This blog post describes our experience debugging a failing test case caused by a cross join query running "too fast." Because the root cause of fail test case spans across multiple layers--from Apache Spark to the JVM JIT compiler-- we wanted to share our analysis in this post.

Suppose, we are given a set of $n$ elements to be clustered into $k$ (unknown) clusters, and an oracle/expert labeler that can interactively answer pair-wise queries of the form, ``do two elements $u$ and $v$ belong to the same cluster?''. The goal is to recover the optimum clustering by asking the minimum number of queries. In this paper, we provide a rigorous theoretical study of this basic problem of query complexity of interactive clustering, and give strong information theoretic lower bounds, as well as nearly matching upper bounds. Most clustering problems come with a similarity matrix, which is used by an automated process to cluster similar points together. To improve accuracy of clustering, a fruitful approach in recent years has been to ask a domain expert or crowd to obtain labeled data interactively. Many heuristics have been proposed, and all of these use a similarity function to come up with a querying strategy. Even so, there is a lack systematic theoretical study. Our main contribution in this paper is to show the dramatic power of side information aka similarity matrix on reducing the query complexity of clustering. A similarity matrix represents noisy pair-wise relationships such as one computed by some function on attributes of the elements. A natural noisy model is where similarity values are drawn independently from some arbitrary probability distribution $f_+$ when the underlying pair of elements belong to the same cluster, and from some $f_-$ otherwise. We show that given such a similarity matrix, the query complexity reduces drastically from $\Theta(nk)$ (no similarity matrix) to $O(\frac{k^2\log{n}}{\cH^2(f_+\|f_-)})$ where $\cH^2$ denotes the squared Hellinger divergence. Moreover, this is also information-theoretic optimal within an $O(\log{n})$ factor. Our algorithms are all efficient, and parameter free, i.e., they work without any knowledge of $k, f_+$ and $f_-$, and only depend logarithmically with $n$.

In this paper we address cardinality estimation problem which is an important subproblem in query optimization. Query optimization is a part of every relational DBMS responsible for finding the best way of the execution for the given query. These ways are called plans. The execution time of different plans may differ by several orders, so query optimizer has a great influence on the whole DBMS performance. We consider cost-based query optimization approach as the most popular one. It was observed that cost-based optimization quality depends much on cardinality estimation quality. Cardinality of the plan node is the number of tuples returned by it. In the paper we propose a novel cardinality estimation approach with the use of machine learning methods. The main point of the approach is using query execution statistics of the previously executed queries to improve cardinality estimations. We called this approach adaptive cardinality estimation to reflect this point. The approach is general, flexible, and easy to implement. The experimental evaluation shows that this approach significantly increases the quality of cardinality estimation, and therefore increases the DBMS performance for some queries by several times or even by several dozens of times.

Learning novel concepts and relations from relational databases is an important problem with many applications in database systems and machine learning. Relational learning algorithms learn the definition of a new relation in terms of existing relations in the database. Nevertheless, the same data set may be represented under different schemas for various reasons, such as efficiency, data quality, and usability. Unfortunately, the output of current relational learning algorithms tends to vary quite substantially over the choice of schema, both in terms of learning accuracy and efficiency. This variation complicates their off-the-shelf application. In this paper, we introduce and formalize the property of schema independence of relational learning algorithms, and study both the theoretical and empirical dependence of existing algorithms on the common class of (de) composition schema transformations. We study both sample-based learning algorithms, which learn from sets of labeled examples, and query-based algorithms, which learn by asking queries to an oracle. We prove that current relational learning algorithms are generally not schema independent. For query-based learning algorithms we show that the (de) composition transformations influence their query complexity. We propose Castor, a sample-based relational learning algorithm that achieves schema independence by leveraging data dependencies. We support the theoretical results with an empirical study that demonstrates the schema dependence/independence of several algorithms on existing benchmark and real-world datasets under (de) compositions.

We propose a generalization of the classical database query optimization problem: multi-objective parametric query (MPQ) optimization. MPQ compares alternative processing plans according to multiple execution cost metrics. It also models missing pieces of information on which plan costs depend upon as parameters. Both features are crucial to model query processing on modern data processing platforms. MPQ generalizes previously proposed query optimization variants, such as multi-objective query optimization, parametric query optimization, and traditional query optimization.

