Millimeter-wave massive multiple-input multiple-output employing a large-scale antenna array is a promising technology for 5G and 6G cellular networks. It also provides strong support for high-speed, low-latency communications and diverse applications. In order to enhance the accuracy and efficiency of channel estimation, in this paper, we formulate a tensor-based channel estimation model with sparse regularization aiming at characterizing the sparse structure of a large-scale channel in the delay-angular domain. An efficient subspace Newton least squares algorithm is designed to solve the nonconvex discontinuous tensor-based model, operating in restricted subspaces and being capable of handling singularities of the Hessian matrix. Our proposed algorithm is also proved to enjoy global and linear (or sublinear) convergence. Some numerical simulations are performed, which demonstrate the feasibility of our proposed model and the time validity of our algorithm.

This article aims to seek a selection and estimation procedure for a class of tensor regression problems with multivariate covariates and matrix responses, which can provide theoretical guarantees for model selection in finite samples. Considering the frontal slice sparsity and low-rankness inherited in the coefficient tensor, we formulate the regression procedure as a group SLOPE penalized low-rank tensor optimization problem based on an orthogonal decomposition, namely TgSLOPE. This procedure provably controls the newly introduced tensor group false discovery rate (TgFDR), provided that the predictor matrix is column-orthogonal. Moreover, we establish the asymptotically minimax convergence with respect to the TgSLOPE estimate risk. For efficient problem resolution, we equivalently transform the TgSLOPE problem into a difference-of-convex (DC) program with the level-coercive objective function. This allows us to solve the reformulation problem of TgSLOPE by an efficient proximal DC algorithm (DCA) with global convergence. Numerical studies conducted on synthetic data and a real human brain connection data illustrate the efficacy of the proposed TgSLOPE estimation procedure.

Canonical correlation analysis (CCA) has attracted great interest in multi-view representation. However, most of the CCA methods heavily rely on the matrix structure, which may neglect the prior geometric information in high-order data. To deal with the above issue, we first propose a novel tensor CCA formulation with orthogonality, called TCCA-O, based on the Tucker decomposition to preserve the orthogonality. Then, we incorporate a structured sparse regularization term into the TCCA-O, called TCCA-OS, to improve feature representation. In addition, we develop an efficient alternating direction method of multipliers (ADMM)-based algorithm to solve TCCA-OS and conduct numerical comparisons on four public datasets. The results validate the advantages of the proposed methods in terms of classification accuracy, parameter sensitivity, noise robustness, and model stability. In particular, TCCA-O and TCCA-OS improve the classification accuracy by at least 10.03% and 10.36%, respectively, over the state-of-the-art CCA methods on the Caltech101-7 dataset.

Human mobility prediction is an important task in the field of spatiotemporal sequential data mining and urban computing. Despite the extensive work on mining human mobility behavior, little attention was paid to the problem of successive mobility prediction. The state-of-the-art methods of human mobility prediction are mainly based on supervised learning. To achieve higher predictability and adapt well to the successive mobility prediction, there are four key challenges: 1) disability to the circumstance that the optimizing target is discrete-continuous hybrid and non-differentiable. In our work, we assume that the user's demands are always multi-targeted and can be modeled as a discrete-continuous hybrid function; 2) difficulty to alter the recommendation strategy flexibly according to the changes in user needs in real scenarios; 3) error propagation and exposure bias issues when predicting multiple points in successive mobility prediction; 4) cannot interactively explore user's potential interest that does not appear in the history. While previous methods met these difficulties, reinforcement learning (RL) is an intuitive answer for this task to settle these issues. We innovatively introduce RL to the successive prediction task. In this paper, we formulate this problem as a Markov Decision Process. We further propose a framework - RLMob to solve our problem. A simulated environment is carefully designed. An actor-critic framework with an instance of Proximal Policy Optimization (PPO) is applied to adapt to our scene with a large state space. Experiments show that on the task, the performance of our approach is consistently superior to that of the compared approaches.

To achieve good result quality and short query response time, search engines use specific match plans on Inverted Index to help retrieve a small set of relevant documents from billions of web pages. A match plan is composed of a sequence of match rules, which contain discrete match rule types and continuous stopping quotas. Currently, match plans are manually designed by experts according to their several years’ experience, which encounters difficulty in dealing with heterogeneous queries and varying data distribution. In this work, we formulate the match plan generation as a Partially Observable Markov Decision Process (POMDP) with a parameterized action space, and propose a novel reinforcement learning algorithm Parameterized Action Soft Actor-Critic (PASAC) to effectively enhance the exploration in both spaces. In our scene, we also discover a skew prioritizing issue of the original Prioritized Experience Replay (PER) and introduce Stratified Prioritized Experience Replay (SPER) to address it. We are the first group to generalize this task for all queries as a learning problem with zero prior knowledge and successfully apply deep reinforcement learning in the real web search environment. Our approach greatly outperforms the well-designed production match plans by over 70% reduction of index block accesses with the quality of documents almost unchanged, and 9% reduction of query response time even with model inference cost. Our method also beats the baselines on some open-source benchmarks1.

Predicting human mobility is an important trajectory mining task for various applications, ranging from smart city planning to personalized recommendation system. While most of previous works adopt GPS tracking data to model human mobility, the recent fast-growing geo-tagged social media (GTSM) data brings new opportunities to this task. However, predicting human mobility on GTSM data is not trivial because of three challenges: 1) extreme data sparsity; 2) high order sequential patterns of human mobility and 3) evolving preference of users for tagging.

The octagonal shrinkage and clustering algorithm for regression (OSCAR), equipped with the $\ell_1$-norm and a pair-wise $\ell_{\infty}$-norm regularizer, is a useful tool for feature selection and grouping in high-dimensional data analysis. The computational challenge posed by OSCAR, for high dimensional and/or large sample size data, has not yet been well resolved due to the non-smoothness and non-separability of the regularizer involved. In this paper, we successfully resolve this numerical challenge by proposing a sparse semismooth Newton-based augmented Lagrangian method to solve the more general SLOPE (the sorted L-one penalized estimation) model. By appropriately exploiting the inherent sparse and low-rank property of the generalized Jacobian of the semismooth Newton system in the augmented Lagrangian subproblem, we show how the computational complexity can be substantially reduced. Our algorithm offers a notable computational advantage in the high-dimensional statistical regression settings. Numerical experiments are conducted on real data sets, and the results demonstrate that our algorithm is far superior, in both speed and robustness, to the existing state-of-the-art algorithms based on first-order iterative schemes, including the widely used accelerated proximal gradient (APG) method and the alternating direction method of multipliers (ADMM).