A fast Monte-Carlo method with a Reduced Basis of Control Variates applied to Uncertainty Propagation and Bayesian Estimation

The Reduced-Basis Control-Variate Monte-Carlo method was introduced recently in [S. Boyaval and T. Leli\`evre, CMS, 8 2010] as an improved Monte-Carlo method, for the fast estimation of many parametrized expected values at many parameter values. We provide here a more complete analysis of the method including precise error estimates and convergence results. We also numerically demonstrate that it can be useful to some parametrized frameworks in Uncertainty Quantification, in particular (i) the case where the parametrized expectation is a scalar output of the solution to a Partial Differential Equation (PDE) with stochastic coefficients (an Uncertainty Propagation problem), and (ii) the case where the parametrized expectation is the Bayesian estimator of a scalar output in a similar PDE context. Moreover, in each case, a PDE has to be solved many times for many values of its coefficients. This is costly and we also use a reduced basis of PDE solutions like in [S. Boyaval, C. Le Bris, Nguyen C., Y. Maday and T. Patera, CMAME, 198 2009]. This is the first combination of various Reduced-Basis ideas to our knowledge, here with a view to reducing as much as possible the computational cost of a simple approach to Uncertainty Quantification

Roq: Robust Query Optimization Based on a Risk-aware Learned Cost Model

Query optimizers in relational database management systems (RDBMSs) search for execution plans expected to be optimal for a given queries. They use parameter estimates, often inaccurate, and make assumptions that may not hold in practice. Consequently, they may select execution plans that are suboptimal at runtime, when these estimates and assumptions are not valid, which may result in poor query performance. Therefore, query optimizers do not sufficiently support robust query optimization. Recent years have seen a surge of interest in using machine learning (ML) to improve efficiency of data systems and reduce their maintenance overheads, with promising results obtained in the area of query optimization in particular. In this paper, inspired by these advancements, and based on several years of experience of IBM Db2 in this journey, we propose Robust Optimization of Queries, (Roq), a holistic framework that enables robust query optimization based on a risk-aware learning approach. Roq includes a novel formalization of the notion of robustness in the context of query optimization and a principled approach for its quantification and measurement based on approximate probabilistic ML. It also includes novel strategies and algorithms for query plan evaluation and selection. Roq also includes a novel learned cost model that is designed to predict query execution cost and the associated risks and performs query optimization accordingly. We demonstrate experimentally that Roq provides significant improvements to robust query optimization compared to the state-of-the-art.Comment: 13 pages, 9 figures, submitted to SIGMOD 202

Performance Analysis of Multi-Task Deep Learning Models for Flux Regression in Discrete Fracture Networks

In this work, we investigate the sensitivity of a family of multi-task Deep Neural Networks (DNN) trained to predict fluxes through given Discrete Fracture Networks (DFNs), stochastically varying the fracture transmissivities. In particular, detailed performance and reliability analyses of more than two hundred Neural Networks (NN) are performed, training the models on sets of an increasing number of numerical simulations made on several DFNs with two fixed geometries (158 fractures and 385 fractures) and different transmissibility configurations. A quantitative evaluation of the trained NN predictions is proposed, and rules fitting the observed behavior are provided to predict the number of training simulations that are required for a given accuracy with respect to the variability in the stochastic distribution of the fracture transmissivities. A rule for estimating the cardinality of the training dataset for different configurations is proposed. From the analysis performed, an interesting regularity of the NN behaviors is observed, despite the stochasticity that imbues the whole training process. The proposed approach can be relevant for the use of deep learning models as model reduction methods in the framework of uncertainty quantification analysis for fracture networks and can be extended to similar geological problems (for example, to the more complex discrete fracture matrix models). The results of this study have the potential to grant concrete advantages to real underground flow characterization problems, making computational costs less expensive through the use of NNs

Stability of feature selection algorithms: a study on high-dimensional spaces

With the proliferation of extremely high-dimensional data, feature selection algorithms have become indispensable components of the learning process. Strangely, despite extensive work on the stability of learning algorithms, the stability of feature selection algorithms has been relatively neglected. This study is an attempt to fill that gap by quantifying the sensitivity of feature selection algorithms to variations in the training set. We assess the stability of feature selection algorithms based on the stability of the feature preferences that they express in the form of weights-scores, ranks, or a selected feature subset. We examine a number of measures to quantify the stability of feature preferences and propose an empirical way to estimate them. We perform a series of experiments with several feature selection algorithms on a set of proteomics datasets. The experiments allow us to explore the merits of each stability measure and create stability profiles of the feature selection algorithms. Finally, we show how stability profiles can support the choice of a feature selection algorith

10381 Summary and Abstracts Collection -- Robust Query Processing

Dagstuhl seminar 10381 on robust query processing (held 19.09.10 - 24.09.10) brought together a diverse set of researchers and practitioners with a broad range of expertise for the purpose of fostering discussion and collaboration regarding causes, opportunities, and solutions for achieving robust query processing. The seminar strove to build a unified view across the loosely-coupled system components responsible for the various stages of database query processing. Participants were chosen for their experience with database query processing and, where possible, their prior work in academic research or in product development towards robustness in database query processing. In order to pave the way to motivate, measure, and protect future advances in robust query processing, seminar 10381 focused on developing tests for measuring the robustness of query processing. In these proceedings, we first review the seminar topics, goals, and results, then present abstracts or notes of some of the seminar break-out sessions. We also include, as an appendix, the robust query processing reading list that was collected and distributed to participants before the seminar began, as well as summaries of a few of those papers that were contributed by some participants