. We then define the price of diversity, a measure of the efficiency loss due to enforcing diversity, and give a worst-case theoretical bound. Finally, we demonstrate the efficacy of our methods on three real-world datasets, and show that the price of diversity is not bad in practice

Graph-based Model for Beam Management in Mmwave Vehicular Networks

Mmwave bands are being widely touted as a very promising option for future 5G networks, especially in enabling such networks to meet highly demanding rate requirements. Accordingly, the usage of these bands is also receiving an increasing interest in the context of 5G vehicular networks, where it is expected that connected cars will soon need to transmit and receive large amounts of data. Mmwave communications, however, require the link to be established using narrow directed beams, to overcome harsh propagation conditions. The advanced antenna systems enabling this also allow for a complex beam design at the base station, where multiple beams of different widths can be set up. In this work, we focus on beam management in an urban vehicular network, using a graph-based approach to model the system characteristics and the existing constraints. In particular, unlike previous work, we formulate the beam design problem as a maximum-weight matching problem on a bipartite graph with conflicts, and then we solve it using an efficient heuristic algorithm. Our results show that our approach easily outperforms advanced methods based on clustering algorithms

Balancing Relevance and Diversity in Online Bipartite Matching via Submodularity

In bipartite matching problems, vertices on one side of a bipartite graph are paired with those on the other. In its online variant, one side of the graph is available offline, while the vertices on the other side arrive online. When a vertex arrives, an irrevocable and immediate decision should be made by the algorithm; either match it to an available vertex or drop it. Examples of such problems include matching workers to firms, advertisers to keywords, organs to patients, and so on. Much of the literature focuses on maximizing the total relevance---modeled via total weight---of the matching. However, in many real-world problems, it is also important to consider contributions of diversity: hiring a diverse pool of candidates, displaying a relevant but diverse set of ads, and so on. In this paper, we propose the Online Submodular Bipartite Matching (\osbm) problem, where the goal is to maximize a submodular function $f$ over the set of matched edges. This objective is general enough to capture the notion of both diversity (\emph{e.g.,} a weighted coverage function) and relevance (\emph{e.g.,} the traditional linear function)---as well as many other natural objective functions occurring in practice (\emph{e.g.,} limited total budget in advertising settings). We propose novel algorithms that have provable guarantees and are essentially optimal when restricted to various special cases. We also run experiments on real-world and synthetic datasets to validate our algorithms.Comment: To appear in AAAI 201

Recommender Systems

The ongoing rapid expansion of the Internet greatly increases the necessity of effective recommender systems for filtering the abundant information. Extensive research for recommender systems is conducted by a broad range of communities including social and computer scientists, physicists, and interdisciplinary researchers. Despite substantial theoretical and practical achievements, unification and comparison of different approaches are lacking, which impedes further advances. In this article, we review recent developments in recommender systems and discuss the major challenges. We compare and evaluate available algorithms and examine their roles in the future developments. In addition to algorithms, physical aspects are described to illustrate macroscopic behavior of recommender systems. Potential impacts and future directions are discussed. We emphasize that recommendation has a great scientific depth and combines diverse research fields which makes it of interests for physicists as well as interdisciplinary researchers.Comment: 97 pages, 20 figures (To appear in Physics Reports

Combinatorial Network Optimization with Unknown Variables: Multi-Armed Bandits with Linear Rewards

In the classic multi-armed bandits problem, the goal is to have a policy for dynamically operating arms that each yield stochastic rewards with unknown means. The key metric of interest is regret, defined as the gap between the expected total reward accumulated by an omniscient player that knows the reward means for each arm, and the expected total reward accumulated by the given policy. The policies presented in prior work have storage, computation and regret all growing linearly with the number of arms, which is not scalable when the number of arms is large. We consider in this work a broad class of multi-armed bandits with dependent arms that yield rewards as a linear combination of a set of unknown parameters. For this general framework, we present efficient policies that are shown to achieve regret that grows logarithmically with time, and polynomially in the number of unknown parameters (even though the number of dependent arms may grow exponentially). Furthermore, these policies only require storage that grows linearly in the number of unknown parameters. We show that this generalization is broadly applicable and useful for many interesting tasks in networks that can be formulated as tractable combinatorial optimization problems with linear objective functions, such as maximum weight matching, shortest path, and minimum spanning tree computations

