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Edge networks call for communication efficient (low overhead) and robust distributed optimization (DO) algorithms. These are, in fact, desirable qualities for DO frameworks, such as federated edge learning techniques, in the presence of data and system heterogeneity, and in scenarios where internode communication is the main bottleneck. Although computationally demanding, Newton-type (NT) methods have been recently advocated as enablers of robust convergence rates in challenging DO problems where edge devices have sufficient computational power. Along these lines, in this work we propose Q-SHED, an original NT algorithm for DO featuring a novel bit-allocation scheme based on incremental Hessian eigenvectors quantization. The proposed technique is integrated with the recent SHED algorithm, from which it inherits appealing features like the small number of required Hessian computations, while being bandwidth-versatile at a bit-resolution level. Our empirical evaluation against competing approaches shows that Q-SHED can reduce by up to 60% the number of communication rounds required for convergence.

Deep graph clustering has recently received significant attention due to its ability to enhance the representation learning capabilities of models in unsupervised scenarios. Nevertheless, deep clustering for temporal graphs, which could capture crucial dynamic interaction information, has not been fully explored. It means that in many clustering-oriented real-world scenarios, temporal graphs can only be processed as static graphs. This not only causes the loss of dynamic information but also triggers huge computational consumption. To solve the problem, we propose a general framework for deep Temporal Graph Clustering called TGC, which adjusts deep clustering techniques (clustering assignment distribution and adjacency matrix reconstruction) to suit the interaction sequence-based batch-processing pattern of temporal graphs. In addition, we discuss differences between temporal graph clustering and existing static graph clustering from several levels. To verify the superiority of the proposed framework TGC, we conduct extensive experiments. The experimental results show that temporal graph clustering enables more flexibility in finding a balance between time and space requirements, and our framework can effectively improve the performance of existing temporal graph learning methods. Our code and supplementary material will be released after publication.

A posteriori ratemaking in insurance uses a Bayesian credibility model to upgrade the current premiums of a contract by taking into account policyholders' attributes and their claim history. Most data-driven models used for this task are mathematically intractable, and premiums must be then obtained through numerical methods such as simulation such MCMC. However, these methods can be computationally expensive and prohibitive for large portfolios when applied at the policyholder level. Additionally, these computations become ``black-box" procedures as there is no expression showing how the claim history of policyholders is used to upgrade their premiums. To address these challenges, this paper proposes the use of a surrogate modeling approach to inexpensively derive a closed-form expression for computing the Bayesian credibility premiums for any given model. As a part of the methodology, the paper introduces the ``credibility index", which is a summary statistic of a policyholder's claim history that serves as the main input of the surrogate model and that is sufficient for several distribution families, including the exponential dispersion family. As a result, the computational burden of a posteriori ratemaking for large portfolios is therefore reduced through the direct evaluation of the closed-form expression, which additionally can provide a transparent and interpretable way of computing Bayesian premiums.

Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special cases. In this work we propose a general framework for dynamic matrix recovery of low-rank matrices that evolve smoothly over time. We start from the setting that the observations are independent across time, then extend to the setting that both the design matrix and noise possess certain temporal correlation via modified concentration inequalities. By pooling neighboring observations, we obtain sharp estimation error bounds of both settings, showing the influence of the underlying smoothness, the dependence and effective samples. We propose a dynamic fast iterative shrinkage thresholding algorithm that is computationally efficient, and characterize the interplay between algorithmic and statistical convergence. Simulated and real data examples are provided to support such findings.

