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Relevant bibliographies by topics / Aleatoric uncertainty

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Academic literature on the topic 'Aleatoric uncertainty'

Author: Grafiati

Published: 12 July 2022

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Journal articles on the topic "Aleatoric uncertainty"

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Pamungkas, Yayi Wira. "Penggunaan Aturan Ular Tangga dalam Musik Aleatorik Berbasis Serialisme Integral." Journal of Music Science, Technology, and Industry 3, no. 2 (October 21, 2020): 201–22. http://dx.doi.org/10.31091/jomsti.v3i2.1157.

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Purpose: The author does an experiment by using the rules of snake and ladder to find out and understand how the concept of uncertainty can work in serialism-based aleatoric music: by testing it using the most stringent serialism system, namely the system of integral serialism. Research methods: The process of creating the composition of this artistic research work has five stages, namely the exploration stage, the concept preparation stage, the concept analysis stage, the macro structure preparation stage, and the concept application stage. Results and discussion: The concept of snake and ladder can optimize the concept of uncertainty in serialism-based aleatoric music. The integral serialism system dominates the formation of melody and harmony, while the concept of snake and ladder that is aleatoris is used as phrase control. Implication: There are two phenomena that stimulate the creation of the idea of creation of this artistic research work, namely the problem of stiffness and weak characteristics of the concept of uncertainty in serialism-based aleatoric music.

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Hong, Ming, Jianzhuang Liu, Cuihua Li, and Yanyun Qu. "Uncertainty-Driven Dehazing Network." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 1 (June 28, 2022): 906–13. http://dx.doi.org/10.1609/aaai.v36i1.19973.

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Deep learning has made remarkable achievements for single image haze removal. However, existing deep dehazing models only give deterministic results without discussing the uncertainty of them. There exist two types of uncertainty in the dehazing models: aleatoric uncertainty that comes from noise inherent in the observations and epistemic uncertainty that accounts for uncertainty in the model. In this paper, we propose a novel uncertainty-driven dehazing network (UDN) that improves the dehazing results by exploiting the relationship between the uncertain and confident representations. We first introduce an Uncertainty Estimation Block (UEB) to predict the aleatoric and epistemic uncertainty together. Then, we propose an Uncertainty-aware Feature Modulation (UFM) block to adaptively enhance the learned features. UFM predicts a convolution kernel and channel-wise modulation cofficients conitioned on the uncertainty weighted representation. Moreover, we develop an uncertainty-driven self-distillation loss to improve the uncertain representation by transferring the knowledge from the confident one. Extensive experimental results on synthetic datasets and real-world images show that UDN achieves significant quantitative and qualitative improvements, outperforming the state-of-the-arts.

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Lyu, Yufeng, Zhenyu Liu, Xiang Peng, Jianrong Tan, and Chan Qiu. "Unified Reliability Measure Method Considering Uncertainties of Input Variables and Their Distribution Parameters." Applied Sciences 11, no. 5 (March 4, 2021): 2265. http://dx.doi.org/10.3390/app11052265.

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Aleatoric and epistemic uncertainties can be represented probabilistically in mechanical systems. However, the distribution parameters of epistemic uncertainties are also uncertain due to sparsely available or inaccurate uncertainty information. Therefore, a unified reliability measure method that considers uncertainties of input variables and their distribution parameters simultaneously is proposed. The uncertainty information for distribution parameters of epistemic uncertainties could be as a result of insufficient data or interval information, which is represented with evidence theory. The probability density function of uncertain distribution parameters is constructed through fusing insufficient data and interval information based on a Gaussian interpolation algorithm, and the epistemic uncertainties are represented using a weighted sum of probability variables based on discrete distribution parameters. The reliability index considering aleatoric and epistemic uncertainties is calculated around the most probable point. The effectiveness of the proposed algorithm is demonstrated through comparison with the Monte Carlo method in the engineering example of a crank-slider mechanism and composite laminated plate.

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Mehltretter, M. "JOINT ESTIMATION OF DEPTH AND ITS UNCERTAINTY FROM STEREO IMAGES USING BAYESIAN DEEP LEARNING." ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences V-2-2022 (May 17, 2022): 69–78. http://dx.doi.org/10.5194/isprs-annals-v-2-2022-69-2022.

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Abstract. The necessity to identify errors in the context of image-based 3D reconstruction has motivated the development of various methods for the estimation of uncertainty associated with depth estimates in recent years. Most of these methods exclusively estimate aleatoric uncertainty, which describes stochastic effects. On the other hand, epistemic uncertainty, which accounts for simplifications or incorrect assumptions with respect to the formulated model hypothesis, is often neglected. However, to accurately quantify the uncertainty inherent in a process, it is necessary to consider all potential sources of uncertainty and to model their stochastic behaviour appropriately. To approach this objective, a holistic method to jointly estimate disparity and uncertainty is presented in this work, taking into account both aleatoric and epistemic uncertainty. For this purpose, the proposed method is based on a Bayesian Neural Network, which is trained with variational inference using a probabilistic loss formulation. To evaluate the performance of the method proposed, extensive experiments are carried out on three datasets considering real-world indoor and outdoor scenes. The results of these experiments demonstrate that the proposed method is able to estimate the uncertainty accurately, while showing a similar and for some scenarios improved depth estimation capability compared to the dense stereo matching approach used as deterministic baseline. Moreover, the evaluation reveals the importance of considering both, aleatoric and epistemic uncertainty, in order to achieve an accurate estimation of the overall uncertainty related to a depth estimate.