Temporal similarity metrics for latent network reconstruction: The role of time-lag decay

When investigating the spreading of a piece of information or the diffusion of an innovation, we often lack information on the underlying propagation network. Reconstructing the hidden propagation paths based on the observed diffusion process is a challenging problem which has recently attracted attention from diverse research fields. To address this reconstruction problem, based on static similarity metrics commonly used in the link prediction literature, we introduce new node-node temporal similarity metrics. The new metrics take as input the time-series of multiple independent spreading processes, based on the hypothesis that two nodes are more likely to be connected if they were often infected at similar points in time. This hypothesis is implemented by introducing a time-lag function which penalizes distant infection times. We find that the choice of this time-lag strongly affects the metrics' reconstruction accuracy, depending on the network's clustering coefficient and we provide an extensive comparative analysis of static and temporal similarity metrics for network reconstruction. Our findings shed new light on the notion of similarity between pairs of nodes in complex networks

Matching Algorithm Design in E-Commerce: Harnessing the Power of Machine Learning via Stochastic Optimization

Internet-based matching markets have gained great attention during the last decade, such as Internet advertising (matching keywords and advertisers), ridesharing platforms (pairing riders and drivers), crowdsourcing markets (assigning tasks to workers), online dating (pairing romantically attracted partners), etc. A fundamental challenge is the presence of \emph{uncertainty}, which manifests in the following two ways. The first is on the arrival of agents in the system, e.g., \emph{drivers} and \emph{riders} in ridesharing services, \emph{keywords} in the Internet advertising, and \emph{online workers} in crowdsourcing markets. The second is on the outcome of interaction. For example, two users may \emph{like} or \emph{dislike} each other after a dating arranged by a match-making firm, a user may \emph{click} or \emph{not click} the link of an advertisement shown by an Ad company, to name a few. We are now living in an era of big data, fortunately. Thus, by applying powerful machine learning techniques to huge volumes of historical data, we can often get very accurate estimates of the uncertainty in the system as described above. Given this, the question then is as follows: \emph{How can we exploit estimates for our benefits as a matching-policy designer}? This dissertation aims to address this question. We have built an AI toolbox, which takes as input the estimates over uncertainty in the system, appropriate objectives (e.g., maximization of the total profit, maximization of fairness, etc.), and outputs a matching policy which works well both theoretically and experimentally on those pre-specified targets. The key ingredients are two matching models: stochastic matching and online matching. We have made several foundational algorithmic progress for these two models. Additionally, we have successfully utilized these two models to harness estimates from powerful machine learning algorithms, and designed improved matching policies for various real matching markets including ridesharing, crowdsourcing, and online recommendation applications

Recommending on graphs: a comprehensive review from a data perspective

Recent advances in graph-based learning approaches have demonstrated their effectiveness in modelling users' preferences and items' characteristics for Recommender Systems (RSS). Most of the data in RSS can be organized into graphs where various objects (e.g., users, items, and attributes) are explicitly or implicitly connected and influence each other via various relations. Such a graph-based organization brings benefits to exploiting potential properties in graph learning (e.g., random walk and network embedding) techniques to enrich the representations of the user and item nodes, which is an essential factor for successful recommendations. In this paper, we provide a comprehensive survey of Graph Learning-based Recommender Systems (GLRSs). Specifically, we start from a data-driven perspective to systematically categorize various graphs in GLRSs and analyze their characteristics. Then, we discuss the state-of-the-art frameworks with a focus on the graph learning module and how they address practical recommendation challenges such as scalability, fairness, diversity, explainability and so on. Finally, we share some potential research directions in this rapidly growing area.Comment: Accepted by UMUA