Query optimization is a fundamental problem in data management. Simply put, most database query languages are declarative rather than imperative--that is, they specify properties the answer should satisfy, rather than give an algorithm to compute the answer. The best known and most widely used database query language--SQL--is a prime example of a language for which optimization is essential. By "essential," I mean that database optimization is not a matter of shaving 10% or even a factor of 2x from a query's execution time. In database query evaluation, the difference between a good plan and a bad or even average plan can be multiple orders of magnitude--so successful query optimization makes the difference between a plan that runs quickly and one that never finishes at all.

This is a joint engineering effort between Databricks' Apache Spark engineering team (Sameer Agarwal and Wenchen Fan) and Huawei's engineering team (Ron Hu and Zhenhua Wang) Apache Spark 2.2 recently shipped with a state-of-art cost-based optimization framework that collects and leverages a variety of per-column data statistics (e.g., cardinality, number of distinct values, NULL values, max/min, average/max length, etc.) to improve the quality of query execution plans. Leveraging these statistics helps Spark to make better decisions in picking the most optimal query plan. Examples of these optimizations include selecting the correct build side in a hash-join, choosing the right join type (broadcast hash-join vs. shuffled hash-join) or adjusting a multi-way join order, among others. In this blog, we'll take a deep dive into Spark's Cost Based Optimizer (CBO) and discuss how Spark collects and stores these statistics, optimizes queries, and show its performance impact on TPC-DS benchmark queries. At its core, Spark's Catalyst optimizer is a general library for representing query plans as trees and sequentially applying a number of optimization rules to manipulate them.

Conversational interfaces with computers have been the talk of tech since the days of Star Trek. Mostly associated with voice response, frustrating experiences interacting with Siri, chatbots, or the interactive voice response (IVR) systems of call centers reveal what a long slog it's been for getting computers to understand natural language, regardless of whether it's in the form of voice or text. But it took the Amazon Echo's Alexa, which was designed as a conversational voice to Amazon's retail and entertainment services, to show that natural language interfaces could actually perform useful services. When we saw SAS founder Dr. James Goodnight demonstrate how Alexa could be used to query SAS Visual Analytics, we thought that was pretty cool. But when you look at this video, you'll realize that Alexa has only been taught a few things and has a long way to go before it will replace your keyboard or touchpad.

Suppose, we are given a set of $n$ elements to be clustered into $k$ (unknown) clusters, and an oracle/expert labeler that can interactively answer pair-wise queries of the form, "do two elements $u$ and $v$ belong to the same cluster?". The goal is to recover the optimum clustering by asking the minimum number of queries. In this paper, we initiate a rigorous theoretical study of this basic problem of query complexity of interactive clustering, and provide strong information theoretic lower bounds, as well as nearly matching upper bounds. Most clustering problems come with a similarity matrix, which is used by an automated process to cluster similar points together. Our main contribution in this paper is to show the dramatic power of side information aka similarity matrix on reducing the query complexity of clustering. A similarity matrix represents noisy pair-wise relationships such as one computed by some function on attributes of the elements. A natural noisy model is where similarity values are drawn independently from some arbitrary probability distribution $f_+$ when the underlying pair of elements belong to the same cluster, and from some $f_-$ otherwise. We show that given such a similarity matrix, the query complexity reduces drastically from $\Theta(nk)$ (no similarity matrix) to $O(\frac{k^2\log{n}}{\cH^2(f_+\|f_-)})$ where $\cH^2$ denotes the squared Hellinger divergence. Moreover, this is also information-theoretic optimal within an $O(\log{n})$ factor. Our algorithms are all efficient, and parameter free, i.e., they work without any knowledge of $k, f_+$ and $f_-$, and only depend logarithmically with $n$. Along the way, our work also reveals intriguing connection to popular community detection models such as the {\em stochastic block model}, significantly generalizes them, and opens up many venues for interesting future research.

As most database users cannot precisely express their information needs, it is challenging for database management systems to understand them. We propose a novel formal framework for representing and understanding information needs in database querying and exploration. Our framework considers querying as a collaboration between the user and the database management system to establish a it mutual language for representing information needs. We formalize this collaboration as a signaling game, where each mutual language is an equilibrium for the game. A query interface is more effective if it establishes a less ambiguous mutual language faster. We discuss some equilibria, strategies, and the convergence in this game. In particular, we propose a reinforcement learning mechanism and analyze it within our framework. We prove that this adaptation mechanism for the query interface improves the effectiveness of answering queries stochastically speaking, and converges almost surely. We extend out results for the cases that the user also modifies her strategy during the interaction.