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The parallel alternating direction method of multipliers (ADMM) algorithms have gained popularity in statistics and machine learning for their efficient handling of large sample data problems. However, the parallel structure of these algorithms is based on the consensus problem, which can lead to an excessive number of auxiliary variables for high-dimensional data. In this paper, we propose a partition-insensitive parallel framework based on the linearized ADMM (LADMM) algorithm and apply it to solve nonconvex penalized smooth quantile regression problems. Compared to existing parallel ADMM algorithms, our algorithm does not rely on the consensus problem, resulting in a significant reduction in the number of variables that need to be updated at each iteration. It is worth noting that the solution of our algorithm remains unchanged regardless of how the total sample is divided, which is also known as partition-insensitivity. Furthermore, under some mild assumptions, we prove that the iterative sequence generated by the parallel LADMM algorithm converges to a critical point of the nonconvex optimization problem. Numerical experiments on synthetic and real datasets demonstrate the feasibility and validity of the proposed algorithm.

We introduce a new debiasing framework for high-dimensional linear regression that bypasses the restrictions on covariate distributions imposed by modern debiasing technology. We study the prevalent setting where the number of features and samples are both large and comparable. In this context, state-of-the-art debiasing technology uses a degrees-of-freedom correction to remove shrinkage bias of regularized estimators and conduct inference. However, this method requires that the observed samples are i.i.d., the covariates follow a mean zero Gaussian distribution, and reliable covariance matrix estimates for observed features are available. This approach struggles when (i) covariates are non-Gaussian with heavy tails or asymmetric distributions, (ii) rows of the design exhibit heterogeneity or dependencies, and (iii) reliable feature covariance estimates are lacking. To address these, we develop a new strategy where the debiasing correction is a rescaled gradient descent step (suitably initialized) with step size determined by the spectrum of the sample covariance matrix. Unlike prior work, we assume that eigenvectors of this matrix are uniform draws from the orthogonal group. We show this assumption remains valid in diverse situations where traditional debiasing fails, including designs with complex row-column dependencies, heavy tails, asymmetric properties, and latent low-rank structures. We establish asymptotic normality of our proposed estimator (centered and scaled) under various convergence notions. Moreover, we develop a consistent estimator for its asymptotic variance. Lastly, we introduce a debiased Principal Component Regression (PCR) technique using our Spectrum-Aware approach. In varied simulations and real data experiments, we observe that our method outperforms degrees-of-freedom debiasing by a margin.

The myriad complex systems with multiway interactions motivate the extension of graph-based pairwise connections to higher-order relations. In particular, the simplicial complex has inspired generalizations of graph neural networks (GNNs) to simplicial complex-based models. Learning on such systems requires large amounts of data, which can be expensive or impossible to obtain. We propose data augmentation of simplicial complexes through both linear and nonlinear mixup mechanisms that return mixtures of existing labeled samples. In addition to traditional pairwise mixup, we present a convex clustering mixup approach for a data-driven relationship among several simplicial complexes. We theoretically demonstrate that the resultant synthetic simplicial complexes interpolate among existing data with respect to homomorphism densities. Our method is demonstrated on both synthetic and real-world datasets for simplicial complex classification.

This paper settles an open and challenging question pertaining to the design of simple and optimal high-order methods for solving smooth and monotone variational inequalities (VIs). A VI involves finding $x^\star \in \mathcal{X}$ such that $\langle F(x), x - x^\star\rangle \geq 0$ for all $x \in \mathcal{X}$. We consider the setting in which $F$ is smooth with up to $(p-1)^{th}$-order derivatives. For $p = 2$, the cubic regularized Newton method was extended to VIs with a global rate of $O(\epsilon^{-1})$. An improved rate of $O(\epsilon^{-2/3}\log\log(1/\epsilon))$ can be obtained via an alternative second-order method, but this method requires a nontrivial line-search procedure as an inner loop. Similarly, high-order methods based on line-search procedures have been shown to achieve a rate of $O(\epsilon^{-2/(p+1)}\log\log(1/\epsilon))$. As emphasized by Nesterov, however, such procedures do not necessarily imply practical applicability in large-scale applications, and it would be desirable to complement these results with a simple high-order VI method that retains the optimality of the more complex methods. We propose a $p^{th}$-order method that does \textit{not} require any line search procedure and provably converges to a weak solution at a rate of $O(\epsilon^{-2/(p+1)})$. We prove that our $p^{th}$-order method is optimal in the monotone setting by establishing a matching lower bound under a generalized linear span assumption. Our method with restarting attains a linear rate for smooth and strictly monotone VIs and a local superlinear rate for smooth and strongly monotone VIs. Our method also achieves a global rate of $O(\epsilon^{-2/p})$ for solving smooth and nonmonotone VIs satisfying the Minty condition and when augmented with restarting it attains a global linear and local superlinear rate for smooth and nonmonotone VIs satisfying the strictly/strong Minty condition.

