arXiv subjects

Dan Suciu

Publications and source records attributed to Dan Suciu.

At least 55 records · Page 3Linked to original sources

arXiv2022

A Near-Optimal Parallel Algorithm for Joining Binary Relations

We present a constant-round algorithm in the massively parallel computation (MPC) model for evaluating a natural join where every input relation has two attributes. Our algorithm achieves a load of $\tilde{O}(m/p^{1/ρ})$ where $m$ is the total size of the input relations, $p$ is the number of machines, $ρ$ is the join's fractional edge covering number, and $\tilde{O}(.)$ hides a polylogarithmic factor. The load matches a known lower bound up to a polylogarithmic factor. At the core of the proposed algorithm is a new theorem (which we name the "isolated cartesian product theorem") that provides fresh insight into the problem's mathematical structure. Our result implies that the subgraph enumeration problem, where the goal is to report all the occurrences of a constant-sized subgraph pattern, can be settled optimally (up to a polylogarithmic factor) in the MPC model.

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arXiv2022

Degree Sequence Bound For Join Cardinality Estimation

Recent work has demonstrated the catastrophic effects of poor cardinality estimates on query processing time. In particular, underestimating query cardinality can result in overly optimistic query plans which take orders of magnitude longer to complete than one generated with the true cardinality. Cardinality bounding avoids this pitfall by computing a strict upper bound on the query's output size using statistics about the database such as table sizes and degrees, i.e. value frequencies. In this paper, we extend this line of work by proving a novel bound called the Degree Sequence Bound which takes into account the full degree sequences and the max tuple multiplicity. This bound improves upon previous work incorporating degree constraints which focused on the maximum degree rather than the degree sequence. Further, we describe how to practically compute this bound using a learned approximation of the true degree sequences.

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arXiv2022

Optimizing Recursive Queries with Program Synthesis

Most work on query optimization has concentrated on loop-free queries. However, data science and machine learning workloads today typically involve recursive or iterative computation. In this work, we propose a novel framework for optimizing recursive queries using methods from program synthesis. In particular, we introduce a simple yet powerful optimization rule called the "FGH-rule" which aims to find a faster way to evaluate a recursive program. The solution is found by making use of powerful tools, such as a program synthesizer, an SMT-solver, and an equality saturation system. We demonstrate the strength of the optimization by showing that the FGH-rule can lead to speedups up to 4 orders of magnitude on three, already optimized Datalog systems.

cs.DB↗

arXiv2022

Integrity Constraints Revisited: From Exact to Approximate Implication

Integrity constraints such as functional dependencies (FD) and multi-valued dependencies (MVD) are fundamental in database schema design. Likewise, probabilistic conditional independences (CI) are crucial for reasoning about multivariate probability distributions. The implication problem studies whether a set of constraints (antecedents) implies another constraint (consequent), and has been investigated in both the database and the AI literature, under the assumption that all constraints hold exactly. However, many applications today consider constraints that hold only approximately. In this paper we define an approximate implication as a linear inequality between the degree of satisfaction of the antecedents and consequent, and we study the relaxation problem: when does an exact implication relax to an approximate implication? We use information theory to define the degree of satisfaction, and prove several results. First, we show that any implication from a set of data dependencies (MVDs+FDs) can be relaxed to a simple linear inequality with a factor at most quadratic in the number of variables; when the consequent is an FD, the factor can be reduced to 1. Second, we prove that there exists an implication between CIs that does not admit any relaxation; however, we prove that every implication between CIs relaxes "in the limit". Then, we show that the implication problem for differential constraints in market basket analysis also admits a relaxation with a factor equal to 1. Finally, we show how some of the results in the paper can be derived using the I-measure theory, which relates between information theoretic measures and set theory. Our results recover, and sometimes extend, previously known results about the implication problem: the implication of MVDs and FDs can be checked by considering only 2-tuple relations.

