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Video background subtraction is one of the fundamental problems in computer vision that aims to segment all moving objects. Robust principal component analysis has been identified as a promising unsupervised paradigm for background subtraction tasks in the last decade thanks to its competitive performance in a number of benchmark datasets. Tensor robust principal component analysis variations have improved background subtraction performance further. However, because moving object pixels in the sparse component are treated independently and do not have to adhere to spatial-temporal structured-sparsity constraints, performance is reduced for sequences with dynamic backgrounds, camouflaged, and camera jitter problems. In this work, we present a spatial-temporal regularized tensor sparse RPCA algorithm for precise background subtraction. Within the sparse component, we impose spatial-temporal regularizations in the form of normalized graph-Laplacian matrices. To do this, we build two graphs, one across the input tensor spatial locations and the other across its frontal slices in the time domain. While maximizing the objective function, we compel the tensor sparse component to serve as the spatiotemporal eigenvectors of the graph-Laplacian matrices. The disconnected moving object pixels in the sparse component are preserved by the proposed graph-based regularizations since they both comprise of spatiotemporal subspace-based structure. Additionally, we propose a unique objective function that employs batch and online-based optimization methods to jointly maximize the background-foreground and spatial-temporal regularization components. Experiments are performed on six publicly available background subtraction datasets that demonstrate the superior performance of the proposed algorithm compared to several existing methods. Our source code will be available very soon.

Trajectory optimization under uncertainty underpins a wide range of applications in robotics. However, existing methods are limited in terms of reasoning about sources of epistemic and aleatoric uncertainty, space and time correlations, nonlinear dynamics, and non-convex constraints. In this work, we first introduce a continuous-time planning formulation with an average-value-at-risk constraint over the entire planning horizon. Then, we propose a sample-based approximation that unlocks an efficient and general-purpose algorithm for risk-averse trajectory optimization. We prove that the method is asymptotically optimal and derive finite-sample error bounds. Simulations demonstrate the high speed and reliability of the approach on problems with stochasticity in nonlinear dynamics, obstacle fields, interactions, and terrain parameters.

Ordered sequences of data, specified with a join operation to combine sequences, serve as a foundation for the implementation of parallel functional algorithms. This abstract data type can be elegantly and efficiently implemented using balanced binary trees, where a join operation is provided to combine two trees and rebalance as necessary. In this work, we present a verified implementation and cost analysis of joinable red-black trees in $\textbf{calf}$, a dependent type theory for cost analysis. We implement red-black trees and auxiliary intermediate data structures in such a way that all correctness invariants are intrinsically maintained. Then, we describe and verify precise cost bounds on the operations, making use of the red-black tree invariants. Finally, we implement standard algorithms on sequences using the simple join-based signature and bound their cost in the case that red-black trees are used as the underlying implementation. All proofs are formally mechanized using the embedding of $\textbf{calf}$ in the Agda theorem prover.

We introduce a general random model of a combinatorial optimization problem with geometric structure that encapsulates both linear programming and integer linear programming. Let $Q$ be a bounded set called the feasible set, $E$ be an arbitrary set called the constraint set, and $A$ be a random linear transform. We introduce and study the $\ell^q$-\textit{margin},$M_q := d_q(AQ, E)$. The margin quantifies the feasibility of finding $y \in AQ$ satisfying the constraint $y \in E$. Our contribution is to establish strong concentration of the margin for any $q \in (2,\infty]$, assuming only that $E$ has permutation symmetry. The case of $q = \infty$ is of particular interest in applications -- specifically to combinatorial ``balancing'' problems -- and is markedly out of the reach of the classical isoperimetric and concentration-of-measure tools that suffice for $q \le 2$. Generality is a key feature of this result: we assume permutation symmetry of the constraint set and nothing else. This allows us to encode many optimization problems in terms of the margin, including random versions of: the closest vector problem, integer linear feasibility, perceptron-type problems, $\ell^q$-combinatorial discrepancy for $2 \le q \le \infty$, and matrix balancing. Concentration of the margin implies a host of new sharp threshold results in these models, and also greatly simplifies and extends some key known results.

Intelligent reflecting surface (IRS) has emerged as a promising technique to extend the wireless signal coverage of access point (AP) and improve the communication performance cost-effectively. In order to reduce the path-loss of the cascaded user-IRS-AP channels, the IRS-integrated AP architecture has been proposed to deploy the IRSs and the antenna array of the AP within the same antenna radome. To reduce the pilot overhead for estimating all IRS-involved channels, in this paper, we propose a novel codebook-based IRS reflection design for the IRS-integrated AP to enhance the coverage performance in a given area. In particular, the codebook consisting of a small number of codewords is designed offline by employing an efficient sector division strategy based on the azimuth angle. To ensure the performance of each sector, we optimize its corresponding codeword for IRS reflection pattern to maximize the sector-min-average-effective-channel-power (SMAECP) by applying the alternating optimization (AO) and semidefinite relaxation (SDR) methods. With the designed codebook, the AP performs the IRS reflection training by sequentially applying all codewords and selects the one achieving the best communication performance for data transmission. Numerical results show that our proposed codebook design can enhance the average channel power of the whole coverage area, as compared to the system without IRS. Moreover, our proposed codebook-based IRS reflection design is shown to achieve significant performance gain over other benchmark schemes in both single-user and multi-user transmissions.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.

A large number of real-world graphs or networks are inherently heterogeneous, involving a diversity of node types and relation types. Heterogeneous graph embedding is to embed rich structural and semantic information of a heterogeneous graph into low-dimensional node representations. Existing models usually define multiple metapaths in a heterogeneous graph to capture the composite relations and guide neighbor selection. However, these models either omit node content features, discard intermediate nodes along the metapath, or only consider one metapath. To address these three limitations, we propose a new model named Metapath Aggregated Graph Neural Network (MAGNN) to boost the final performance. Specifically, MAGNN employs three major components, i.e., the node content transformation to encapsulate input node attributes, the intra-metapath aggregation to incorporate intermediate semantic nodes, and the inter-metapath aggregation to combine messages from multiple metapaths. Extensive experiments on three real-world heterogeneous graph datasets for node classification, node clustering, and link prediction show that MAGNN achieves more accurate prediction results than state-of-the-art baselines.

Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.

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.

Collaborative filtering often suffers from sparsity and cold start problems in real recommendation scenarios, therefore, researchers and engineers usually use side information to address the issues and improve the performance of recommender systems. In this paper, we consider knowledge graphs as the source of side information. We propose MKR, a Multi-task feature learning approach for Knowledge graph enhanced Recommendation. MKR is a deep end-to-end framework that utilizes knowledge graph embedding task to assist recommendation task. The two tasks are associated by cross&compress units, which automatically share latent features and learn high-order interactions between items in recommender systems and entities in the knowledge graph. We prove that cross&compress units have sufficient capability of polynomial approximation, and show that MKR is a generalized framework over several representative methods of recommender systems and multi-task learning. Through extensive experiments on real-world datasets, we demonstrate that MKR achieves substantial gains in movie, book, music, and news recommendation, over state-of-the-art baselines. MKR is also shown to be able to maintain a decent performance even if user-item interactions are sparse.