Edge Dithering for Robust Adaptive Graph Convolutional Networks

Graph convolutional networks (GCNs) are vulnerable to perturbations of the graph structure that are either random, or, adversarially designed. The perturbed links modify the graph neighborhoods, which critically affects the performance of GCNs in semi-supervised learning (SSL) tasks. Aiming at robustifying GCNs conditioned on the perturbed graph, the present paper generates multiple auxiliary graphs, each having its binary 0-1 edge weights flip values with probabilities designed to enhance robustness. The resultant edge-dithered auxiliary graphs are leveraged by an adaptive (A)GCN that performs SSL. Robustness is enabled through learnable graph-combining weights along with suitable regularizers. Relative to GCN, the novel AGCN achieves markedly improved performance in tests with noisy inputs, graph perturbations, and state-of-the-art adversarial attacks. Further experiments with protein interaction networks showcase the competitive performance of AGCN for SSL over multiple graphs.

GraphSAC: Detecting anomalies in large-scale graphs

A graph-based sampling and consensus (GraphSAC) approach is introduced to effectively detect anomalous nodes in large-scale graphs. Existing approaches rely on connectivity and attributes of all nodes to assign an anomaly score per node. However, nodal attributes and network links might be compromised by adversaries, rendering these holistic approaches vulnerable. Alleviating this limitation, GraphSAC randomly draws subsets of nodes, and relies on graph-aware criteria to judiciously filter out sets contaminated by anomalous nodes, before employing a semi-supervised learning (SSL) module to estimate nominal label distributions per node. These learned nominal distributions are minimally affected by the anomalous nodes, and hence can be directly adopted for anomaly detection. Rigorous analysis provides performance guarantees for GraphSAC, by bounding the required number of draws. The per-draw complexity grows linearly with the number of edges, which implies efficient SSL, while draws can be run in parallel, thereby ensuring scalability to large graphs. GraphSAC is tested under different anomaly generation models based on random walks, clustered anomalies, as well as contemporary adversarial attacks for graph data. Experiments with real-world graphs showcase the advantage of GraphSAC relative to state-of-the-art alternatives.

Adaptive Step Sizes in Variance Reduction via Regularization

The main goal of this work is equipping convex and nonconvex problems with Barzilai-Borwein (BB) step size. With the adaptivity of BB step sizes granted, they can fail when the objective function is not strongly convex. To overcome this challenge, the key idea here is to bridge (non)convex problems and strongly convex ones via regularization. The proposed regularization schemes are \textit{simple} yet effective. Wedding the BB step size with a variance reduction method, known as SARAH, offers a free lunch compared with vanilla SARAH in convex problems. The convergence of BB step sizes in nonconvex problems is also established and its complexity is no worse than other adaptive step sizes such as AdaGrad. As a byproduct, our regularized SARAH methods for convex functions ensure that the complexity to find $\mathbb{E}[\| \nabla f(\mathbf{x}) \|^2]\leq \epsilon$ is ${\cal O}\big( (n+\frac{1}{\sqrt{\epsilon}})\ln{\frac{1}{\epsilon}}\big)$, improving $\epsilon$ dependence over existing results. Numerical tests further validate the merits of proposed approaches.

Communication-Efficient Distributed Learning via Lazily Aggregated Quantized Gradients

The present paper develops a novel aggregated gradient approach for distributed machine learning that adaptively compresses the gradient communication. The key idea is to first quantize the computed gradients, and then skip less informative quantized gradient communications by reusing outdated gradients. Quantizing and skipping result in `lazy' worker-server communications, which justifies the term Lazily Aggregated Quantized gradient that is henceforth abbreviated as LAQ. Our LAQ can provably attain the same linear convergence rate as the gradient descent in the strongly convex case, while effecting major savings in the communication overhead both in transmitted bits as well as in communication rounds. Empirically, experiments with real data corroborate a significant communication reduction compared to existing gradient- and stochastic gradient-based algorithms.

A Multistep Lyapunov Approach for Finite-Time Analysis of Biased Stochastic Approximation

Motivated by the widespread use of temporal-difference (TD-) and Q-learning algorithms in reinforcement learning, this paper studies a class of biased stochastic approximation (SA) procedures under a mild "ergodic-like" assumption on the underlying stochastic noise sequence. Building upon a carefully designed multistep Lyapunov function that looks ahead to several future updates to accommodate the stochastic perturbations (for control of the gradient bias), we prove a general result on the convergence of the iterates, and use it to derive non-asymptotic bounds on the mean-square error in the case of constant stepsizes. This novel looking-ahead viewpoint renders finite-time analysis of biased SA algorithms under a large family of stochastic perturbations possible. For direct comparison with existing contributions, we also demonstrate these bounds by applying them to TD- and Q-learning with linear function approximation, under the practical Markov chain observation model. The resultant finite-time error bound for both the TD- as well as the Q-learning algorithms is the first of its kind, in the sense that it holds i) for the unmodified versions (i.e., without making any modifications to the parameter updates) using even nonlinear function approximators; as well as for Markov chains ii) under general mixing conditions and iii) starting from any initial distribution, at least one of which has to be violated for existing results to be applicable.