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arXiv2021

Bag Query Containment and Information Theory

The query containment problem is a fundamental algorithmic problem in data management. While this problem is well understood under set semantics, it is by far less understood under bag semantics. In particular, it is a long-standing open question whether or not the conjunctive query containment problem under bag semantics is decidable. We unveil tight connections between information theory and the conjunctive query containment under bag semantics. These connections are established using information inequalities, which are considered to be the laws of information theory. Our first main result asserts that deciding the validity of maxima of information inequalities is many-one equivalent to the restricted case of conjunctive query containment in which the containing query is acyclic; thus, either both these problems are decidable or both are undecidable. Our second main result identifies a new decidable case of the conjunctive query containment problem under bag semantics. Specifically, we give an exponential time algorithm for conjunctive query containment under bag semantics, provided the containing query is chordal and admits a simple junction tree.

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arXiv2021

A Dichotomy for the Generalized Model Counting Problem for Unions of Conjunctive Queries

We study the $generalized~model~counting~problem$, defined as follows: given a database, and a set of deterministic tuples, count the number of subsets of the database that include all deterministic tuples and satisfy the query. This problem is computationally equivalent to the evaluation of the query over a tuple-independent probabilistic database where all tuples have probabilities in $\{0,\frac{1}{2},1\}$. Previous work has established a dichotomy for Unions of Conjunctive Queries (UCQ) when the probabilities are arbitrary rational numbers, showing that, for each query, its complexity is either in polynomial time or #P-hard. The query is called $safe$ in the first case, and $unsafe$ in the second case. Here, we strengthen the hardness proof, by proving that an unsafe UCQ query remains #P-hard even if the probabilities are restricted to $\{0,\frac{1}{2},1\}$. This requires a complete redesign of the hardness proof, using new techniques. A related problem is the $model~counting~problem$, which asks for the probability of the query when the input probabilities are restricted to $\{0,\frac{1}{2}\}$. While our result does not extend to model counting for all unsafe UCQs, we prove that model counting is #P-hard for a class of unsafe queries called Type-I forbidden queries.

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arXiv2021

GeCo: Quality Counterfactual Explanations in Real Time

Machine learning is increasingly applied in high-stakes decision making that directly affect people's lives, and this leads to an increased demand for systems to explain their decisions. Explanations often take the form of counterfactuals, which consists of conveying to the end user what she/he needs to change in order to improve the outcome. Computing counterfactual explanations is challenging, because of the inherent tension between a rich semantics of the domain, and the need for real time response. In this paper we present GeCo, the first system that can compute plausible and feasible counterfactual explanations in real time. At its core, GeCo relies on a genetic algorithm, which is customized to favor searching counterfactual explanations with the smallest number of changes. To achieve real-time performance, we introduce two novel optimizations: $Δ$-representation of candidate counterfactuals, and partial evaluation of the classifier. We compare empirically GeCo against five other systems described in the literature, and show that it is the only system that can achieve both high quality explanations and real time answers.

cs.LG↗

arXiv2021

On the Tractability of SHAP Explanations

SHAP explanations are a popular feature-attribution mechanism for explainable AI. They use game-theoretic notions to measure the influence of individual features on the prediction of a machine learning model. Despite a lot of recent interest from both academia and industry, it is not known whether SHAP explanations of common machine learning models can be computed efficiently. In this paper, we establish the complexity of computing the SHAP explanation in three important settings. First, we consider fully-factorized data distributions, and show that the complexity of computing the SHAP explanation is the same as the complexity of computing the expected value of the model. This fully-factorized setting is often used to simplify the SHAP computation, yet our results show that the computation can be intractable for commonly used models such as logistic regression. Going beyond fully-factorized distributions, we show that computing SHAP explanations is already intractable for a very simple setting: computing SHAP explanations of trivial classifiers over naive Bayes distributions. Finally, we show that even computing SHAP over the empirical distribution is #P-hard.

cs.AI↗

arXiv2020

SPORES: Sum-Product Optimization via Relational Equality Saturation for Large Scale Linear Algebra