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Rajbhandari, E., N. L. Gibson, and C. R. Woodside. "Quantifying uncertainty with stochastic collocation in the kinematic magentohydrodynamic framework." Journal of Physics: Conference Series 2207, no. 1 (March 1, 2022): 012007. http://dx.doi.org/10.1088/1742-6596/2207/1/012007.

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Abstract We discuss an efficient numerical method for the uncertain kinematic magnetohydrodynamic system. We include aleatoric uncertainty in the parameters, and then describe a stochastic collocation method to handle this randomness. Numerical demonstrations of this method are discussed. We find that the shape of the parameter distributions affect not only the mean and variance, but also the shape of the solution distributions.

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Zhong, Z., and M. Mehltretter. "MIXED PROBABILITY MODELS FOR ALEATORIC UNCERTAINTY ESTIMATION IN THE CONTEXT OF DENSE STEREO MATCHING." ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences V-2-2021 (June 17, 2021): 17–26. http://dx.doi.org/10.5194/isprs-annals-v-2-2021-17-2021.

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Abstract. The ability to identify erroneous depth estimates is of fundamental interest. Information regarding the aleatoric uncertainty of depth estimates can be, for example, used to support the process of depth reconstruction itself. Consequently, various methods for the estimation of aleatoric uncertainty in the context of dense stereo matching have been presented in recent years, with deep learning-based approaches being particularly popular. Among these deep learning-based methods, probabilistic strategies are increasingly attracting interest, because the estimated uncertainty can be quantified in pixels or in metric units due to the consideration of real error distributions. However, existing probabilistic methods usually assume a unimodal distribution to describe the error distribution while simply neglecting cases in real-world scenarios that could violate this assumption. To overcome this limitation, we propose two novel mixed probability models consisting of Laplacian and Uniform distributions for the task of aleatoric uncertainty estimation. In this way, we explicitly address commonly challenging regions in the context of dense stereo matching and outlier measurements, respectively. To allow a fair comparison, we adapt a common neural network architecture to investigate the effects of the different uncertainty models. In an extensive evaluation using two datasets and two common dense stereo matching methods, the proposed methods demonstrate state-of-the-art accuracy.

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Pham, Nam, and Sergey Fomel. "Uncertainty and interpretability analysis of encoder-decoder architecture for channel detection." GEOPHYSICS 86, no. 4 (July 1, 2021): O49—O58. http://dx.doi.org/10.1190/geo2020-0409.1.

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We have adopted a method to understand uncertainty and interpretability of a Bayesian convolutional neural network for detecting 3D channel geobodies in seismic volumes. We measure heteroscedastic aleatoric uncertainty and epistemic uncertainty. Epistemic uncertainty captures the uncertainty of the network parameters, whereas heteroscedastic aleatoric uncertainty accounts for noise in the seismic volumes. We train a network modified from U-Net architecture on 3D synthetic seismic volumes, and then we apply it to field data. Tests on 3D field data sets from the Browse Basin, offshore Australia, and from Parihaka in New Zealand prove that uncertainty volumes are related to geologic uncertainty, model mispicks, and input noise. We analyze model interpretability on these data sets by creating saliency volumes with gradient-weighted class activation mapping. We find that the model takes a global-to-local approach to localize channel geobodies as well as the importance of different model components in overall strategy. Using channel probability, uncertainty, and saliency volumes, interpreters can accurately identify channel geobodies in 3D seismic volumes and also understand the model predictions.

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Chowdhary, Kamaljit, and Paul Dupuis. "Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification." ESAIM: Mathematical Modelling and Numerical Analysis 47, no. 3 (March 29, 2013): 635–62. http://dx.doi.org/10.1051/m2an/2012038.

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Senge, Robin, Stefan Bösner, Krzysztof Dembczyński, Jörg Haasenritter, Oliver Hirsch, Norbert Donner-Banzhoff, and Eyke Hüllermeier. "Reliable classification: Learning classifiers that distinguish aleatoric and epistemic uncertainty." Information Sciences 255 (January 2014): 16–29. http://dx.doi.org/10.1016/j.ins.2013.07.030.

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Hüllermeier, Eyke, and Willem Waegeman. "Aleatoric and epistemic uncertainty in machine learning: an introduction to concepts and methods." Machine Learning 110, no. 3 (March 2021): 457–506. http://dx.doi.org/10.1007/s10994-021-05946-3.

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AbstractThe notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often referred to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of attempts so far at handling uncertainty in general and formalizing this distinction in particular.

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Dissertations / Theses on the topic "Aleatoric uncertainty"

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Depeweg, Stefan [Verfasser], Thomas A. [Akademischer Betreuer] Runkler, Laura [Gutachter] Leal-Taixé, José Miguel [Gutachter] Hernández-Lobato, and Thomas A. [Gutachter] Runkler. "Modeling Epistemic and Aleatoric Uncertainty with Bayesian Neural Networks and Latent Variables / Stefan Depeweg ; Gutachter: Laura Leal-Taixé, José Miguel Hernández-Lobato, Thomas A. Runkler ; Betreuer: Thomas A. Runkler." München : Universitätsbibliothek der TU München, 2019. http://d-nb.info/1199537667/34.

