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We study a new two-time-scale stochastic gradient method for solving optimization problems, where the gradients are computed with the aid of an auxiliary variable under samples generated by time-varying Markov random processes parameterized by the underlying optimization variable. These time-varying samples make gradient directions in our update biased and dependent, which can potentially lead to the divergence of the iterates. In our two-time-scale approach, one scale is to estimate the true gradient from these samples, which is then used to update the estimate of the optimal solution. While these two iterates are implemented simultaneously, the former is updated "faster" (using bigger step sizes) than the latter (using smaller step sizes). Our first contribution is to characterize the finite-time complexity of the proposed two-time-scale stochastic gradient method. In particular, we provide explicit formulas for the convergence rates of this method under different structural assumptions, namely, strong convexity, convexity, the Polyak-Lojasiewicz condition, and general non-convexity. We apply our framework to two problems in control and reinforcement learning. First, we look at the standard online actor-critic algorithm over finite state and action spaces and derive a convergence rate of O(k^(-2/5)), which recovers the best known rate derived specifically for this problem. Second, we study an online actor-critic algorithm for the linear-quadratic regulator and show that a convergence rate of O(k^(-2/3)) is achieved. This is the first time such a result is known in the literature. Finally, we support our theoretical analysis with numerical simulations where the convergence rates are visualized.

One fundamental problem in temporal graph analysis is to count the occurrences of small connected subgraph patterns (i.e., motifs), which benefits a broad range of real-world applications, such as anomaly detection, structure prediction, and network representation learning. However, existing works focused on exacting temporal motif are not scalable to large-scale temporal graph data, due to their heavy computational costs or inherent inadequacy of parallelism. In this work, we propose a scalable parallel framework for exactly counting temporal motifs in large-scale temporal graphs. We first categorize the temporal motifs based on their distinct properties, and then design customized algorithms that offer efficient strategies to exactly count the motif instances of each category. Moreover, our compact data structures, namely triple and quadruple counters, enable our algorithms to directly identify the temporal motif instances of each category, according to edge information and the relationship between edges, therefore significantly improving the counting efficiency. Based on the proposed counting algorithms, we design a hierarchical parallel framework that features both inter- and intra-node parallel strategies, and fully leverages the multi-threading capacity of modern CPU to concurrently count all temporal motifs. Extensive experiments on sixteen real-world temporal graph datasets demonstrate the superiority and capability of our proposed framework for temporal motif counting, achieving up to 538* speedup compared to the state-of-the-art methods. The source code of our method is available at: //github.com/steven-ccq/FAST-temporal-motif.

Given a set $P$ of $n$ points in the plane, we consider the problem of computing the number of points of $P$ in a query unit disk (i.e., all query disks have the same radius). We show that the main techniques for simplex range searching in the plane can be adapted to this problem. For example, by adapting Matou\v{s}ek's results, we can build a data structure of $O(n)$ space so that each query can be answered in $O(\sqrt{n})$ time. Our techniques lead to improvements for several other classical problems, such as batched range searching, counting/reporting intersecting pairs of unit circles, distance selection, discrete 2-center, etc. For example, given a set of $n$ unit disks and a set of $n$ points in the plane, the batched range searching problem is to compute for each disk the number of points in it. Previous work [Katz and Sharir, 1997] solved the problem in $O(n^{4/3}\log n)$ time while our new algorithm runs in $O(n^{4/3})$ time.

Recruitment in large organisations often involves interviewing a large number of candidates. The process is resource intensive and complex. Therefore, it is important to carry it out efficiently and effectively. Planning the selection process consists of several problems, each of which maps to one or the other well-known computing problem. Research that looks at each of these problems in isolation is rich and mature. However, research that takes an integrated view of the problem is not common. In this paper, we take two of the most important aspects of the application processing problem, namely review/interview panel creation and interview scheduling. We have implemented our approach as a prototype system and have used it to automatically plan the interview process of a real-life data set. Our system provides a distinctly better plan than the existing practice, which is predominantly manual. We have explored various algorithmic options and have customised them to solve these panel creation and interview scheduling problems. We have evaluated these design options experimentally on a real data set and have presented our observations. Our prototype and experimental process and results may be a very good starting point for a full-fledged development project for automating application processing process.

Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured dependence--remains a challenge. We introduce a Bayesian decision analysis for subset selection with LMMs. Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear coefficients for (i) any given subset of variables and (ii) all subsets of variables that satisfy a cardinality constraint. Crucially, these estimates inherit shrinkage or regularization and uncertainty quantification from the underlying Bayesian model, and apply for any well-specified Bayesian LMM. More broadly, our decision analysis strategy deemphasizes the role of a single "best" subset, which is often unstable and limited in its information content, and instead favors a collection of near-optimal subsets. This collection is summarized by key member subsets and variable-specific importance metrics. Customized subset search and out-of-sample approximation algorithms are provided for more scalable computing. These tools are applied to simulated data and a longitudinal physical activity dataset, and demonstrate excellent prediction, estimation, and selection ability.