Machine learning algorithms are commonly specified in linear algebra (LA). LA expressions can be rewritten into more efficient forms, by taking advantage of input properties such as sparsity, as well as program properties such as common subexpressions and fusible operators. The complex interaction among these properties' impact on the execution cost poses a challenge to optimizing compilers. Existing compilers resort to intricate heuristics that complicate the codebase and add maintenance cost but fail to search through the large space of equivalent LA expressions to find the cheapest one. We introduce a general optimization technique for LA expressions, by converting the LA expressions into Relational Algebra (RA) expressions, optimizing the latter, then converting the result back to (optimized) LA expressions. One major advantage of this method is that it is complete, meaning that any equivalent LA expression can be found using the equivalence rules in RA. The challenge is the major size of the search space, and we address this by adopting and extending a technique used in compilers, called equality saturation. We integrate the optimizer into SystemML and validate it empirically across a spectrum of machine learning tasks; we show that we can derive all existing hand-coded optimizations in SystemML, and perform new optimizations that lead to speedups from 1.2X to 5X.

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arXiv2020

Causality-based Explanation of Classification Outcomes

We propose a simple definition of an explanation for the outcome of a classifier based on concepts from causality. We compare it with previously proposed notions of explanation, and study their complexity. We conduct an experimental evaluation with two real datasets from the financial domain.

cs.LG↗

arXiv2020

Decision Problems in Information Theory

Constraints on entropies are considered to be the laws of information theory. Even though the pursuit of their discovery has been a central theme of research in information theory, the algorithmic aspects of constraints on entropies remain largely unexplored. Here, we initiate an investigation of decision problems about constraints on entropies by placing several different such problems into levels of the arithmetical hierarchy. We establish the following results on checking the validity over all almost-entropic functions: first, validity of a Boolean information constraint arising from a monotone Boolean formula is co-recursively enumerable; second, validity of "tight" conditional information constraints is in $Π^0_3$. Furthermore, under some restrictions, validity of conditional information constraints "with slack" is in $Σ^0_2$, and validity of information inequality constraints involving max is Turing equivalent to validity of information inequality constraints (with no max involved). We also prove that the classical implication problem for conditional independence statements is co-recursively enumerable.

cs.IT↗

arXiv2020

Causal Relational Learning

Causal inference is at the heart of empirical research in natural and social sciences and is critical for scientific discovery and informed decision making. The gold standard in causal inference is performing randomized controlled trials; unfortunately these are not always feasible due to ethical, legal, or cost constraints. As an alternative, methodologies for causal inference from observational data have been developed in statistical studies and social sciences. However, existing methods critically rely on restrictive assumptions such as the study population consisting of homogeneous elements that can be represented in a single flat table, where each row is referred to as a unit. In contrast, in many real-world settings, the study domain naturally consists of heterogeneous elements with complex relational structure, where the data is naturally represented in multiple related tables. In this paper, we present a formal framework for causal inference from such relational data. We propose a declarative language called CaRL for capturing causal background knowledge and assumptions and specifying causal queries using simple Datalog-like rules.CaRL provides a foundation for inferring causality and reasoning about the effect of complex interventions in relational domains. We present an extensive experimental evaluation on real relational data to illustrate the applicability of CaRL in social sciences and healthcare.

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arXiv2020

Sample Debiasing in the Themis Open World Database System (Extended Version)

Open world database management systems assume tuples not in the database still exist and are becoming an increasingly important area of research. We present Themis, the first open world database that automatically rebalances arbitrarily biased samples to approximately answer queries as if they were issued over the entire population. We leverage apriori population aggregate information to develop and combine two different approaches for automatic debiasing: sample reweighting and Bayesian network probabilistic modeling. We build a prototype of Themis and demonstrate that Themis achieves higher query accuracy than the default AQP approach, an alternative sample reweighting technique, and a variety of Bayesian network models while maintaining interactive query response times. We also show that \name is robust to differences in the support between the sample and population, a key use case when using social media samples.