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Nguyen, Vu-Linh. "Imprecision in machine learning problems." Thesis, Compiègne, 2018. http://www.theses.fr/2018COMP2433.

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Nous nous sommes concentrés sur la modélisation et l'imprécision dans les problèmes d'apprentissage automatique, où les données ou connaissances disponibles souffrent d'imperfections importantes. Dans ce travail, les données imparfaites font référence à des situations où certaines caractéristiques ou les étiquettes sont imparfaitement connues, c'est-à-dire peuvent être spécifiées par des ensembles de valeurs possibles plutôt que par des valeurs précises. Les apprentissages à partir de données partielles sont couramment rencontrés dans divers domaines, tels que la biostatistique, l'agronomie ou l'économie. Ces données peuvent être générées par des mesures grossières ou censurées, ou peuvent être obtenues à partir d'avis d'experts. D'autre part, la connaissance imparfaite fait référence aux situations où les données sont spécifiées avec précision, cependant, il existe des classes qui ne peuvent pas être distinguées en raison d'un manque de connaissances (également appelée incertitude épistémique) ou en raison d'une forte incertitude (également appelée incertitude aléatoire). Considérant le problème de l'apprentissage à partir de données partiellement spécifiées, nous soulignons les problèmes potentiels liés au traitement de plusieurs classes optimales et de plusieurs modèles optimaux dans l'étape d'inférence et d'apprentissage, respectivement. Nous avons proposé des approches d'apprentissage actif pour réduire l'imprécision dans ces situations. Pourtant, la distinction incertitude épistémique/aléatoire a été bien étudiée dans la littérature. Pour faciliter les applications ultérieures d'apprentissage automatique, nous avons développé des procédures pratiques pour estimer ces degrés pour les classificateurs populaires. En particulier, nous avons exploré l'utilisation de cette distinction dans les contextes d'apprentissage actif et prudent
We have focused on imprecision modeling in machine learning problems, where available data or knowledge suffers from important imperfections. In this work, imperfect data refers to situations where either some features or the labels are imperfectly known, that is can be specified by sets of possible values rather than precise ones. Learning from partial data are commonly encountered in various fields, such as bio-statistics, agronomy, or economy. These data can be generated by coarse or censored measurements, or can be obtained from expert opinions. On the other hand, imperfect knowledge refers to the situations where data are precisely specified, however, there are classes, that cannot be distinguished due to a lack of knowledge (also known as epistemic uncertainty) or due to a high uncertainty (also known as aleatoric uncertainty). Considering the problem of learning from partially specified data, we highlight the potential issues of dealing with multiple optimal classes and multiple optimalmodels in the inference and learning step, respectively. We have proposed active learning approaches to reduce the imprecision in these situations. Yet, the distinction epistemic/aleatoric uncertainty has been well-studied in the literature. To facilitate subsequent machine learning applications, we have developed practical procedures to estimate these degrees for popular classifiers. In particular, we have explored the use of this distinction in the contexts of active learning and cautious inferences

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Blumer, Joel David. "Cross-scale model validation with aleatory and epistemic uncertainty." Thesis, Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/53571.

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Nearly every decision must be made with a degree of uncertainty regarding the outcome. Decision making based on modeling and simulation predictions needs to incorporate and aggregate uncertain evidence. To validate multiscale simulation models, it may be necessary to consider evidence collected at a length scale that is different from the one at which a model predicts. In addition, traditional methods of uncertainty analysis do not distinguish between two types of uncertainty: uncertainty due to inherently random inputs, and uncertainty due to lack of information about the inputs. This thesis examines and applies a Bayesian approach for model parameter validation that uses generalized interval probability to separate these two types of uncertainty. A generalized interval Bayes’ rule (GIBR) is used to combine the evidence and update belief in the validity of parameters. The sensitivity of completeness and soundness for interval range estimation in GIBR is investigated. Several approaches to represent complete ignorance of probabilities’ values are tested. The result from the GIBR method is verified using Monte Carlo simulations. The method is first applied to validate the parameter set for a molecular dynamics simulation of defect formation due to radiation. Evidence is supplied by the comparison with physical experiments. Because the simulation includes variables whose effects are not directly observable, an expanded form of GIBR is implemented to incorporate the uncertainty associated with measurement in belief update. In a second example, the proposed method is applied to combining the evidence from two models of crystal plasticity at different length scales.

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Grabaskas, David. "Analysis of Transient Overpower Scenarios in Sodium Fast Reactors." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1265726176.

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Watson, Jason Daniel. "A Multi-Objective Optimization Method for Maximizing the Value of System Evolvability Under Uncertainty." BYU ScholarsArchive, 2015. https://scholarsarchive.byu.edu/etd/5598.