In 3D face reconstruction, orthogonal projection has been widely employed to substitute perspective projection to simplify the fitting process. This approximation performs well when the distance between camera and face is far enough. However, in some scenarios that the face is very close to camera or moving along the camera axis, the methods suffer from the inaccurate reconstruction and unstable temporal fitting due to the distortion under the perspective projection. In this paper, we aim to address the problem of single-image 3D face reconstruction under perspective projection. Specifically, a deep neural network, Perspective Network (PerspNet), is proposed to simultaneously reconstruct 3D face shape in canonical space and learn the correspondence between 2D pixels and 3D points, by which the 6DoF (6 Degrees of Freedom) face pose can be estimated to represent perspective projection. Besides, we contribute a large ARKitFace dataset to enable the training and evaluation of 3D face reconstruction solutions under the scenarios of perspective projection, which has 902,724 2D facial images with ground-truth 3D face mesh and annotated 6DoF pose parameters. Experimental results show that our approach outperforms current state-of-the-art methods by a significant margin. The code and data are available at //github.com/cbsropenproject/6dof_face.

In this paper we give an overview of the graph invariants queue number and stack number (the latter also called the page number or book thickness). Due to their similarity, it has been studied for a long time, whether one of them is bounded in terms of the other. It is now known that the stack number is not bounded by the queue number. We present a simplified proof of this result. We also survey the known results about possible stack number bound on the queue number. This preprint is a rework of the bachelor thesis [29].

Our paper proposes a direct sparse visual odometry method that combines event and RGB-D data to estimate the pose of agile-legged robots during dynamic locomotion and acrobatic behaviors. Event cameras offer high temporal resolution and dynamic range, which can eliminate the issue of blurred RGB images during fast movements. This unique strength holds a potential for accurate pose estimation of agile-legged robots, which has been a challenging problem to tackle. Our framework leverages the benefits of both RGB-D and event cameras to achieve robust and accurate pose estimation, even during dynamic maneuvers such as jumping and landing a quadruped robot, the Mini-Cheetah. Our major contributions are threefold: Firstly, we introduce an adaptive time surface (ATS) method that addresses the whiteout and blackout issue in conventional time surfaces by formulating pixel-wise decay rates based on scene complexity and motion speed. Secondly, we develop an effective pixel selection method that directly samples from event data and applies sample filtering through ATS, enabling us to pick pixels on distinct features. Lastly, we propose a nonlinear pose optimization formula that simultaneously performs 3D-2D alignment on both RGB-based and event-based maps and images, allowing the algorithm to fully exploit the benefits of both data streams. We extensively evaluate the performance of our framework on both public datasets and our own quadruped robot dataset, demonstrating its effectiveness in accurately estimating the pose of agile robots during dynamic movements.

With the explosive growth of information technology, multi-view graph data have become increasingly prevalent and valuable. Most existing multi-view clustering techniques either focus on the scenario of multiple graphs or multi-view attributes. In this paper, we propose a generic framework to cluster multi-view attributed graph data. Specifically, inspired by the success of contrastive learning, we propose multi-view contrastive graph clustering (MCGC) method to learn a consensus graph since the original graph could be noisy or incomplete and is not directly applicable. Our method composes of two key steps: we first filter out the undesirable high-frequency noise while preserving the graph geometric features via graph filtering and obtain a smooth representation of nodes; we then learn a consensus graph regularized by graph contrastive loss. Results on several benchmark datasets show the superiority of our method with respect to state-of-the-art approaches. In particular, our simple approach outperforms existing deep learning-based methods.

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.

Learning latent representations of nodes in graphs is an important and ubiquitous task with widespread applications such as link prediction, node classification, and graph visualization. Previous methods on graph representation learning mainly focus on static graphs, however, many real-world graphs are dynamic and evolve over time. In this paper, we present Dynamic Self-Attention Network (DySAT), a novel neural architecture that operates on dynamic graphs and learns node representations that capture both structural properties and temporal evolutionary patterns. Specifically, DySAT computes node representations by jointly employing self-attention layers along two dimensions: structural neighborhood and temporal dynamics. We conduct link prediction experiments on two classes of graphs: communication networks and bipartite rating networks. Our experimental results show that DySAT has a significant performance gain over several different state-of-the-art graph embedding baselines.