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Uncertainty about Uncertainty: Optimal Adaptive Algorithms for Estimating Mixtures of Unknown Coins [article]

Jasper C.H. Lee, Paul Valiant
2021 arXiv   pre-print
Given a mixture between two populations of coins, "positive" coins that each have – unknown and potentially different – bias ≥1/2+Δ and "negative" coins with bias ≤1/2-Δ, we consider the task of estimating  ...  We achieve an upper and lower bound of Θ(ρ/ϵ^2Δ^2log1/δ) samples for a 1-δ probability of success, where crucially, our lower bound applies to all fully-adaptive algorithms.  ...  Designing Optimal Estimators when Coin Biases are Known By contrast with the above results that analyze the "uncertainty about uncertainty" regime with unknown populations of coins, we shed light on the  ... 
arXiv:1904.09228v3 fatcat:luucmz7dmbb77cxtddrnhpuot4

What We Talk About When We Talk About Uncertainty. Toward a Unified, Data-Driven Framework for Uncertainty Characterization in Hydrogeology

Falk Heße, Alessandro Comunian, Sabine Attinger
2019 Frontiers in Earth Science  
In case a database meeting these desiderata becomes successful, the algorithm for prior derivation has to be adapted to the specifics of the MPS paradigm.  ...  Using the now (in)famous epistemology of the former US Secretary of Defense Donald Rumsfeld (2002) , probability describes the known unknowns whereas ignorance is about the unknown unknowns.  ...  Conflict of Interest Statement: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest  ... 
doi:10.3389/feart.2019.00118 fatcat:4bqsmvkwijh6xisgtn66f4fvzu

Uncertainty about the value of quantum probability for cognitive modeling

Christina Behme
2013 Behavioral and Brain Sciences  
The article fails, however, to provide convincing evidence for the proposal that QPT offers unique insights regarding cognition and the nature of human rationality.  ...  ACKNOWLEDGMENTS We are grateful to Diederik Aerts, Harald Atmanspacher, Thomas Filk, James Hampton, Mike Oaksford, Steven Sloman, Jennifer Trueblood, and Christoph Weidemann for their helpful comments.  ...  For example, prior to flipping a coin I assign Prob(Heads) = 0.5 (aleatory uncertainty); however, I still assign Prob(Heads) = 0.5 if the coin has been flipped but is covered (epistemic uncertainty).  ... 
doi:10.1017/s0140525x12002889 pmid:23673026 fatcat:wowhoqf2ivemvn2k2wo57ic26a

Mispronunciation Detection in Non-native (L2) English with Uncertainty Modeling [article]

Daniel Korzekwa, Jaime Lorenzo-Trueba, Szymon Zaporowski, Shira Calamaro, Thomas Drugman, Bozena Kostek
2021 arXiv   pre-print
We propose a novel approach to overcome this problem based on two principles: a) taking into account uncertainty in the automatic phoneme recognition step, b) accounting for the fact that there may be  ...  This approach makes two simplifying assumptions: a) phonemes can be recognized from speech with high accuracy, b) there is a single correct way for a sentence to be pronounced.  ...  We found that to optimize precision, it is more important to account for the phonetic variability of speech than accounting for uncertainty in phoneme recognition.  ... 
arXiv:2101.06396v2 fatcat:5tizoceu5vacxa2khlioehnzae

UNCERTAINTY AND VARIABILITY IN DEMOGRAPHY AND POPULATION GROWTH: A HIERARCHICAL APPROACH

James S. Clark
2003 Ecology  
Estimates of uncertainty are the basis for inference of population risk.  ...  I adapt a hierarchical approach to the problem of estimating population growth rates and their uncertainties when individuals vary and that variability cannot be assigned to specific causes.  ...  ., (x; ␤), where ␤ are estimated parameters (e.g., logistic regression). Inference is made about the collection of j estimates (for discrete groups) or about parameters ␤.  ... 
doi:10.1890/0012-9658(2003)084[1370:uavida]2.0.co;2 fatcat:ou5edxwz55fohjqmop3wowv4uy

Adaptive learning under strategic and structural uncertainty: the case of auction games [article]

Mario Martinez-Saito, Alexis Belianin, Anna Shestakova, Boris Gutkin, Vasily Klucharev
2020 bioRxiv   pre-print
AbstractIn games of incomplete information individual players make decisions facing a combination of structural uncertainty about the underlying parameters of the environment, and strategic uncertainty  ...  We use a double auction task with different competitive and informational environments to characterize learning abilities of the single human participants (buyers) in a range of adaptive learning models  ...  The DL heuristic we employ in this study is not a conventional RL rule, but a mixture of counterfactual (belief learning) and adaptive learning (Grosskopf, 2003) , which incorporates knowledge of the  ... 
doi:10.1101/2020.08.22.262469 fatcat:a356mmojnnd3fcgsiacnhnl7j4

Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification

Rohit K. Tripathy, Ilias Bilionis
2018 Journal of Computational Physics  
State-of-the-art computer codes for simulating real physical systems are often characterized by a vast number of input parameters.  ...  Performing uncertainty quantification (UQ) tasks with Monte Carlo (MC) methods is almost always infeasible because of the need to perform hundreds of thousands or even millions of forward model evaluations  ...  While there are multiple variants of the SGD method that have demonstrated improvements over vanilla SGD, in this work, we solve Eq. (11) with the Adaptive Moments (ADAM) optimization algorithm [48] .  ... 
doi:10.1016/j.jcp.2018.08.036 fatcat:3gsabqs4arc4xeiu7lf2yfmij4

Aleatoric and epistemic uncertainty in machine learning: an introduction to concepts and methods