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System evolvability is vital to the longevity of large-scale complex engineered systems. The need for evolvability in complex systems is a result of their long service lives, rapid advances to their integrated technologies, unforeseen operating conditions, and emerging system requirements. In recent years, quantifiable metrics have been introduced for measuring the evolvability of complex systems based on the amount of excess capability in the system. These metrics have opened opportunities for optimization of systems with evolvability as an objective. However, there are several aspects of such an optimization that require further consideration. For example, there is a trade-off between the cost of excess capability initially built into complex systems and the benefit that is added to the system for future evolution. This trade-off must be represented in the optimization problem formulation. Additionally, uncertainty in future requirements and parameters of complex systems can result in an inaccurate representation of the design space. This thesis addresses these considerations through multi-objective optimization and uncertainty analysis. The resulting analysis gives insight into the effects of designing for evolvability. We show that there is a limit to the value added by increasing evolvability. We also show that accounting for uncertainty changes the optimal amount of evolvability that should be designed into a system. The developed theories and methods are demonstrated on the design of a military ground vehicle.

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Sui, Liqi. "Uncertainty management in parameter identification." Thesis, Compiègne, 2017. http://www.theses.fr/2017COMP2330/document.

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Afin d'obtenir des simulations plus prédictives et plus précises du comportement mécanique des structures, des modèles matériau de plus en plus complexes ont été développés. Aujourd'hui, la caractérisation des propriétés des matériaux est donc un objectif prioritaire. Elle exige des méthodes et des tests d'identification dédiés dans des conditions les plus proches possible des cas de service. Cette thèse vise à développer une méthodologie d'identification efficace pour trouver les paramètres des propriétés matériau, en tenant compte de toutes les informations disponibles. L'information utilisée pour l'identification est à la fois théorique, expérimentale et empirique : l'information théorique est liée aux modèles mécaniques dont l'incertitude est épistémique; l'information expérimentale provient ici de la mesure de champs cinématiques obtenues pendant l'essai ct dont l'incertitude est aléatoire; l'information empirique est liée à l'information à priori associée à une incertitude épistémique ainsi. La difficulté principale est que l'information disponible n'est pas toujours fiable et que les incertitudes correspondantes sont hétérogènes. Cette difficulté est surmontée par l'utilisation de la théorie des fonctions de croyance. En offrant un cadre général pour représenter et quantifier les incertitudes hétérogènes, la performance de l'identification est améliorée. Une stratégie basée sur la théorie des fonctions de croyance est proposée pour identifier les propriétés élastiques macro et micro des matériaux multi-structures. Dans cette stratégie, les incertitudes liées aux modèles et aux mesures sont analysées et quantifiées. Cette stratégie est ensuite étendue pour prendre en compte l'information à priori et quantifier l'incertitude associée
In order to obtain more predictive and accurate simulations of mechanical behaviour in the practical environment, more and more complex material models have been developed. Nowadays, the characterization of material properties remains a top-priority objective. It requires dedicated identification methods and tests in conditions as close as possible to the real ones. This thesis aims at developing an effective identification methodology to find the material property parameters, taking advantages of all available information. The information used for the identification is theoretical, experimental, and empirical: the theoretical information is linked to the mechanical models whose uncertainty is epistemic; the experimental information consists in the full-field measurement whose uncertainty is aleatory; the empirical information is related to the prior information with epistemic uncertainty as well. The main difficulty is that the available information is not always reliable and its corresponding uncertainty is heterogeneous. This difficulty is overcome by the introduction of the theory of belief functions. By offering a general framework to represent and quantify the heterogeneous uncertainties, the performance of the identification is improved. The strategy based on the belief function is proposed to identify macro and micro elastic properties of multi-structure materials. In this strategy, model and measurement uncertainties arc analysed and quantified. This strategy is subsequently developed to take prior information into consideration and quantify its corresponding uncertainty

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Burgos, Simón Clara. "Advances on Uncertainty Quantification Techniques for Dynamical Systems: Theory and Modelling." Doctoral thesis, Universitat Politècnica de València, 2021. http://hdl.handle.net/10251/166442.