Knowledge-enhanced neural machine reasoning has garnered significant attention as a cutting-edge yet challenging research area with numerous practical applications. Over the past few years, plenty of studies have leveraged various forms of external knowledge to augment the reasoning capabilities of deep models, tackling challenges such as effective knowledge integration, implicit knowledge mining, and problems of tractability and optimization. However, there is a dearth of a comprehensive technical review of the existing knowledge-enhanced reasoning techniques across the diverse range of application domains. This survey provides an in-depth examination of recent advancements in the field, introducing a novel taxonomy that categorizes existing knowledge-enhanced methods into two primary categories and four subcategories. We systematically discuss these methods and highlight their correlations, strengths, and limitations. Finally, we elucidate the current application domains and provide insight into promising prospects for future research.

Deep neural network based recommendation systems have achieved great success as information filtering techniques in recent years. However, since model training from scratch requires sufficient data, deep learning-based recommendation methods still face the bottlenecks of insufficient data and computational inefficiency. Meta-learning, as an emerging paradigm that learns to improve the learning efficiency and generalization ability of algorithms, has shown its strength in tackling the data sparsity issue. Recently, a growing number of studies on deep meta-learning based recommenddation systems have emerged for improving the performance under recommendation scenarios where available data is limited, e.g. user cold-start and item cold-start. Therefore, this survey provides a timely and comprehensive overview of current deep meta-learning based recommendation methods. Specifically, we propose a taxonomy to discuss existing methods according to recommendation scenarios, meta-learning techniques, and meta-knowledge representations, which could provide the design space for meta-learning based recommendation methods. For each recommendation scenario, we further discuss technical details about how existing methods apply meta-learning to improve the generalization ability of recommendation models. Finally, we also point out several limitations in current research and highlight some promising directions for future research in this area.

Convolutional neural networks have made significant progresses in edge detection by progressively exploring the context and semantic features. However, local details are gradually suppressed with the enlarging of receptive fields. Recently, vision transformer has shown excellent capability in capturing long-range dependencies. Inspired by this, we propose a novel transformer-based edge detector, \emph{Edge Detection TransformER (EDTER)}, to extract clear and crisp object boundaries and meaningful edges by exploiting the full image context information and detailed local cues simultaneously. EDTER works in two stages. In Stage I, a global transformer encoder is used to capture long-range global context on coarse-grained image patches. Then in Stage II, a local transformer encoder works on fine-grained patches to excavate the short-range local cues. Each transformer encoder is followed by an elaborately designed Bi-directional Multi-Level Aggregation decoder to achieve high-resolution features. Finally, the global context and local cues are combined by a Feature Fusion Module and fed into a decision head for edge prediction. Extensive experiments on BSDS500, NYUDv2, and Multicue demonstrate the superiority of EDTER in comparison with state-of-the-arts.

With the rise of knowledge graph (KG), question answering over knowledge base (KBQA) has attracted increasing attention in recent years. Despite much research has been conducted on this topic, it is still challenging to apply KBQA technology in industry because business knowledge and real-world questions can be rather complicated. In this paper, we present AliMe-KBQA, a bold attempt to apply KBQA in the E-commerce customer service field. To handle real knowledge and questions, we extend the classic "subject-predicate-object (SPO)" structure with property hierarchy, key-value structure and compound value type (CVT), and enhance traditional KBQA with constraints recognition and reasoning ability. We launch AliMe-KBQA in the Marketing Promotion scenario for merchants during the "Double 11" period in 2018 and other such promotional events afterwards. Online results suggest that AliMe-KBQA is not only able to gain better resolution and improve customer satisfaction, but also becomes the preferred knowledge management method by business knowledge staffs since it offers a more convenient and efficient management experience.

Most existing knowledge graphs suffer from incompleteness, which can be alleviated by inferring missing links based on known facts. One popular way to accomplish this is to generate low-dimensional embeddings of entities and relations, and use these to make inferences. ConvE, a recently proposed approach, applies convolutional filters on 2D reshapings of entity and relation embeddings in order to capture rich interactions between their components. However, the number of interactions that ConvE can capture is limited. In this paper, we analyze how increasing the number of these interactions affects link prediction performance, and utilize our observations to propose InteractE. InteractE is based on three key ideas -- feature permutation, a novel feature reshaping, and circular convolution. Through extensive experiments, we find that InteractE outperforms state-of-the-art convolutional link prediction baselines on FB15k-237. Further, InteractE achieves an MRR score that is 9%, 7.5%, and 23% better than ConvE on the FB15k-237, WN18RR and YAGO3-10 datasets respectively. The results validate our central hypothesis -- that increasing feature interaction is beneficial to link prediction performance. We make the source code of InteractE available to encourage reproducible research.

With the capability of modeling bidirectional contexts, denoising autoencoding based pretraining like BERT achieves better performance than pretraining approaches based on autoregressive language modeling. However, relying on corrupting the input with masks, BERT neglects dependency between the masked positions and suffers from a pretrain-finetune discrepancy. In light of these pros and cons, we propose XLNet, a generalized autoregressive pretraining method that (1) enables learning bidirectional contexts by maximizing the expected likelihood over all permutations of the factorization order and (2) overcomes the limitations of BERT thanks to its autoregressive formulation. Furthermore, XLNet integrates ideas from Transformer-XL, the state-of-the-art autoregressive model, into pretraining. Empirically, XLNet outperforms BERT on 20 tasks, often by a large margin, and achieves state-of-the-art results on 18 tasks including question answering, natural language inference, sentiment analysis, and document ranking.