We consider the problem of minimizing the number of matrix-vector queries needed for accurate trace estimation in the dynamic setting where our underlying matrix is changing slowly, such as during an optimization process. Specifically, for any $m$ matrices $A_1,...,A_m$ with consecutive differences bounded in Schatten-$1$ norm by $\alpha$, we provide a novel binary tree summation procedure that simultaneously estimates all $m$ traces up to $\epsilon$ error with $\delta$ failure probability with an optimal query complexity of $\widetilde{O}\left(m \alpha\sqrt{\log(1/\delta)}/\epsilon + m\log(1/\delta)\right)$, improving the dependence on both $\alpha$ and $\delta$ from Dharangutte and Musco (NeurIPS, 2021). Our procedure works without additional norm bounds on $A_i$ and can be generalized to a bound for the $p$-th Schatten norm for $p \in [1,2]$, giving a complexity of $\widetilde{O}\left(m \alpha\left(\sqrt{\log(1/\delta)}/\epsilon\right)^p +m \log(1/\delta)\right)$. By using novel reductions to communication complexity and information-theoretic analyses of Gaussian matrices, we provide matching lower bounds for static and dynamic trace estimation in all relevant parameters, including the failure probability. Our lower bounds (1) give the first tight bounds for Hutchinson's estimator in the matrix-vector product model with Frobenius norm error even in the static setting, and (2) are the first unconditional lower bounds for dynamic trace estimation, resolving open questions of prior work.

Recent advances have shown the success of using reinforcement learning and search to solve NP-hard graph-related tasks, such as Traveling Salesman Optimization, Graph Edit Distance computation, etc. However, it remains unclear how one can efficiently and accurately detect the occurrences of a small query graph in a large target graph, which is a core operation in graph database search, biomedical analysis, social group finding, etc. This task is called Subgraph Matching which essentially performs subgraph isomorphism check between a query graph and a large target graph. One promising approach to this classical problem is the "learning-to-search" paradigm, where a reinforcement learning (RL) agent is designed with a learned policy to guide a search algorithm to quickly find the solution without any solved instances for supervision. However, for the specific task of Subgraph Matching, though the query graph is usually small given by the user as input, the target graph is often orders-of-magnitude larger. It poses challenges to the neural network design and can lead to solution and reward sparsity. S with two innovations to tackle the challenges: (1) A novel encoder-decoder neural network architecture to dynamically compute the matching information between the query and the target graphs at each search state; (2) A novel look-ahead loss function for training the policy network. S can significantly improve the subgraph matching performance. With the growing amount of graph data that naturally arises in many domains, solving graph-related tasks via machine learning has gained increasing attention.

Building query graphs from natural language questions is an important step in complex question answering over knowledge graph (Complex KGQA). In general, a question can be correctly answered if its query graph is built correctly and the right answer is then retrieved by issuing the query graph against the KG. Therefore, this paper focuses on query graph generation from natural language questions. Existing approaches for query graph generation ignore the semantic structure of a question, resulting in a large number of noisy query graph candidates that undermine prediction accuracies. In this paper, we define six semantic structures from common questions in KGQA and develop a novel Structure-BERT to predict the semantic structure of a question. By doing so, we can first filter out noisy candidate query graphs, and then rank the remaining candidates with a BERT-based ranking model. Extensive experiments on two popular benchmarks MetaQA and WebQuestionsSP (WSP) demonstrate the effectiveness of our method as compared to state-of-the-arts.

Answering complex queries over knowledge graphs (KG) is an important yet challenging task because of the KG incompleteness issue and cascading errors during reasoning. Recent query embedding (QE) approaches to embed the entities and relations in a KG and the first-order logic (FOL) queries into a low dimensional space, answering queries by dense similarity search. However, previous works mainly concentrate on the target answers, ignoring intermediate entities' usefulness, which is essential for relieving the cascading error problem in logical query answering. In addition, these methods are usually designed with their own geometric or distributional embeddings to handle logical operators like union, intersection, and negation, with the sacrifice of the accuracy of the basic operator - projection, and they could not absorb other embedding methods to their models. In this work, we propose a Neural and Symbolic Entangled framework (ENeSy) for complex query answering, which enables the neural and symbolic reasoning to enhance each other to alleviate the cascading error and KG incompleteness. The projection operator in ENeSy could be any embedding method with the capability of link prediction, and the other FOL operators are handled without parameters. With both neural and symbolic reasoning results contained, ENeSy answers queries in ensembles. ENeSy achieves the SOTA performance on several benchmarks, especially in the setting of the training model only with the link prediction task.