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[ES] La cuantificación de la incertidumbre está compuesta por una serie de métodos y técnicas computacionales cuyo objetivo principal es describir la aleatoriedad presente en problemas de diversa índole. Estos métodos son de utilidad en la modelización de procesos biológicos, físicos, naturales o sociales, ya que en ellos aparecen ciertos aspectos que no pueden ser determinados de manera exacta. Por ejemplo, la tasa de contagio de una enfermedad epidemiológica o el factor de crecimiento de un volumen tumoral dependen de factores genéticos, ambientales o conductuales. Estos no siempre pueden definirse en su totalidad y por tanto conllevan una aleatoriedad intrínseca que afecta en el desarrollo final. El objetivo principal de esta tesis es extender técnicas para cuantificar la incertidumbre en dos áreas de las matemáticas: el cálculo de ecuaciones diferenciales fraccionarias y la modelización matemática. Las derivadas de orden fraccionario permiten modelizar comportamientos que las derivadas clásicas no pueden, como por ejemplo los efectos de memoria o la viscoelasticidad en algunos materiales. En esta tesis, desde un punto de vista teórico, se extenderá el cálculo fraccionario a un ambiente de incertidumbre, concretamente en el sentido de la media cuadrática. Se presentarán problemas de valores iniciales fraccionarios aleatorios. El cálculo de la solución, la obtención de las aproximaciones de la media y varianza de la solución y la aproximación de la primera función de densidad de probabilidad de la solución son conceptos que se abordarán en los próximos capítulos. Sin embargo, no siempre es sencillo obtener la solución exacta de un problema de valores iniciales fraccionario aleatorio. Por ello en esta tesis también se dedicará un capítulo para describir un procedimiento numérico que aproxime su solución. Por otro lado, desde un punto de vista más aplicado, se desarrollan técnicas computacionales para cuantificar la incertidumbre en modelos matemáticos. Combinando estas técnicas junto con modelos matemáticos apropiados, se estudiarán problemas de dinámica biológica. En primer lugar, se determinará la cantidad de portadores de meningococo en España con un modelo de competencia de Lotka-Volterra fraccionario aleatorio. A continuación, el volumen de un tumor mamario se modelizará mediante un modelo logístico con incertidumbre. Finalmente ayudándonos de un modelo matemático que describe el nivel de glucosa en sangre de un paciente diabético, se pretende dar una recomendación de carbohidratos e insulina que se debe de ingerir para que el nivel de glucosa del paciente esté dentro de una banda de confianza saludable. Es importante subrayar que para poder realizar estos estudios se requieren datos reales, los cuales pueden estar alterados debido a los errores de medición o proceso que se han cometido para obtenerlos. Por este motivo, modelizar correctamente el problema junto con la incertidumbre en los datos es de vital importancia.
[CA] La quantificació de la incertesa està composada per una sèrie de mètodes i tècniques computacionals, l'objectiu principal de les quals és descriure l'aleatorietat present en problemes de diversa índole. Aquests mètodes són d'utilitat en la modelització de processos biològics, físics, naturals o socials, ja que en ells apareixen certs aspectes que no poden ser determinats de manera exacta. Per exemple, la taxa de contagi d'una malaltia epidemiològica o el factor de creixement d'un volum tumoral depenen de factors genètics, ambientals o conductuals. Aquests no sempre poden definir-se íntegrament i per tant, comporten una aleatorietat intrínseca que afecta en el desenvolupament final. L'objectiu principal d'aquesta tesi doctoral és estendre tècniques per a quantificar la incertesa en dues àrees de les matemàtiques: el càlcul d'equacions diferencials fraccionàries i la modelització matemàtica. Les derivades d'ordre fraccionari permeten modelitzar comportaments que les derivades clàssiques no poden, com per exemple, els efectes de memòria o la viscoelasticitat en alguns materials. En aquesta tesi, des d'un punt de vista teòric, s'estendrà el càlcul fraccionari a un ambient d'incertesa, concretament en el sentit de la mitjana quadràtica. Es presentaran problemes de valors inicials fraccionaris aleatoris. El càlcul de la solució, l'obtenció de les aproximacions de la mitjana i, la variància de la solució i l'aproximació de la primera funció de densitat de probabilitat de la solució són conceptes que s'abordaran en els pròxims capítols. No obstant això, no sempre és senzill obtindre la solució exacta d'un problema de valors inicials fraccionari aleatori. Per això en aquesta tesi també es dedicarà un capítol per a descriure un procediment numèric que aproxime la seua solució. D'altra banda, des d'un punt de vista més aplicat, es desenvolupen tècniques computacionals per a quantificar la incertesa en models matemàtics. Combinant aquestes tècniques juntament amb models matemàtics apropiats, s'estudiaran problemes de dinàmica biològica. En primer lloc, es determinarà la quantitat de portadors de meningococ a Espanya amb un model de competència de Lotka-Volterra fraccionari aleatori. A continuació, el volum d'un tumor mamari es modelitzará mitjançant un model logístic amb incertesa. Finalment ajudant-nos d'un model matemàtic que descriu el nivell de glucosa en sang d'un pacient diabètic, es pretén donar una recomanació de carbohidrats i insulina que s'ha d'ingerir perquè el nivell de glucosa del pacient estiga dins d'una banda de confiança saludable. És important subratllar que per a poder realitzar aquests estudis es requereixen dades reals, els quals poden estar alterats a causa dels errors de mesurament o per la forma en que s'han obtés. Per aquest motiu, modelitzar correctament el problema juntament amb la incertesa en les dades és de vital importància.
[EN] Uncertainty quantification collects different methods and computational techniques aimed at describing the randomness in real phenomena. These methods are useful in the modelling of different processes as biological, physical, natural or social, since they present some aspects that can not be determined exactly. For example, the contagious rate of a epidemiological disease or the growth factor of a tumour volume depend on genetic, environmental or behavioural factors. They may not always be fully described and therefore involve uncertainties that affects on the final result. The main objective of this PhD thesis is to extend techniques to quantify the uncertainty in two mathematical areas: fractional calculus and mathematical modelling. Fractional derivatives allow us to model some behaviours that classical derivatives cannot, such as memory effects or the viscoelasticity of some materials. In this PhD thesis, from a theoretical point of view, fractional calculus is extended into the random framework, concretely in the mean square sense. Initial value problems will be studied. The calculus of the analytic solution, approximations for the mean and for the variance and the computation of the first probability density function are concepts we deal with them thought the following chapters. Nevertheless, it is not always possible to obtain the analytic solution of an initial value problem. Therefore, in this dissertation a chapter is addressed to describe a numerical procedure to approximate the solution for an initial value problem. On the other hand, from a modelling point of view, computational techniques to quantify the uncertainty in mathematical models are developed. Merging these techniques with appropriate mathematical models, problems of biological dynamics are studied. Firstly, the carriers of meningococcus in Spain are determined using a competition Lotka-Volterra random fractional model. Then, the volume of breast tumours is modelled by a random logistic model. Finally, taking advantage of a mathematical model which describes the glucose level of a diabetic patient, a recommendation of insulin shots and carbohydrate intakes is proposed to a patient in order to maintain her/his glucose level in a healthy confidence range. An important observation is that to carry out these studies real data is required and they may include uncertainties contained in the measurements on the process to perform the corresponding study. This it is the reason why it is crucial to properly model the problem taking also into account the randomness of the data.
Burgos Simón, C. (2021). Advances on Uncertainty Quantification Techniques for Dynamical Systems: Theory and Modelling [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/166442
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Shahtaheri, Yasaman. "A Probabilistic Decision Support System for a Performance-Based Design of Infrastructures." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/96804.