This paper presents new deterministic and distributed low-diameter decomposition algorithms for weighted graphs. In particular, we show that if one can efficiently compute approximate distances in a parallel or a distributed setting, one can also efficiently compute low-diameter decompositions. This consequently implies solutions to many fundamental distance based problems using a polylogarithmic number of approximate distance computations. Our low-diameter decomposition generalizes and extends the line of work starting from [Rozho\v{n}, Ghaffari STOC 2020] to weighted graphs in a very model-independent manner. Moreover, our clustering results have additional useful properties, including strong-diameter guarantees, separation properties, restricting cluster centers to specified terminals, and more. Applications include: -- The first near-linear work and polylogarithmic depth randomized and deterministic parallel algorithm for low-stretch spanning trees (LSST) with polylogarithmic stretch. Previously, the best parallel LSST algorithm required $m \cdot n^{o(1)}$ work and $n^{o(1)}$ depth and was inherently randomized. No deterministic LSST algorithm with truly sub-quadratic work and sub-linear depth was known. -- The first near-linear work and polylogarithmic depth deterministic algorithm for computing an $\ell_1$-embedding into polylogarithmic dimensional space with polylogarithmic distortion. The best prior deterministic algorithms for $\ell_1$-embeddings either require large polynomial work or are inherently sequential. Even when we apply our techniques to the classical problem of computing a ball-carving with strong-diameter $O(\log^2 n)$ in an unweighted graph, our new clustering algorithm still leads to an improvement in round complexity from $O(\log^{10} n)$ rounds [Chang, Ghaffari PODC 21] to $O(\log^{4} n)$.

Stochastic optimization algorithms implemented on distributed computing architectures are increasingly used to tackle large-scale machine learning applications. A key bottleneck in such distributed systems is the communication overhead for exchanging information such as stochastic gradients between different workers. Sparse communication with memory and the adaptive aggregation methodology are two successful frameworks among the various techniques proposed to address this issue. In this paper, we exploit the advantages of Sparse communication and Adaptive aggregated Stochastic Gradients to design a communication-efficient distributed algorithm named SASG. Specifically, we determine the workers who need to communicate with the parameter server based on the adaptive aggregation rule and then sparsify the transmitted information. Therefore, our algorithm reduces both the overhead of communication rounds and the number of communication bits in the distributed system. We define an auxiliary sequence and provide convergence results of the algorithm with the help of Lyapunov function analysis. Experiments on training deep neural networks show that our algorithm can significantly reduce the communication overhead compared to the previous methods, with little impact on training and testing accuracy.

We demonstrate that merely analog transmissions and match filtering can realize the function of an edge server in federated learning (FL). Therefore, a network with massively distributed user equipments (UEs) can achieve large-scale FL without an edge server. We also develop a training algorithm that allows UEs to continuously perform local computing without being interrupted by the global parameter uploading, which exploits the full potential of UEs' processing power. We derive convergence rates for the proposed schemes to quantify their training efficiency. The analyses reveal that when the interference obeys a Gaussian distribution, the proposed algorithm retrieves the convergence rate of a server-based FL. But if the interference distribution is heavy-tailed, then the heavier the tail, the slower the algorithm converges. Nonetheless, the system run time can be largely reduced by enabling computation in parallel with communication, whereas the gain is particularly pronounced when communication latency is high. These findings are corroborated via excessive simulations.

Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graph-specific, pooling methods based on SC must perform a new optimization for each new sample. In this paper, we propose a graph clustering approach that addresses these limitations of SC. We formulate a continuous relaxation of the normalized minCUT problem and train a GNN to compute cluster assignments that minimize this objective. Our GNN-based implementation is differentiable, does not require to compute the spectral decomposition, and learns a clustering function that can be quickly evaluated on out-of-sample graphs. From the proposed clustering method, we design a graph pooling operator that overcomes some important limitations of state-of-the-art graph pooling techniques and achieves the best performance in several supervised and unsupervised tasks.

In recent years, Graph Neural Networks (GNNs), which can naturally integrate node information and topological structure, have been demonstrated to be powerful in learning on graph data. These advantages of GNNs provide great potential to advance social recommendation since data in social recommender systems can be represented as user-user social graph and user-item graph; and learning latent factors of users and items is the key. However, building social recommender systems based on GNNs faces challenges. For example, the user-item graph encodes both interactions and their associated opinions; social relations have heterogeneous strengths; users involve in two graphs (e.g., the user-user social graph and the user-item graph). To address the three aforementioned challenges simultaneously, in this paper, we present a novel graph neural network framework (GraphRec) for social recommendations. In particular, we provide a principled approach to jointly capture interactions and opinions in the user-item graph and propose the framework GraphRec, which coherently models two graphs and heterogeneous strengths. Extensive experiments on two real-world datasets demonstrate the effectiveness of the proposed framework GraphRec. Our code is available at \url{//github.com/wenqifan03/GraphRec-WWW19}