Factor Graph Neural Networks

In recent years, we have witnessed a surge of Graph Neural Networks (GNNs), most of which can learn powerful representations in an end-to-end fashion with great success in many real-world applications. They have resemblance to Probabilistic Graphical Models (PGMs), but break free from some limitations of PGMs. By aiming to provide expressive methods for representation learning instead of computing marginals or most likely configurations, GNNs provide flexibility in the choice of information flowing rules while maintaining good performance. Despite their success and inspirations, they lack efficient ways to represent and learn higher-order relations among variables/nodes. More expressive higher-order GNNs which operate on k-tuples of nodes need increased computational resources in order to process higher-order tensors. We propose Factor Graph Neural Networks (FGNNs) to effectively capture higher-order relations for inference and learning. To do so, we first derive an efficient approximate Sum-Product loopy belief propagation inference algorithm for discrete higher-order PGMs. We then neuralize the novel message passing scheme into a Factor Graph Neural Network (FGNN) module by allowing richer representations of the message update rules; this facilitates both efficient inference and powerful end-to-end learning. We further show that with a suitable choice of message aggregation operators, our FGNN is also able to represent Max-Product belief propagation, providing a single family of architecture that can represent both Max and Sum-Product loopy belief propagation. Our extensive experimental evaluation on synthetic as well as real datasets demonstrates the potential of the proposed model.Comment: Accepted by JML

Community detection and stochastic block models: recent developments

The stochastic block model (SBM) is a random graph model with planted clusters. It is widely employed as a canonical model to study clustering and community detection, and provides generally a fertile ground to study the statistical and computational tradeoffs that arise in network and data sciences. This note surveys the recent developments that establish the fundamental limits for community detection in the SBM, both with respect to information-theoretic and computational thresholds, and for various recovery requirements such as exact, partial and weak recovery (a.k.a., detection). The main results discussed are the phase transitions for exact recovery at the Chernoff-Hellinger threshold, the phase transition for weak recovery at the Kesten-Stigum threshold, the optimal distortion-SNR tradeoff for partial recovery, the learning of the SBM parameters and the gap between information-theoretic and computational thresholds. The note also covers some of the algorithms developed in the quest of achieving the limits, in particular two-round algorithms via graph-splitting, semi-definite programming, linearized belief propagation, classical and nonbacktracking spectral methods. A few open problems are also discussed

Gunrock: GPU Graph Analytics

For large-scale graph analytics on the GPU, the irregularity of data access and control flow, and the complexity of programming GPUs, have presented two significant challenges to developing a programmable high-performance graph library. "Gunrock", our graph-processing system designed specifically for the GPU, uses a high-level, bulk-synchronous, data-centric abstraction focused on operations on a vertex or edge frontier. Gunrock achieves a balance between performance and expressiveness by coupling high performance GPU computing primitives and optimization strategies with a high-level programming model that allows programmers to quickly develop new graph primitives with small code size and minimal GPU programming knowledge. We characterize the performance of various optimization strategies and evaluate Gunrock's overall performance on different GPU architectures on a wide range of graph primitives that span from traversal-based algorithms and ranking algorithms, to triangle counting and bipartite-graph-based algorithms. The results show that on a single GPU, Gunrock has on average at least an order of magnitude speedup over Boost and PowerGraph, comparable performance to the fastest GPU hardwired primitives and CPU shared-memory graph libraries such as Ligra and Galois, and better performance than any other GPU high-level graph library.Comment: 52 pages, invited paper to ACM Transactions on Parallel Computing (TOPC), an extended version of PPoPP'16 paper "Gunrock: A High-Performance Graph Processing Library on the GPU