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arXiv2020

Mosaic: A Sample-Based Database System for Open World Query Processing

Data scientists have relied on samples to analyze populations of interest for decades. Recently, with the increase in the number of public data repositories, sample data has become easier to access. It has not, however, become easier to analyze. This sample data is arbitrarily biased with an unknown sampling probability, meaning data scientists must manually debias the sample with custom techniques to avoid inaccurate results. In this vision paper, we propose Mosaic, a database system that treats samples as first-class citizens and allows users to ask questions over populations represented by these samples. Answering queries over biased samples is non-trivial as there is no existing, standard technique to answer population queries when the sampling probability is unknown. In this paper, we show how our envisioned system solves this problem by having a unique sample-based data model with extensions to the SQL language. We propose how to perform population query answering using biased samples and give preliminary results for one of our novel query answering techniques.

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arXiv2019

Mining Approximate Acyclic Schemes from Relations

Acyclic schemes have numerous applications in databases and in machine learning, such as improved design, more efficient storage, and increased performance for queries and machine learning algorithms. Multivalued dependencies (MVDs) are the building blocks of acyclic schemes. The discovery from data of both MVDs and acyclic schemes is more challenging than other forms of data dependencies, such as Functional Dependencies, because these dependencies do not hold on subsets of data, and because they are very sensitive to noise in the data; for example a single wrong or missing tuple may invalidate the schema. In this paper we present Maimon, a system for discovering approximate acyclic schemes and MVDs from data. We give a principled definition of approximation, by using notions from information theory, then describe the two components of Maimon: mining for approximate MVDs, then reconstructing acyclic schemes from approximate MVDs. We conduct an experimental evaluation of Maimon on 20 real-world datasets, and show that it can scale up to 1M rows, and up to 30 columns.

cs.DB↗

arXiv2019

EntropyDB: A Probabilistic Approach to Approximate Query Processing

We present EntropyDB, an interactive data exploration system that uses a probabilistic approach to generate a small, query-able summary of a dataset. Departing from traditional summarization techniques, we use the Principle of Maximum Entropy to generate a probabilistic representation of the data that can be used to give approximate query answers. We develop the theoretical framework and formulation of our probabilistic representation and show how to use it to answer queries. We then present solving techniques, give two critical optimizations to improve preprocessing time and query execution time, and explore methods to reduce query error. Lastly, we experimentally evaluate our work using a 5 GB dataset of flights within the United States and a 210 GB dataset from an astronomy particle simulation. While our current work only supports linear queries, we show that our technique can successfully answer queries faster than sampling while introducing, on average, no more error than sampling and can better distinguish between rare and nonexistent values. We also discuss extensions that can allow for data updates and linear queries over joins.

cs.DB↗

arXiv2019

Capuchin: Causal Database Repair for Algorithmic Fairness

Fairness is increasingly recognized as a critical component of machine learning systems. However, it is the underlying data on which these systems are trained that often reflect discrimination, suggesting a database repair problem. Existing treatments of fairness rely on statistical correlations that can be fooled by statistical anomalies, such as Simpson's paradox. Proposals for causality-based definitions of fairness can correctly model some of these situations, but they require specification of the underlying causal models. In this paper, we formalize the situation as a database repair problem, proving sufficient conditions for fair classifiers in terms of admissible variables as opposed to a complete causal model. We show that these conditions correctly capture subtle fairness violations. We then use these conditions as the basis for database repair algorithms that provide provable fairness guarantees about classifiers trained on their training labels. We evaluate our algorithms on real data, demonstrating improvement over the state of the art on multiple fairness metrics proposed in the literature while retaining high utility.

cs.DB↗

arXiv2019

Data Management for Causal Algorithmic Fairness

Fairness is increasingly recognized as a critical component of machine learning systems. However, it is the underlying data on which these systems are trained that often reflects discrimination, suggesting a data management problem. In this paper, we first make a distinction between associational and causal definitions of fairness in the literature and argue that the concept of fairness requires causal reasoning. We then review existing works and identify future opportunities for applying data management techniques to causal algorithmic fairness.

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