25,874 research outputs found
Numerical Sensitivity and Efficiency in the Treatment of Epistemic and Aleatory Uncertainty
The treatment of both aleatory and epistemic uncertainty by recent methods
often requires an high computational effort. In this abstract, we propose a
numerical sampling method allowing to lighten the computational burden of
treating the information by means of so-called fuzzy random variables
Quantification of Uncertainty with Adversarial Models
Quantifying uncertainty is important for actionable predictions in real-world
applications. A crucial part of predictive uncertainty quantification is the
estimation of epistemic uncertainty, which is defined as an integral of the
product between a divergence function and the posterior. Current methods such
as Deep Ensembles or MC dropout underperform at estimating the epistemic
uncertainty, since they primarily consider the posterior when sampling models.
We suggest Quantification of Uncertainty with Adversarial Models (QUAM) to
better estimate the epistemic uncertainty. QUAM identifies regions where the
whole product under the integral is large, not just the posterior.
Consequently, QUAM has lower approximation error of the epistemic uncertainty
compared to previous methods. Models for which the product is large correspond
to adversarial models (not adversarial examples!). Adversarial models have both
a high posterior as well as a high divergence between their predictions and
that of a reference model. Our experiments show that QUAM excels in capturing
epistemic uncertainty for deep learning models and outperforms previous methods
on challenging tasks in the vision domain
Fuzzy-Analysis in a Generic Polymorphic Uncertainty Quantification Framework
In this thesis, a framework for generic uncertainty analysis is developed. The two basic uncertainty characteristics aleatoric and epistemic uncertainty are differentiated. Polymorphic uncertainty as the combination of these two characteristics is discussed. The main focus is on epistemic uncertainty, with fuzziness as an uncertainty model. Properties and classes of fuzzy quantities are discussed. Some information reduction measures to reduce a fuzzy quantity to a characteristic value, are briefly debated. Analysis approaches for aleatoric, epistemic and polymorphic uncertainty are discussed. For fuzzy analysis α-level-based and α-level-free methods are described. As a hybridization of both methods, non-flat α-level-optimization is proposed.
For numerical uncertainty analysis, the framework PUQpy, which stands for “Polymorphic Uncertainty Quantification in Python” is introduced. The conception, structure, data structure, modules and design principles of PUQpy are documented. Sequential Weighted Sampling (SWS) is presented as an optimization algorithm for general purpose optimization, as well as for fuzzy analysis. Slice Sampling as a component of SWS is shown. Routines to update Pareto-fronts, which are required for optimization are benchmarked.
Finally, PUQpy is used to analyze example problems as a proof of concept. In those problems analytical functions with uncertain parameters, characterized by fuzzy and polymorphic uncertainty, are examined
Evidential uncertainties on rich labels for active learning
Recent research in active learning, and more precisely in uncertainty
sampling, has focused on the decomposition of model uncertainty into reducible
and irreducible uncertainties. In this paper, we propose to simplify the
computational phase and remove the dependence on observations, but more
importantly to take into account the uncertainty already present in the labels,
\emph{i.e.} the uncertainty of the oracles. Two strategies are proposed,
sampling by Klir uncertainty, which addresses the exploration-exploitation
problem, and sampling by evidential epistemic uncertainty, which extends the
reducible uncertainty to the evidential framework, both using the theory of
belief functions
A Deeper Look into Aleatoric and Epistemic Uncertainty Disentanglement
Neural networks are ubiquitous in many tasks, but trusting their predictions
is an open issue. Uncertainty quantification is required for many applications,
and disentangled aleatoric and epistemic uncertainties are best. In this paper,
we generalize methods to produce disentangled uncertainties to work with
different uncertainty quantification methods, and evaluate their capability to
produce disentangled uncertainties. Our results show that: there is an
interaction between learning aleatoric and epistemic uncertainty, which is
unexpected and violates assumptions on aleatoric uncertainty, some methods like
Flipout produce zero epistemic uncertainty, aleatoric uncertainty is unreliable
in the out-of-distribution setting, and Ensembles provide overall the best
disentangling quality. We also explore the error produced by the number of
samples hyper-parameter in the sampling softmax function, recommending N > 100
samples. We expect that our formulation and results help practitioners and
researchers choose uncertainty methods and expand the use of disentangled
uncertainties, as well as motivate additional research into this topic.Comment: 8 pages, 12 figures, with supplementary. LatinX in CV Workshop @ CVPR
2022 Camera Read
Product Design Optimization Under Epistemic Uncertainty
abstract: This dissertation is to address product design optimization including reliability-based design optimization (RBDO) and robust design with epistemic uncertainty. It is divided into four major components as outlined below. Firstly, a comprehensive study of uncertainties is performed, in which sources of uncertainty are listed, categorized and the impacts are discussed. Epistemic uncertainty is of interest, which is due to lack of knowledge and can be reduced by taking more observations. In particular, the strategies to address epistemic uncertainties due to implicit constraint function are discussed. Secondly, a sequential sampling strategy to improve RBDO under implicit constraint function is developed. In modern engineering design, an RBDO task is often performed by a computer simulation program, which can be treated as a black box, as its analytical function is implicit. An efficient sampling strategy on learning the probabilistic constraint function under the design optimization framework is presented. The method is a sequential experimentation around the approximate most probable point (MPP) at each step of optimization process. It is compared with the methods of MPP-based sampling, lifted surrogate function, and non-sequential random sampling. Thirdly, a particle splitting-based reliability analysis approach is developed in design optimization. In reliability analysis, traditional simulation methods such as Monte Carlo simulation may provide accurate results, but are often accompanied with high computational cost. To increase the efficiency, particle splitting is integrated into RBDO. It is an improvement of subset simulation with multiple particles to enhance the diversity and stability of simulation samples. This method is further extended to address problems with multiple probabilistic constraints and compared with the MPP-based methods. Finally, a reliability-based robust design optimization (RBRDO) framework is provided to integrate the consideration of design reliability and design robustness simultaneously. The quality loss objective in robust design, considered together with the production cost in RBDO, are used formulate a multi-objective optimization problem. With the epistemic uncertainty from implicit performance function, the sequential sampling strategy is extended to RBRDO, and a combined metamodel is proposed to tackle both controllable variables and uncontrollable variables. The solution is a Pareto frontier, compared with a single optimal solution in RBDO.Dissertation/ThesisPh.D. Industrial Engineering 201
Stochastic and epistemic uncertainty propagation in LCA
Purpose: When performing uncertainty propagation, most LCA practitioners choose to represent uncertainties by single probability distributions and to propagate them using stochastic methods. However the selection of single probability distributions appears often arbitrary when faced with scarce information or expert judgement (epistemic uncertainty). Possibility theory has been developed over the last decades to address this problem. The objective of this study is to present a methodology that combines probability and possibility theories to represent stochastic and epistemic uncertainties in a consistent manner and apply it to LCA. A case study is used to show the uncertainty propagation performed with the proposed method and compare it to propagation performed using probability and possibility theories alone. Methods: Basic knowledge on the probability theory is first recalled, followed by a detailed description of hal-00811827, version 1- 11 Apr 2013 epistemic uncertainty representation using fuzzy intervals. The propagation methods used are the Monte Carlo analysis for probability distribution and an optimisation on alpha-cuts for fuzzy intervals. The proposed method (noted IRS) generalizes the process of random sampling to probability distributions as well as fuzzy intervals, thus making the simultaneous use of both representations possible
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