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Infrastructures are the most fundamental facilities and systems serving the society. Due to the existence of infrastructures in economic, social, and environmental contexts, all lifecycle phases of such fundamental facilities should maximize utility for the designers, occupants, and the society. With respect to the nature of the decision problem, two main types of uncertainties may exist: 1) the aleatory uncertainty associated with the nature of the built environment (i.e., the economic, social, and environmental impacts of infrastructures must be described as probabilistic); and 2) the epistemic uncertainty associated with the lack of knowledge of decision maker utilities. Although a number of decision analysis models exist that consider the uncertainty associated with the nature of the built environment, they do not provide a systematic framework for including aleatory and epistemic uncertainties, and decision maker utilities in the decision analysis process. In order to address the identified knowledge gap, a three-phase modular decision analysis methodology is proposed. Module one uses a formal preference assessment methodology (i.e., utility function/indifference curve) for assessing decision maker utility functions with respect to a range of alternative design configurations. Module two utilizes the First Order Reliability Method (FORM) in a systems reliability approach for assessing the reliability of alternative infrastructure design configurations with respect to the probabilistic decision criteria and decision maker defined utility functions (indifference curves), and provides a meaningful feedback loop for improving the reliability of the alternative design configurations. Module three provides a systematic framework to incorporate both aleatory and epistemic uncertainties in the decision analysis methodology (i.e., uncertain utility functions and group decision making). The multi-criteria, probabilistic decision analysis framework is tested on a nine-story office building in a seismic zone with the probabilistic decision criteria of: building damage and business interruption costs, casualty costs, and CO2 emission costs. Twelve alternative design configurations and four decision maker utility functions under aleatory and epistemic uncertainties are utilized. The results of the decision analysis methodology revealed that the high-performing design configurations with an initial cost of up to $3.2M (in a cost range between $1.7M and $3.2M), a building damage and business interruption cost as low as $303K (in a cost range between $303K and $6.2M), a casualty cost as low as $43K (in a cost range between $43K and $1.2M), and a CO2 emission as low as $146K (in a cost range between $133K to $150K) can be identified by having a higher probability (i.e., up to 80%) of meeting the decision makers' preferences. The modular, holistic, decision analysis framework allows decision makers to make more informed performance-based design decisions—and allows designers to better incorporate the preferences of the decision makers—during the early design process.
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Oskarsson, Joel. "Probabilistic Regression using Conditional Generative Adversarial Networks." Thesis, Linköpings universitet, Statistik och maskininlärning, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-166637.

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Regression is a central problem in statistics and machine learning with applications everywhere in science and technology. In probabilistic regression the relationship between a set of features and a real-valued target variable is modelled as a conditional probability distribution. There are cases where this distribution is very complex and not properly captured by simple approximations, such as assuming a normal distribution. This thesis investigates how conditional Generative Adversarial Networks (GANs) can be used to properly capture more complex conditional distributions. GANs have seen great success in generating complex high-dimensional data, but less work has been done on their use for regression problems. This thesis presents experiments to better understand how conditional GANs can be used in probabilistic regression. Different versions of GANs are extended to the conditional case and evaluated on synthetic and real datasets. It is shown that conditional GANs can learn to estimate a wide range of different distributions and be competitive with existing probabilistic regression models.

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Books on the topic "Aleatoric uncertainty"

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Franklin, James. Pre-history of Probability. Edited by Alan Hájek and Christopher Hitchcock. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199607617.013.3.

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The history of the evaluation of uncertain evidence before the quantification of probability in 1654 is a mass of examples relevant to current debates. They deal with matters that in general are as unquantified now as ever – the degree to which evidence supports theory, the strength and justification of inductive inferences, the weight of testimony, the combination of pieces of uncertain evidence, the price of risk, the philosophical nature of chance, and the problem of acting in case of doubt. Concepts similar to modern “proof beyond reasonable doubt” were developed especially in the legal theory of evidence. Moral theology discussed “probabilism”, the doctrine that one could follow a probable opinion in ethics even if the opposite was more probable. Philosophers understood the difficult problem of induction. Legal discussion of “aleatory contracts” such as insurance and games of chance developed the framework in which the quantification of probability eventually took place.

