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Register a new userTensor Relational Algebra for Machine Learning System Design
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Added by
Binhang Yuan
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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We consider the question: what is the abstraction that should be implemented by the computational engine of a machine learning system? Current machine learning systems typically push whole tensors through a series of compute kernels such as matrix multiplications or activation functions, where each kernel runs on an AI accelerator (ASIC) such as a GPU. This implementation abstraction provides little built-in support for ML systems to scale past a single machine, or for handling large models with matrices or tensors that do not easily fit into the RAM of an ASIC. In this paper, we present an alternative implementation abstraction called the tensor relational algebra (TRA). The TRA is a set-based algebra based on the relational algebra. Expressions in the TRA operate over binary tensor relations, where keys are multi-dimensional arrays and values are tensors. The TRA is easily executed with high efficiency in a parallel or distributed environment, and amenable to automatic optimization. Our empirical study shows that the optimized TRA-based back-end can significantly outperform alternatives for running ML workflows in distributed clusters.
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Financial transactions, internet search, and data analysis are all placing increasing demands on databases. SQL, NoSQL, and NewSQL databases have been developed to meet these demands and each offers unique benefits. SQL, NoSQL, and NewSQL databases also rely on different underlying mathematical models. Polystores seek to provide a mechanism to allow applications to transparently achieve the benefits of diverse databases while insulating applications from the details of these databases. Integrating the underlying mathematics of these diverse databases can be an important enabler for polystores as it enables effective reasoning across different databases. Associative arrays provide a common approach for the mathematics of polystores by encompassing the mathematics found in different databases: sets (SQL), graphs (NoSQL), and matrices (NewSQL). Prior work presented the SQL relational model in terms of associative arrays and identified key mathematical properties that are preserved within SQL. This work provides the rigorous mathematical definitions, lemmas, and theorems underlying these properties. Specifically, SQL Relational Algebra deals primarily with relations - multisets of tuples - and operations on and between these relations. These relations can be modeled as associative arrays by treating tuples as non-zero rows in an array. Operations in relational algebra are built as compositions of standard operations on associative arrays which mirror their matrix counterparts. These constructions provide insight into how relational algebra can be handled via array operations. As an example application, the composition of two projection operations is shown to also be a projection, and the projection of a union is shown to be equal to the union of the projections.
This tutorial overviews principles behind recent works on training and maintaining machine learning models over relational data, with an emphasis on the exploitation of the relational data structure to improve the runtime performance of the learning task. The tutorial has the following parts: 1) Database research for data science 2) Three main ideas to achieve performance improvements 2.1) Turn the ML problem into a DB problem 2.2) Exploit structure of the data and problem 2.3) Exploit engineering tools of a DB researcher 3) Avenues for future research
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.
Modeling the joint distribution of high-dimensional data is a central task in unsupervised machine learning. In recent years, many interests have been attracted to developing learning models based on tensor networks, which have advantages of theoretical understandings of the expressive power using entanglement properties, and as a bridge connecting the classical computation and the quantum computation. Despite the great potential, however, existing tensor-network-based unsupervised models only work as a proof of principle, as their performances are much worse than the standard models such as the restricted Boltzmann machines and neural networks. In this work, we present the Autoregressive Matrix Product States (AMPS), a tensor-network-based model combining the matrix product states from quantum many-body physics and the autoregressive models from machine learning. The model enjoys exact calculation of normalized probability and unbiased sampling, as well as a clear theoretical understanding of expressive power. We demonstrate the performance of our model using two applications, the generative modeling on synthetic and real-world data, and the reinforcement learning in statistical physics. Using extensive numerical experiments, we show that the proposed model significantly outperforms the existing tensor-network-based models and the restricted Boltzmann machines, and is competitive with the state-of-the-art neural network models.
Relational databases are valuable resources for learning novel and interesting relations and concepts. In order to constraint the search through the large space of candidate definitions, users must tune the algorithm by specifying a language bias. Unfortunately, specifying the language bias is done via trial and error and is guided by the experts intuitions. We propose AutoBias, a system that leverages information in the schema and content of the database to automatically induce the language bias used by popular relational learning systems. We show that AutoBias delivers the same accuracy as using manually-written language bias by imposing only a slight overhead on the running time of the learning algorithm.
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