Access plan recommendation is a query optimization approach that executes new queries using prior created query execution plans (QEPs). The query optimizer divides the query space into clusters in the mentioned method. However, traditional clustering algorithms take a significant amount of execution time for clustering such large datasets. The MapReduce distributed computing model provides efficient solutions for storing and processing vast quantities of data. Apache Spark and Apache Hadoop frameworks are used in the present investigation to cluster different sizes of query datasets in the MapReduce-based access plan recommendation method. The performance evaluation is performed based on execution time. The results of the experiments demonstrated the effectiveness of parallel query clustering in achieving high scalability. Furthermore, Apache Spark achieved better performance than Apache Hadoop, reaching an average speedup of 2x.

Graph representations for real-world social networks in the past have missed two important elements: the multiplexity of connections as well as representing time. To this end, in this paper, we present a new dynamic heterogeneous graph representation for social networks which includes time in every single component of the graph, i.e., nodes and edges, each of different types that captures heterogeneity. We illustrate the power of this representation by presenting four time-dependent queries and deep learning problems that cannot easily be handled in conventional homogeneous graph representations commonly used. As a proof of concept we present a detailed representation of a new social media platform (Steemit), which we use to illustrate both the dynamic querying capability as well as prediction tasks using graph neural networks (GNNs). The results illustrate the power of the dynamic heterogeneous graph representation to model social networks. Given that this is a relatively understudied area we also illustrate opportunities for future work in query optimization as well as new dynamic prediction tasks on heterogeneous graph structures.

We demonstrate Tensor Query Processor (TQP): a query processor that automatically compiles relational operators into tensor programs. By leveraging tensor runtimes such as PyTorch, TQP is able to: (1) integrate with ML tools (e.g., Pandas for data ingestion, Tensorboard for visualization); (2) target different hardware (e.g., CPU, GPU) and software (e.g., browser) backends; and (3) end-to-end accelerate queries containing both relational and ML operators. TQP is generic enough to support the TPC-H benchmark, and it provides performance that is comparable to, and often better than, that of specialized CPU and GPU query processors.

We rank all we rely on item retrieval from marketplace inventory. With retrieved items by the sum of tf-idf scores from matched words, feedback to expand query scope, we discuss keyword expansion and keep the items with total tf-idf scores above a threshold. The candidate selection using word embedding similarity, and an retrieval based system works well to discover relevant enhanced tf-idf formula for expanded words in search ranking.

Machine learning is rapidly being used in database research to improve the effectiveness of numerous tasks included but not limited to query optimization, workload scheduling, physical design, etc. Currently, the research focus has been on replacing a single database component responsible for one task by its learning-based counterpart. However, query performance is not simply determined by the performance of a single component, but by the cooperation of multiple ones. As such, learning based database components need to collaborate during both training and execution in order to develop policies that meet end performance goals. Thus, the paper attempts to address the question "Is it possible to design a database consisting of various learned components that cooperatively work to improve end-to-end query latency?". To answer this question, we introduce MADB (Multi-Agent DB), a proof-of-concept system that incorporates a learned query scheduler and a learned query optimizer. MADB leverages a cooperative multi-agent reinforcement learning approach that allows the two components to exchange the context of their decisions with each other and collaboratively work towards reducing the query latency. Preliminary results demonstrate that MADB can outperform the non-cooperative integration of learned components.

One could imagine many simple heuristics, query scheduling with the explicit goal of reducing disk reads such as greedily selecting the next query with the highest and thus implicitly increasing query performance. We introduce expected buffer usage, to solve this problem. However, a SmartQueue, a learned scheduler that leverages overlapping hand-designed policy to handle the complexity of the entire data reads among incoming queries and learns a problem, including different buffer sizes, shifting query scheduling strategy that improves cache hits. SmartQueue workloads, heterogeneous data types (e.g., index files vs base relies on deep reinforcement learning to produce workloadspecific relations), and balancing short-term gains against long-term scheduling strategies that focus on long-term performance strategy is much more difficult to conceive.