Query-Driven Sampling for Collective Entity Resolution

Probabilistic databases play a preeminent role in the processing and management of uncertain data. Recently, many database research efforts have integrated probabilistic models into databases to support tasks such as information extraction and labeling. Many of these efforts are based on batch oriented inference which inhibits a realtime workflow. One important task is entity resolution (ER). ER is the process of determining records (mentions) in a database that correspond to the same real-world entity. Traditional pairwise ER methods can lead to inconsistencies and low accuracy due to localized decisions. Leading ER systems solve this problem by collectively resolving all records using a probabilistic graphical model and Markov chain Monte Carlo (MCMC) inference. However, for large datasets this is an extremely expensive process. One key observation is that, such exhaustive ER process incurs a huge up-front cost, which is wasteful in practice because most users are interested in only a small subset of entities. In this paper, we advocate pay-as-you-go entity resolution by developing a number of query-driven collective ER techniques. We introduce two classes of SQL queries that involve ER operators --- selection-driven ER and join-driven ER. We implement novel variations of the MCMC Metropolis Hastings algorithm to generate biased samples and selectivity-based scheduling algorithms to support the two classes of ER queries. Finally, we show that query-driven ER algorithms can converge and return results within minutes over a database populated with the extraction from a newswire dataset containing 71 million mentions

Compressive Sensing and Recovery of Structured Sparse Signals

In the recent years, numerous disciplines including telecommunications, medical imaging, computational biology, and neuroscience benefited from increasing applications of high dimensional datasets. This calls for efficient ways of data capturing and data processing. Compressive sensing (CS), which is introduced as an efficient sampling (data capturing) method, is addressing this need. It is well-known that the signals, which belong to an ambient high-dimensional space, have much smaller dimensionality in an appropriate domain. CS taps into this principle and dramatically reduces the number of samples that is required to be captured to avoid any distortion in the information content of the data. This reduction in the required number of samples enables many new applications that were previously infeasible using classical sampling techniques. Most CS-based approaches take advantage of the inherent low-dimensionality in many datasets. They try to determine a sparse representation of the data, in an appropriately chosen basis using only a few significant elements. These approaches make no extra assumptions regarding possible relationships among the significant elements of that basis. In this dissertation, different ways of incorporating the knowledge about such relationships are integrated into the data sampling and the processing schemes. We first consider the recovery of temporally correlated sparse signals and show that using the time correlation model. The recovery performance can be significantly improved. Next, we modify the sampling process of sparse signals to incorporate the signal structure in a more efficient way. In the image processing application, we show that exploiting the structure information in both signal sampling and signal recovery improves the efficiency of the algorithm. In addition, we show that region-of-interest information can be included in the CS sampling and recovery steps to provide a much better quality for the region-of-interest area compared the rest of the image or video. In spectrum sensing applications, CS can dramatically improve the sensing efficiency by facilitating the coordination among spectrum sensors. A cluster-based spectrum sensing with coordination among spectrum sensors is proposed for geographically disperse cognitive radio networks. Further, CS has been exploited in this problem for simultaneous sensing and localization. Having access to this information dramatically facilitates the implementation of advanced communication technologies as required by 5G communication networks

A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems

International audienceSzeliski et al. published an influential study in 2006 on energy minimization methods for Markov Random Fields (MRF). This study provided valuable insights in choosing the best optimization technique for certain classes of problems. While these insights remain generally useful today, the phenomenal success of random field models means that the kinds of inference problems that have to be solved changed significantly. Specifically , the models today often include higher order interactions, flexible connectivity structures, large label-spaces of different car-dinalities, or learned energy tables. To reflect these changes, we provide a modernized and enlarged study. We present an empirical comparison of more than 27 state-of-the-art optimization techniques on a corpus of 2,453 energy minimization instances from diverse applications in computer vision. To ensure reproducibility, we evaluate all methods in the OpenGM 2 framework and report extensive results regarding runtime and solution quality. Key insights from our study agree with the results of Szeliski et al. for the types of models they studied. However, on new and challenging types of models our findings disagree and suggest that polyhedral methods and integer programming solvers are competitive in terms of runtime and solution quality over a large range of model types