Core (graph theory)

Abstract: Exponential-family random graph models (ERGMs) represent the processes that govern the formation of links in networks through the terms selected by the user. The terms specify network statistics that are sufficient to represent the probability distribution over the space of networks of that size. Many classes of statistics can be used. In this article we describe the classes of statistics that are currently available in the ergm package. We also describe means for controlling the Markov chain Monte Carlo (MCMC) algorithm that the package uses for estimation. These controls affect either the proposal distribution on the sample space used by the underlying Metropolis-Hastings algorithm or the constraints on the sample space itself. Finally, we describe various other arguments to core functions of the ergm package.

Abstract: We abstract out the core search problem of active learning schemes, to better understand the extent to which adaptive labeling can improve sample complexity. We give various upper and lower bounds on the number of labels which need to be queried, and we prove that a popular greedy active learning rule is approximately as good as any other strategy for minimizing this number of labels.

Abstract: Sequential recommendation aims to leverage users' historical behaviors to predict their next interaction. Existing works have not yet addressed two main challenges in sequential recommendation. First, user behaviors in their rich historical sequences are often implicit and noisy preference signals, they cannot sufficiently reflect users' actual preferences. In addition, users' dynamic preferences often change rapidly over time, and hence it is difficult to capture user patterns in their historical sequences. In this work, we propose a graph neural network model called SURGE (short forSeqUential Recommendation with Graph neural nEtworks) to address these two issues. Specifically, SURGE integrates different types of preferences in long-term user behaviors into clusters in the graph by re-constructing loose item sequences into tight item-item interest graphs based on metric learning. This helps explicitly distinguish users' core interests, by forming dense clusters in the interest graph. Then, we perform cluster-aware and query-aware graph convolutional propagation and graph pooling on the constructed graph. It dynamically fuses and extracts users' current activated core interests from noisy user behavior sequences. We conduct extensive experiments on both public and proprietary industrial datasets. Experimental results demonstrate significant performance gains of our proposed method compared to state-of-the-art methods. Further studies on sequence length confirm that our method can model long behavioral sequences effectively and efficiently.