Kernel techniques are among the most influential approaches in data science and statistics. Under mild conditions, the reproducing kernel Hilbert space associated to a kernel is capable of encoding the independence of $M\ge 2$ random variables. Probably the most widespread independence measure relying on kernels is the so-called Hilbert-Schmidt independence criterion (HSIC; also referred to as distance covariance in the statistics literature). Despite various existing HSIC estimators designed since its introduction close to two decades ago, the fundamental question of the rate at which HSIC can be estimated is still open. In this work, we prove that the minimax optimal rate of HSIC estimation on $\mathbb R^d$ for Borel measures containing the Gaussians with continuous bounded translation-invariant characteristic kernels is $\mathcal O\!\left(n^{-1/2}\right)$. Specifically, our result implies the optimality in the minimax sense of many of the most-frequently used estimators (including the U-statistic, the V-statistic, and the Nystr\"om-based one) on $\mathbb R^d$.

The effectiveness of Evolutionary Neural Architecture Search (ENAS) is influenced by the design of the search space. Nevertheless, common methods including the global search space, scalable search space and hierarchical search space have certain limitations. Specifically, the global search space requires a significant amount of computational resources and time, the scalable search space sacrifices the diversity of network structures and the hierarchical search space increases the search cost in exchange for network diversity. To address above limitation, we propose a novel paradigm of searching neural network architectures and design the Multiple Population Alternate Evolution Neural Architecture Search (MPAE), which can achieve module diversity with a smaller search cost. MPAE converts the search space into L interconnected units and sequentially searches the units, then the above search of the entire network be cycled several times to reduce the impact of previous units on subsequent units. To accelerate the population evolution process, we also propose the the population migration mechanism establishes an excellent migration archive and transfers the excellent knowledge and experience in the migration archive to new populations. The proposed method requires only 0.3 GPU days to search a neural network on the CIFAR dataset and achieves the state-of-the-art results.

Though numerous solvers have been proposed for the MaxSAT problem, and the benchmark environment such as MaxSAT Evaluations provides a platform for the comparison of the state-of-the-art solvers, existing assessments were usually evaluated based on the quality, e.g., fitness, of the best-found solutions obtained within a given running time budget. However, concerning solely the final obtained solutions regarding specific time budgets may restrict us from comprehending the behavior of the solvers along the convergence process. This paper demonstrates that Empirical Cumulative Distribution Functions can be used to compare MaxSAT local search solvers' anytime performance across multiple problem instances and various time budgets. The assessment reveals distinctions in solvers' performance and displays that the (dis)advantages of solvers adjust along different running times. This work also exhibits that the quantitative and high variance assessment of anytime performance can guide machines, i.e., automatic configurators, to search for better parameter settings. Our experimental results show that the hyperparameter optimization tool, i.e., SMAC, generally achieves better parameter settings of local search when using the anytime performance as the cost function, compared to using the fitness of the best-found solutions.

A recent research trend involves treating database index structures as Machine Learning (ML) models. In this domain, single or multiple ML models are trained to learn the mapping from keys to positions inside a data set. This class of indexes is known as "Learned Indexes." Learned indexes have demonstrated improved search performance and reduced space requirements for one-dimensional data. The concept of one-dimensional learned indexes has naturally been extended to multi-dimensional (e.g., spatial) data, leading to the development of "Learned Multi-dimensional Indexes". This survey focuses on learned multi-dimensional index structures. Specifically, it reviews the current state of this research area, explains the core concepts behind each proposed method, and classifies these methods based on several well-defined criteria. We present a taxonomy that classifies and categorizes each learned multi-dimensional index, and survey the existing literature on learned multi-dimensional indexes according to this taxonomy. Additionally, we present a timeline to illustrate the evolution of research on learned indexes. Finally, we highlight several open challenges and future research directions in this emerging and highly active field.

Recently, neural networks (NN) have made great strides in combinatorial optimization. However, they face challenges when solving the capacitated arc routing problem (CARP) which is to find the minimum-cost tour covering all required edges on a graph, while within capacity constraints. In tackling CARP, NN-based approaches tend to lag behind advanced metaheuristics, since they lack directed arc modeling and efficient learning methods tailored for complex CARP. In this paper, we introduce an NN-based solver to significantly narrow the gap with advanced metaheuristics while exhibiting superior efficiency. First, we propose the direction-aware attention model (DaAM) to incorporate directionality into the embedding process, facilitating more effective one-stage decision-making. Second, we design a supervised reinforcement learning scheme that involves supervised pre-training to establish a robust initial policy for subsequent reinforcement fine-tuning. It proves particularly valuable for solving CARP that has a higher complexity than the node routing problems (NRPs). Finally, a path optimization method is proposed to adjust the depot return positions within the path generated by DaAM. Experiments illustrate that our approach surpasses heuristics and achieves decision quality comparable to state-of-the-art metaheuristics for the first time while maintaining superior efficiency.

