The Optimal Uncertainty Algorithm in the Mystic Framework

We have recently proposed a rigorous framework for Uncertainty Quantification (UQ) in which UQ objectives and assumption/information set are brought into the forefront, providing a framework for the communication and comparison of UQ results. In particular, this framework does not implicitly impose inappropriate assumptions nor does it repudiate relevant information. This framework, which we call Optimal Uncertainty Quantification (OUQ), is based on the observation that given a set of assumptions and information, there exist bounds on uncertainties obtained as values of optimization problems and that these bounds are optimal. It provides a uniform environment for the optimal solution of the problems of validation, certification, experimental design, reduced order modeling, prediction, extrapolation, all under aleatoric and epistemic uncertainties. OUQ optimization problems are extremely large, and even though under general conditions they have finite-dimensional reductions, they must often be solved numerically. This general algorithmic framework for OUQ has been implemented in the mystic optimization framework. We describe this implementation, and demonstrate its use in the context of the Caltech surrogate model for hypervelocity impact

Optimal Uncertainty Quantification

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call Optimal Uncertainty Quantification (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as extreme values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information. Although OUQ optimization problems are extremely large, we show that under general conditions, they have finite-dimensional reductions. As an application, we develop Optimal Concentration Inequalities (OCI) of Hoeffding and McDiarmid type. Surprisingly, contrary to the classical sensitivity analysis paradigm, these results show that uncertainties in input parameters do not necessarily propagate to output uncertainties. In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact, suggesting the feasibility of the framework for important complex systems

Disaggregating times series data

This report describes our experiences with disaggregating time series data. Suppose we have gathered data every two seconds and want to guess the data at one-second intervals. Under certain assumptions, there are several reasonable disaggregation methods as well as several performance measures to judge their performance. Here we present results for both simulated and real data for two methods using several performance criteria

Optimal Uncertainty Quantification

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information. Although OUQ optimization problems are extremely large, we show that under general conditions they have finite-dimensional reductions. As an application, we develop \emph{Optimal Concentration Inequalities} (OCI) of Hoeffding and McDiarmid type. Surprisingly, these results show that uncertainties in input parameters, which propagate to output uncertainties in the classical sensitivity analysis paradigm, may fail to do so if the transfer functions (or probability distributions) are imperfectly known. We show how, for hierarchical structures, this phenomenon may lead to the non-propagation of uncertainties or information across scales. In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact and on the seismic safety assessment of truss structures, suggesting the feasibility of the framework for important complex systems. The introduction of this paper provides both an overview of the paper and a self-contained mini-tutorial about basic concepts and issues of UQ.Comment: 90 pages. Accepted for publication in SIAM Review (Expository Research Papers). See SIAM Review for higher quality figure

Native Speaker Perceptions of Accented Speech: The English Pronunciation of Macedonian EFL Learners

The paper reports on the results of a study that aimed to describe the vocalic and consonantal features of the English pronunciation of Macedonian EFL learners as perceived by native speakers of English and to find out whether native speakers who speak different standard variants of English perceive the same segments as non-native. A specially designed computer web application was employed to gather two types of data: a) quantitative (frequency of segment variables and global foreign accent ratings on a 5-point scale), and b) qualitative (open-ended questions). The result analysis points out to three most frequent markers of foreign accent in the English speech of Macedonian EFL learners: final obstruent devoicing, vowel shortening and substitution of English dental fricatives with Macedonian dental plosives. It also reflects additional phonetic aspects poorly explained in the available reference literature such as allophonic distributional differences between the two languages and intonational mismatch

Inter-generational transmission in a minority language setting: Stop consonant production by Bangladeshi heritage children and adults

Aims and objectives: The purpose of this study was to gain a better understanding of speech development across successive generations of heritage language users, examining how cross-linguistic, developmental and socio-cultural factors affect stop consonant production. Design: To this end, we recorded Sylheti and English stop productions of two sets of Bangladeshi heritage families: (1) first-generation adult migrants from Bangladesh and their (second-generation) UK-born children, and (2) second-generation UK-born adult heritage language users and their (third-generation) UK-born children. Data and analysis: The data were analysed auditorily, using whole-word transcription, and acoustically, examining voice onset time. Comparisons were then made in both languages across the four groups of participants, and cross-linguistically. Findings: The results revealed non-native productions of English stops by the first-generation migrants but largely target-like patterns by the remaining sets of participants. The Sylheti stops exhibited incremental changes across successive generations of speakers, with the third-generation children’s productions showing the greatest influence from English. Originality: This is one of few studies to examine both the host and heritage language in an ethnic minority setting, and the first to demonstrate substantial differences in heritage language accent between age-matched second- and third-generation children. The study shows that current theories of bilingual speech learning do not go far enough in explaining how speech develops in heritage language settings. Implications: These findings have important implications for the maintenance, transmission and long-term survival of heritage languages, and show that investigations need to go beyond second-generation speakers, in particular in communities that do not see a steady influx of new migrants

Towards Machine Wald

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed \emph{by humans} because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page

Qualitative Robustness of Bootstrap Approximations for Kernel Based Methods

status: publishe