A Variational Bayes Approach to Adaptive Radio Tomography

Radio tomographic imaging (RTI) is an emerging technology for localization of physical objects in a geographical area covered by wireless networks. With attenuation measurements collected at spatially distributed sensors, RTI capitalizes on spatial loss fields (SLFs) measuring the absorption of radio frequency waves at spatial locations along the propagation path. These SLFs can be utilized for interference management in wireless communication networks, environmental monitoring, and survivor localization after natural disasters such as earthquakes. Key to the success of RTI is to accurately model shadowing as the weighted line integral of the SLF. To learn the SLF exhibiting statistical heterogeneity induced by spatially diverse environments, the present work develops a Bayesian framework entailing a piecewise homogeneous SLF with an underlying hidden Markov random field model. Utilizing variational Bayes techniques, the novel approach yields efficient field estimators at affordable complexity. A data-adaptive sensor selection strategy is also introduced to collect informative measurements for effective reconstruction of the SLF. Numerical tests using synthetic and real datasets demonstrate the capabilities of the proposed approach to radio tomography and channel-gain estimation.

Almost Tune-Free Variance Reduction

The variance reduction class of algorithms including the representative ones, abbreviated as SVRG and SARAH, have well documented merits for empirical risk minimization tasks. However, they require grid search to optimally tune parameters (step size and the number of iterations per inner loop) for best performance. This work introduces `almost tune-free' SVRG and SARAH schemes by equipping them with Barzilai-Borwein (BB) step sizes. To achieve the best performance, both i) averaging schemes; and, ii) the inner loop length are adjusted according to the BB step size. SVRG and SARAH are first reexamined through an `estimate sequence' lens. Such analysis provides new averaging methods that tighten the convergence rates of both SVRG and SARAH theoretically, and improve their performance empirically when the step size is chosen large. Then a simple yet effective means of adjusting the number of iterations per inner loop is developed, which completes the tune-free variance reduction together with BB step sizes. Numerical tests corroborate the proposed methods.

Unsupervised Ensemble Classification with Dependent Data

Ensemble learning, the machine learning paradigm where multiple algorithms are combined, has exhibited promising perfomance in a variety of tasks. The present work focuses on unsupervised ensemble classification. The term unsupervised refers to the ensemble combiner who has no knowledge of the ground-truth labels that each classifier has been trained on. While most prior works on unsupervised ensemble classification are designed for independent and identically distributed (i.i.d.) data, the present work introduces an unsupervised scheme for learning from ensembles of classifiers in the presence of data dependencies. Two types of data dependencies are considered: sequential data and networked data whose dependencies are captured by a graph. Moment matching and Expectation Maximization algorithms are developed for the aforementioned cases, and their performance is evaluated on synthetic and real datasets.

Generalization error bounds for kernel matrix completion and extrapolation

Prior information can be incorporated in matrix completion to improve estimation accuracy and extrapolate the missing entries. Reproducing kernel Hilbert spaces provide tools to leverage the said prior information, and derive more reliable algorithms. This paper analyzes the generalization error of such approaches, and presents numerical tests confirming the theoretical results.

On the Convergence of SARAH and Beyond

The main theme of this work is a unifying algorithm, abbreviated as L2S, that can deal with (strongly) convex and nonconvex empirical risk minimization (ERM) problems. It broadens a recently developed variance reduction method known as SARAH. L2S enjoys a linear convergence rate for strongly convex problems, which also implies the last iteration of SARAH's inner loop converges linearly. For convex problems, different from SARAH, L2S can afford step and mini-batch sizes not dependent on the data size $n$, and the complexity needed to guarantee $\mathbb{E}[\|\nabla F(\mathbf{x}) \|^2] \leq \epsilon$ is ${\cal O}(n+ n/\epsilon)$. For nonconvex problems on the other hand, the complexity is ${\cal O}(n+ \sqrt{n}/\epsilon)$. Parallel to L2S there are a few side results. Leveraging an aggressive step size, D2S is proposed, which provides a more efficient alternative to L2S and SARAH-like algorithms. Specifically, D2S requires a reduced IFO complexity of ${\cal O}\big( (n+ \bar{\kappa}) \ln (1/\epsilon) \big)$ for strongly convex problems. Moreover, to avoid the tedious selection of the optimal step size, an automatic tuning scheme is developed, which obtains comparable empirical performance with SARAH using judiciously tuned step size.