Trade-offs in Large-Scale Distributed Tuplewise Estimation and Learning

The development of cluster computing frameworks has allowed practitioners to scale out various statistical estimation and machine learning algorithms with minimal programming effort. This is especially true for machine learning problems whose objective function is nicely separable across individual data points, such as classification and regression. In contrast, statistical learning tasks involving pairs (or more generally tuples) of data points - such as metric learning, clustering or ranking do not lend themselves as easily to data-parallelism and in-memory computing. In this paper, we investigate how to balance between statistical performance and computational efficiency in such distributed tuplewise statistical problems. We first propose a simple strategy based on occasionally repartitioning data across workers between parallel computation stages, where the number of repartitioning steps rules the trade-off between accuracy and runtime. We then present some theoretical results highlighting the benefits brought by the proposed method in terms of variance reduction, and extend our results to design distributed stochastic gradient descent algorithms for tuplewise empirical risk minimization. Our results are supported by numerical experiments in pairwise statistical estimation and learning on synthetic and real-world datasets.Comment: 23 pages, 6 figures, ECML 201

Trade-offs in Large-Scale Distributed Tuplewise Estimation and Learning

International audienceThe development of cluster computing frameworks has allowed practitioners to scale out various statistical estimation and machine learning algorithms with minimal programming effort. This is especially true for machine learning problems whose objective function is nicely separable across individual data points, such as classification and regression. In contrast, statistical learning tasks involving pairs (or more generally tuples) of data points-such as metric learning, clustering or ranking-do not lend themselves as easily to data-parallelism and in-memory computing. In this paper, we investigate how to balance between statistical performance and computational efficiency in such distributed tuplewise statistical problems. We first propose a simple strategy based on occasionally repartitioning data across workers between parallel computation stages, where the number of repartition-ing steps rules the trade-off between accuracy and runtime. We then present some theoretical results highlighting the benefits brought by the proposed method in terms of variance reduction, and extend our results to design distributed stochastic gradient descent algorithms for tuplewise empirical risk minimization. Our results are supported by numerical experiments in pairwise statistical estimation and learning on synthetic and real-world datasets

Inductive biases and metaknowledge representations for search-based optimization

"What I do not understand, I can still create."- H. Sayama The following work follows closely the aforementioned bonmot. Guided by questions such as: ``How can evolutionary processes exhibit learning behavior and consolidate knowledge?´´, ``What are cognitive models of problem-solving?´´ and ``How can we harness these altogether as computational techniques?´´, we clarify within this work essentials required to implement them for metaheuristic search and optimization.We therefore look into existing models of computational problem-solvers and compare these with existing methodology in literature. Particularly, we find that the meta-learning model, which frames problem-solving in terms of domain-specific inductive biases and the arbitration thereof through means of high-level abstractions resolves outstanding issues with methodology proposed within the literature. Noteworthy, it can be also related to ongoing research on algorithm selection and configuration frameworks. We therefore look in what it means to implement such a model by first identifying inductive biases in terms of algorithm components and modeling these with density estimation techniques. And secondly, propose methodology to process metadata generated by optimization algorithms in an automated manner through means of deep pattern recognition architectures for spatio-temporal feature extraction. At last we look into an exemplary shape optimization problem which allows us to gain insight into what it means to apply our methodology to application scenarios. We end our work with a discussion on future possible directions to explore and discuss the limitations of such frameworks for system deployment

An Algebraic Approach to XQuery Optimization

As more data is stored in XML and more applications need to process this data, XML query optimization becomes performance critical. While optimization techniques for relational databases have been developed over the last thirty years, the optimization of XML queries poses new challenges. Query optimizers for XQuery, the standard query language for XML data, need to consider both document order and sequence order. Nevertheless, algebraic optimization proved powerful in query optimizers in relational and object oriented databases. Thus, this dissertation presents an algebraic approach to XQuery optimization. In this thesis, an algebra over sequences is presented that allows for a simple translation of XQuery into this algebra. The formal definitions of the operators in this algebra allow us to reason formally about algebraic optimizations. This thesis leverages the power of this formalism when unnesting nested XQuery expressions. In almost all cases unnesting nested queries in XQuery reduces query execution times from hours to seconds or milliseconds. Moreover, this dissertation presents three basic algebraic patterns of nested queries. For every basic pattern a decision tree is developed to select the most effective unnesting equivalence for a given query. Query unnesting extends the search space that can be considered during cost-based optimization of XQuery. As a result, substantially more efficient query execution plans may be detected. This thesis presents two more important cases where the number of plan alternatives leads to substantially shorter query execution times: join ordering and reordering location steps in path expressions. Our algebraic framework detects cases where document order or sequence order is destroyed. However, state-of-the-art techniques for order optimization in cost-based query optimizers have efficient mechanisms to repair order in these cases. The results obtained for query unnesting and cost-based optimization of XQuery underline the need for an algebraic approach to XQuery optimization for efficient XML query processing. Moreover, they are applicable to optimization in relational databases where order semantics are considered

Trade-offs in Large-Scale Distributed Tuplewise Estimation and Learning

International audienceThe development of cluster computing frameworks has allowed practitioners to scale out various statistical estimation and machine learning algorithms with minimal programming effort. This is especially true for machine learning problems whose objective function is nicely separable across individual data points, such as classification and regression. In contrast, statistical learning tasks involving pairs (or more generally tuples) of data points-such as metric learning, clustering or ranking-do not lend themselves as easily to data-parallelism and in-memory computing. In this paper, we investigate how to balance between statistical performance and computational efficiency in such distributed tuplewise statistical problems. We first propose a simple strategy based on occasionally repartitioning data across workers between parallel computation stages, where the number of repartition-ing steps rules the trade-off between accuracy and runtime. We then present some theoretical results highlighting the benefits brought by the proposed method in terms of variance reduction, and extend our results to design distributed stochastic gradient descent algorithms for tuplewise empirical risk minimization. Our results are supported by numerical experiments in pairwise statistical estimation and learning on synthetic and real-world datasets