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Book chapters on the topic "Aleatoric uncertainty"

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Segalman, Daniel J., and Matthew R. W. Brake. "Epistemic and Aleatoric Uncertainty in Modeling." In The Mechanics of Jointed Structures, 593–603. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56818-8_33.

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Shaker, Mohammad Hossein, and Eyke Hüllermeier. "Aleatoric and Epistemic Uncertainty with Random Forests." In Lecture Notes in Computer Science, 444–56. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44584-3_35.

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Robertson, Brett A., Matthew S. Bonney, Chiara Gastaldi, and Matthew R. W. Brake. "Quantifying Epistemic and Aleatoric Uncertainty in the Ampair 600 Wind Turbine." In Dynamics of Coupled Structures, Volume 4, 125–38. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15209-7_12.

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Robertson, Brett A., Matthew S. Bonney, Chiara Gastaldi, and Matthew R. W. Brake. "Quantifying Epistemic and Aleatoric Uncertainty in the Ampair 600 Wind Turbine." In The Mechanics of Jointed Structures, 651–72. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56818-8_36.

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Urbina, Angel, and Sankaran Mahadevan. "Quantification of Aleatoric and Epistemic Uncertainty in Computational Models of Complex Systems." In Structural Dynamics, Volume 3, 519–35. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-9834-7_47.

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Kepp, Timo, Julia Andresen, Helge Sudkamp, Claus von der Burchard, Johann Roider, Gereon Hüttmann, Jan Ehrhardt, and Heinz Handels. "Epistemic and Aleatoric Uncertainty Estimation for PED, Segmentation in Home OCT Images." In Informatik aktuell, 32–37. Wiesbaden: Springer Fachmedien Wiesbaden, 2022. http://dx.doi.org/10.1007/978-3-658-36932-3_7.

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Valiuddin, M. M. Amaan, Christiaan G. A. Viviers, Ruud J. G. van Sloun, Peter H. N. de With, and Fons van der Sommen. "Improving Aleatoric Uncertainty Quantification in Multi-annotated Medical Image Segmentation with Normalizing Flows." In Uncertainty for Safe Utilization of Machine Learning in Medical Imaging, and Perinatal Imaging, Placental and Preterm Image Analysis, 75–88. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-87735-4_8.

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Dutta, Palash, and Tazid Ali. "Aleatory and Epistemic Uncertainty Quantification." In Applied Mathematics, 209–17. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2547-8_20.

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McFarland, John, and David Riha. "Variance Decomposition in the Presence of Epistemic and Aleatory Uncertainty." In Linking Models and Experiments, Volume 2, 417–30. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-9305-2_32.

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Giupponi, Carlo. "Operationalizing Climate Proofing in Decision/Policy Making." In Springer Climate, 225–32. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-86211-4_26.

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AbstractThe purpose of this work is to present an operational approach to include consideration of global change drivers (climatic, economic, social, etc.) in support to the design of local policies or investment plans. In both cases decision/policy makers typically have sets of plausible solutions and decisions to be taken in terms of choices among sets of plausible solutions with the best knowledge about the future dynamics of endogenous and exogenous system variables. The ambition is to identify the preferable solution(s) (in terms of technical performances, acceptance by stakeholders, cost–benefit ratio, etc.) in a medium term perspective, (e.g., 10–40 years), with current knowledge about the problem and under the effect of important sources of uncertainty (both aleatory and epistemic). Common to most decision contexts in a medium term perspective typical of both investment decisions and adaptation policies is the prevalence of economic signals in the shorter term and of climatic signals in the longer term. Models play a fundamental role in both cases, but they rarely cover the whole set of variables needed for decision making and the outcomes usually require integration of qualitative expert knowledge or simply subjective judgements. Multi-criteria analysis coupled with uncertainty analysis can contribute with methodologically sound and operational solutions. This paper elaborates on a series of recent cases with the ambition to extract common elements for a general methodological framework.

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Conference papers on the topic "Aleatoric uncertainty"

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Segalman, Daniel J., Matthew R. Brake, Lawrence A. Bergman, Alexander F. Vakakis, and Kai Willner. "Epistemic and Aleatoric Uncertainty in Modeling." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13234.

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One major difficulty that exists in reconciling model predictions of a system with experimental measurements is assessing and accounting for the uncertainties in the system. There are several enumerated sources of uncertainty in model prediction of physical phenomena, the primary ones being: 1) Model form error, 2) Aleatoric uncertainty of model parameters, 3) Epistemic uncertainty of model parameters, and 4) Model solution error. These forms of uncertainty can have insidious consequences for modeling if not properly identified and accounted for. In particular, confusion between aleatoric and epistemic uncertainty can lead to a fundamentally incorrect model being inappropriately fit to data such that the model seems to be correct. As a consequence, model predictions may be nonphysical or nonsensical outside of the regime for which the model was calibrated. This research looks at the effects of aleatoric and epistemic uncertainty in order to make recommendations for properly accounting for them in a modeling framework.