Feature augmentation from one-to-many relationship tables is a critical but challenging problem in ML model development. To augment good features, data scientists need to come up with SQL queries manually, which is time-consuming. Featuretools [1] is a widely used tool by the data science community to automatically augment the training data by extracting new features from relevant tables. It represents each feature as a group-by aggregation SQL query on relevant tables and can automatically generate these SQL queries. However, it does not include predicates in these queries, which significantly limits its application in many real-world scenarios. To overcome this limitation, we propose FEATAUG, a new feature augmentation framework that automatically extracts predicate-aware SQL queries from one-to-many relationship tables. This extension is not trivial because considering predicates will exponentially increase the number of candidate queries. As a result, the original Featuretools framework, which materializes all candidate queries, will not work and needs to be redesigned. We formally define the problem and model it as a hyperparameter optimization problem. We discuss how the Bayesian Optimization can be applied here and propose a novel warm-up strategy to optimize it. To make our algorithm more practical, we also study how to identify promising attribute combinations for predicates. We show that how the beam search idea can partially solve the problem and propose several techniques to further optimize it. Our experiments on four real-world datasets demonstrate that FeatAug extracts more effective features compared to Featuretools and other baselines. The code is open-sourced at https://github.com/sfu-db/FeatAug

In recent years, there has been a significant amount of research focused on expanding the expressivity of Graph Neural Networks (GNNs) beyond the Weisfeiler-Lehman (1-WL) framework. While many of these studies have yielded advancements in expressivity, they have frequently come at the expense of decreased efficiency or have been restricted to specific types of graphs. In this study, we investigate the expressivity of GNNs from the perspective of graph search. Specifically, we propose a new vertex colouring scheme and demonstrate that classical search algorithms can efficiently compute graph representations that extend beyond the 1-WL. We show the colouring scheme inherits useful properties from graph search that can help solve problems like graph biconnectivity. Furthermore, we show that under certain conditions, the expressivity of GNNs increases hierarchically with the radius of the search neighbourhood. To further investigate the proposed scheme, we develop a new type of GNN based on two search strategies, breadth-first search and depth-first search, highlighting the graph properties they can capture on top of 1-WL. Our code is available at https://github.com/seanli3/lvc.

In this paper, we study a facility location problem within a competitive market context, where customer demand is predicted by a random utility choice model. Unlike prior research, which primarily focuses on simple constraints such as a cardinality constraint on the number of selected locations, we introduce routing constraints that necessitate the selection of locations in a manner that guarantees the existence of a tour visiting all chosen locations while adhering to a specified tour length upper bound. Such routing constraints find crucial applications in various real-world scenarios. The problem at hand features a non-linear objective function, resulting from the utilization of random utilities, together with complex routing constraints, making it computationally challenging. To tackle this problem, we explore three types of valid cuts, namely, outer-approximation and submodular cuts to handle the nonlinear objective function, as well as sub-tour elimination cuts to address the complex routing constraints. These lead to the development of two exact solution methods: a nested cutting plane and nested branch-and-cut algorithms, where these valid cuts are iteratively added to a master problem through two nested loops. We also prove that our nested cutting plane method always converges to optimality after a finite number of iterations. Furthermore, we develop a local search-based metaheuristic tailored for solving large-scale instances and show its pros and cons compared to exact methods. Extensive experiments are conducted on problem instances of varying sizes, demonstrating that our approach excels in terms of solution quality and computation time when compared to other baseline approaches.

Graph neural architecture search (GraphNAS) has recently aroused considerable attention in both academia and industry. However, two key challenges seriously hinder the further research of GraphNAS. First, since there is no consensus for the experimental setting, the empirical results in different research papers are often not comparable and even not reproducible, leading to unfair comparisons. Secondly, GraphNAS often needs extensive computations, which makes it highly inefficient and inaccessible to researchers without access to large-scale computation. To solve these challenges, we propose NAS-Bench-Graph, a tailored benchmark that supports unified, reproducible, and efficient evaluations for GraphNAS. Specifically, we construct a unified, expressive yet compact search space, covering 26,206 unique graph neural network (GNN) architectures and propose a principled evaluation protocol. To avoid unnecessary repetitive training, we have trained and evaluated all of these architectures on nine representative graph datasets, recording detailed metrics including train, validation, and test performance in each epoch, the latency, the number of parameters, etc. Based on our proposed benchmark, the performance of GNN architectures can be directly obtained by a look-up table without any further computation, which enables fair, fully reproducible, and efficient comparisons. To demonstrate its usage, we make in-depth analyses of our proposed NAS-Bench-Graph, revealing several interesting findings for GraphNAS. We also showcase how the benchmark can be easily compatible with GraphNAS open libraries such as AutoGL and NNI. To the best of our knowledge, our work is the first benchmark for graph neural architecture search.

To develop a strategy to design VQC in an automated way, i.e. quantum architecture search (QAS), some researchers Considering the noise level limit, one crucial aspect have turned their attention to the classical Neural Architecture for quantum machine learning is to design a highperforming Search (NAS) framework. NAS focuses on automating variational quantum circuit architecture the design of neural network structures [Elsken et al., with small number of quantum gates. As the classical 2019], but often grapple with the challenge of evaluating a neural architecture search (NAS), quantum architecture vast number of possible network architectures. The Monte search methods (QAS) employ methods Carlo Tree Search (MCTS) algorithm addresses this issue by like reinforcement learning, evolutionary algorithms iteratively exploring and evaluating segments of the search and supernet optimization to improve the space, thereby identifying promising neural network structures search efficiency. In this paper, we propose a novel without exhaustive enumeration [Silver et al., 2016; qubit-wise architecture search (QWAS) method, Wang et al., 2020]. However, the efficiency of the search is which progressively search one-qubit configuration significantly influenced by the manually predefined action per stage, and combine with Monte Carlo Tree space before the tree construction. To address this issue, Search algorithm to find good quantum architectures [Wang et al., 2021] proposed an improved MCTS-based algorithm by partitioning the search space into several called Latent Action Neural Architecture Search good and bad subregions. The numerical experimental (LaNAS) that learns a latent action space that best fits the results indicate that our proposed method can problem to be solved.