Eyke Hüllermeier, Willem Waegeman
2021 Machine Learning  
AbstractThe notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology.  ...  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  ...  Acknowledgements The authors like to thank Sebastian Destercke, Karlson Pfannschmidt, and Ammar Shaker for helpful remarks and comments on the content of this paper.  ... 
doi:10.1007/s10994-021-05946-3 fatcat:6dndhzin5fgnrp4bjfer47mnt4

On the functional form of temporal discounting: An optimized adaptive test

Daniel R. Cavagnaro, Gabriel J. Aranovich, Samuel M. McClure, Mark A. Pitt, Jay I. Myung
2016 Journal of Risk and Uncertainty  
To help bring some clarity to this issue, we propose an Adaptive Design Optimization (ADO) method for fitting and comparing models of temporal discounting.  ...  We first test the method in simulation and compare its performance to several non-adaptive benchmarks.  ...  For parameter estimation trials, we will set u(d, θ m , y) = log p(θ m |y, d) p(θ m ) , (8) which makes U (d) equivalent to the expected reduction in uncertainty (measured by Shannon entropy) about the  ... 
doi:10.1007/s11166-016-9242-y pmid:29332995 pmcid:PMC5764197 fatcat:afr5bupxifcazoikgibhlsnquu

Owning Up to Uncertainty in Macroeconomics

George M von Furstenberg, Jin-Ho Jeong
1988 Geneva papers on risk and insurance. Issues and practice  
For example, assume this prior was equiprobability of heads and tails in a toss of a coin with unknown bias, but a statistically significant bias is revealed when a large number of coins are tossed simultaneously  ...  be advised for arriving at the best estimate of the direction of the bias in a randomly selected coin.  ... 
doi:10.1057/gpp.1988.2 fatcat:6xat5hcmajb2jmvckrfyolm7u4

Mixtures of Gaussians for Uncertainty Description in Bivariate Latent Heat Flux Proxies

R. Wójcik, Peter A. Troch, H. Stricker, P. Torfs, E. Wood, H. Su, Z. Su
2006 Journal of Hydrometeorology  
This paper proposes a new probabilistic approach for describing uncertainty in the ensembles of latent heat flux proxies.  ...  To describe the latter, the use of Gaussian mixture density models-a class of nonparametric, data-adaptive probability density functions-is proposed.  ...  The first two authors are grateful for the financial support from WIMEK, the Wageningen Institute for Environmental and Climate studies. We also wish to acknowledge the constructive comments of Prof.  ... 
doi:10.1175/jhm491.1 fatcat:4vvcgrcvnbd3tgllghefxjlraa

Age differences in learning emerge from an insufficient representation of uncertainty in older adults

Matthew R. Nassar, Rasmus Bruckner, Joshua I. Gold, Shu-Chen Li, Hauke R. Heekeren, Ben Eppinger
2016 Nature Communications  
For example, learning rate should increase when expectations are uncertain (uncertainty), outcomes are surprising (surprise) or contingencies are more likely to change (hazard rate).  ...  These tasks often involve the acquisition of dynamic contingencies, which requires adjusting the rate of learning to environmental statistics.  ...  Acknowledgements We thank Ben Heasly for programming the task and Michael Frank, Joseph Kable, Joseph McGuire, and Yin Li for helpful comments.  ... 
doi:10.1038/ncomms11609 pmid:27282467 pmcid:PMC4906358 fatcat:bawa4eksgjfrhfnugh4sovn2wm

Task complexity interacts with state-space uncertainty in the arbitration between model-based and model-free learning

Dongjae Kim, Geon Yeong Park, John P. O′Doherty, Sang Wan Lee
2019 Nature Communications  
However, the role of task complexity in the arbitration between these two strategies remains largely unknown.  ...  Here, using a combination of novel task design, computational modelling, and model-based fMRI analysis, we examined the role of task complexity alongside state-space uncertainty in the arbitration process  ...  Acknowledgements We thank Peter Dayan for insightful comments and Ralph Lee for his assistance.  ... 
doi:10.1038/s41467-019-13632-1 pmid:31844060 pmcid:PMC6915739 fatcat:ef32q76h5relncmybjoeo2y5ie

What We Talk About When We Talk About Uncertainty

Falk Heße, Alessandro Comunian, Sabine Attinger
2019
In case a database meeting these desiderata becomes successful, the algorithm for prior derivation has to be adapted to the specifics of the MPS paradigm.  ...  Using the now (in)famous epistemology of the former US Secretary of Defense Donald Rumsfeld (2002) , probability describes the known unknowns whereas ignorance is about the unknown unknowns.  ...  Conflict of Interest Statement: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest  ... 
doi:10.25932/publishup-43658 fatcat:yymg24ywj5ffnpna3feon5gqzu

Robust solutions to the pollution-routing problem with demand and travel time uncertainty

Reza Eshtehadi, Mohammad Fathian, Emrah Demir
2017 Transportation Research Part D: Transport and Environment  
The importance of the present study is to consider demand and travel time uncertainty in green transport planning by proposing several robust optimization techniques; soft worst case, hard worst case and  ...  Acknowledgements Thanks are due to the Editor and two anonymous reviewers for their useful comments and for raising interesting points for discussion.  ...  Robust VRP (RVRP) was introduced by Bertsimas and Simchi-Levi (1996) for the SVRP and is applied when the probability distribution of uncertain parameter is unknown (i.e., deep uncertainty).  ... 
doi:10.1016/j.trd.2017.01.003 fatcat:evz4kkuuuzhu7anbeqo6bb5io4
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