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Liu, Jiawei, Jing Zhang, and Nick Barnes. "Modeling Aleatoric Uncertainty for Camouflaged Object Detection." In 2022 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV). IEEE, 2022. http://dx.doi.org/10.1109/wacv51458.2022.00267.

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Singh Sambyal, Abhishek, Narayanan C. Krishnan, and Deepti R. Bathula. "Towards Reducing Aleatoric Uncertainty for Medical Imaging Tasks." In 2022 IEEE 19th International Symposium on Biomedical Imaging (ISBI). IEEE, 2022. http://dx.doi.org/10.1109/isbi52829.2022.9761638.

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Singh Sambyal, Abhishek, Narayanan C. Krishnan, and Deepti R. Bathula. "Towards Reducing Aleatoric Uncertainty for Medical Imaging Tasks." In 2022 IEEE 19th International Symposium on Biomedical Imaging (ISBI). IEEE, 2022. http://dx.doi.org/10.1109/isbi52829.2022.9761638.

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Nguyen, Vu-Linh, Sébastien Destercke, Marie-Hélène Masson, and Eyke Hüllermeier. "Reliable Multi-class Classification based on Pairwise Epistemic and Aleatoric Uncertainty." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/706.

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We propose a method for reliable prediction in multi-class classification, where reliability refers to the possibility of partial abstention in cases of uncertainty. More specifically, we allow for predictions in the form of preorder relations on the set of classes, thereby generalizing the idea of set-valued predictions. Our approach relies on combining learning by pairwise comparison with a recent proposal for modeling uncertainty in classification, in which a distinction is made between reducible (a.k.a. epistemic) uncertainty caused by a lack of information and irreducible (a.k.a. aleatoric) uncertainty due to intrinsic randomness. The problem of combining uncertain pairwise predictions into a most plausible preorder is then formalized as an integer programming problem. Experimentally, we show that our method is able to appropriately balance reliability and precision of predictions.

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Bae, Gwangbin, Ignas Budvytis, and Roberto Cipolla. "Estimating and Exploiting the Aleatoric Uncertainty in Surface Normal Estimation." In 2021 IEEE/CVF International Conference on Computer Vision (ICCV). IEEE, 2021. http://dx.doi.org/10.1109/iccv48922.2021.01289.

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Liu, Qi, Yanjie Li, Yuecheng Liu, Meiling Chen, Shaohua Lv, and Yunhong Xu. "Exploration via Distributional Reinforcement Learning with Epistemic and Aleatoric Uncertainty Estimation." In 2021 IEEE 17th International Conference on Automation Science and Engineering (CASE). IEEE, 2021. http://dx.doi.org/10.1109/case49439.2021.9551544.

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Kawashima, Takumi, Qina Yu, Akari Asai, Daiki Ikami, and Kiyoharu Aizawa. "The Aleatoric Uncertainty Estimation Using a Separate Formulation with Virtual Residuals." In 2020 25th International Conference on Pattern Recognition (ICPR). IEEE, 2021. http://dx.doi.org/10.1109/icpr48806.2021.9412324.

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Huseljic, Denis, Bernhard Sick, Marek Herde, and Daniel Kottke. "Separation of Aleatoric and Epistemic Uncertainty in Deterministic Deep Neural Networks." In 2020 25th International Conference on Pattern Recognition (ICPR). IEEE, 2021. http://dx.doi.org/10.1109/icpr48806.2021.9412616.

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Mey, Oliver, Andre Schneider, Olaf Enge-Rosenblatt, Yesnier Bravo, and Pit Stenzel. "Prediction of Energy Consumption for Variable Customer Portfolios Including Aleatoric Uncertainty Estimation." In 2021 10th International Conference on Power Science and Engineering (ICPSE). IEEE, 2021. http://dx.doi.org/10.1109/icpse53473.2021.9656857.

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Reports on the topic "Aleatoric uncertainty"

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Johnson, Jay Dean, Jon Craig Helton, William Louis Oberkampf, and Cedric J. Sallaberry. Representation of analysis results involving aleatory and epistemic uncertainty. Office of Scientific and Technical Information (OSTI), August 2008. http://dx.doi.org/10.2172/940535.

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Swiler, Laura Painton, and Michael Scott Eldred. Efficient algorithms for mixed aleatory-epistemic uncertainty quantification with application to radiation-hardened electronics. Part I, algorithms and benchmark results. Office of Scientific and Technical Information (OSTI), September 2009. http://dx.doi.org/10.2172/972887.

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Helton, Jon C., Dusty Marie Brooks, and Cedric Jean-Marie Sallaberry. Probability of Loss of Assured Safety in Systems with Multiple Time-Dependent Failure Modes: Incorporation of Delayed Link Failure in the Presence of Aleatory Uncertainty. Office of Scientific and Technical Information (OSTI), February 2018. http://dx.doi.org/10.2172/1423532.

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Unwin, Stephen D., Paul W. Eslinger, and Kenneth I. Johnson. Robustness of RISMC Insights under Alternative Aleatory/Epistemic Uncertainty Classifications: Draft Report under the Risk-Informed Safety Margin Characterization (RISMC) Pathway of the DOE Light Water Reactor Sustainability Program. Office of Scientific and Technical Information (OSTI), September 2012. http://dx.doi.org/10.2172/1051995.

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