David Ryckelynck, Fabien Casenave, Nissrine Akkari · SpringerBriefs in computer science · 2024
Abstract Consider first data-based machine learning techniques. They rely on large sets of examples provided during the training stage and do not learn with equations. Dealing with a situation that do not belong to the training set variability, namely an out-of-distribution sample, can be very challenging for these techniques. Trusting them could imply being able to guarantee that the training set covers the operational domain of the system to be trained. Besides, data-based AI can lack in robustness: examples have been given of adversarial attacks in which a classifier was tricked to infer a wrong class only by changing a very small percentage of the pixels of the input image. These models often also lack explainability: it is hard to understand what is exactly learned, what phenomenon occurs through the layers of a neural network. In some cases, information on the background of a picture is used by the network in the prediction of the class of an object, or bias present in the training data will be learned by the AI model, like gender bias in recruitment processes.
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Shuhua Hu · 2007
statistical model: X = h(t; q) + ɛ � h: mathematical model such as ODE model, PDE model, algebraic model, etc. � ɛ: random variable with some probability distribution such as normal distribution. � X is a random variable. Under the assumption of ɛ being i.i.d N(0, σ2), we have probability distribution model: g(x|θ) = 1 √ exp
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2005
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Nathalie Japkowicz, Mohak Shah · Cambridge University Press eBooks · 2011
We saw in Chapters 3 and 4 the concerns that arise from having to choose appropriate performance measures. Once a performance measure is decided upon, the next obvious concern is to find a good method for testing the learning algorithm so as to obtain as unbiased an estimate of the chosen performance measure as possible. Also of interest is the related concern of whether the technique we use to obtain such an estimate brings us as close as possible to the true measure value.
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Dieter Dinkler, Ursula Kowalsky · 2023
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2015
ient n fo n is at a orne ds. T e p rop om field re ersingu e harm pplica xternal solutio orrespo [1–6]. been ches. dary ental holtz nda-becomes weakly singularity. The last scheme is a use of ARTICLE IN PRESS Contents lists available at ScienceDirect
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Umberto Minora (3879193), Stefano Maria Iacus (9368356), Filipe Batista e Silva (539718) et al. · Figshare · 2023
<p>Absolute and relative estimation errors of nights spent for each country and years 2020 to 2022.</p>
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Martin Becker (495924), Saverio Caminiti (495925), Donato Fiorella (495926) et al. · Figshare · 2015
<p>Difference between estimated and real dB value vs the number of measurements a user has performed.</p>
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Fabian Fröhlich (848026), Philipp Thomas (319681), Atefeh Kazeroonian (848025) et al. · Figshare · 2016
<p>(a) Mean monomer concentration in the trimerization process for Ω = 6<i>μ</i>m<sup>3</sup> computed from 10<sup>5</sup> SSA trajectory realizations (black line). Approximate mean monomer concentrations obtained using RRE, EMRE and 2MA (colored lines). (b) Mean monomer concentration for RRE, EMRE and 2MA obtained after parameter estimation using the SSA mean as artificial dataset. (c) True (black ×) and optimized parameter values (colored ×) for RRE, EMRE and 2MA. Contour lines of objective function are colored. The opacity increases with increasing likelihood values.</p>
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David Augustin (15811009), Ben Lambert (5060288), Ken Wang (4517578) et al. · Figshare · 2023
<div><p>Variability is an intrinsic property of biological systems and is often at the heart of their complex behaviour. Examples range from cell-to-cell variability in cell signalling pathways to variability in the response to treatment across patients. A popular approach to model and understand this variability is nonlinear mixed effects (NLME) modelling. However, estimating the parameters of NLME models from measurements quickly becomes computationally expensive as the number of measured individuals grows, making NLME inference intractable for datasets with thousands of measured individuals. This shortcoming is particularly limiting for snapshot datasets, common e.g. in cell biology, where high-throughput measurement techniques provide large numbers of single cell measurements. We introduce a novel approach for the estimation of NLME model parameters from snapshot measurements, which we call filter inference. Filter inference uses measurements of simulated individuals to define an approximate likelihood for the model parameters, avoiding the computational limitations of traditional NLME inference approaches and making efficient inferences from snapshot measurements possible. Filter inference also scales well with the number of model parameters, using state-of-the-art gradient-based MCMC algorithms such as the No-U-Turn Sampler (NUTS). We demonstrate the properties of filter inference using examples from early cancer growth modelling and from epidermal growth factor signalling pathway modelling.</p></div>
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Huijie Lei (10321958), Yanwei Zhang (690019), Xikun Lu (20074143) · Figshare · 2025
<div> This study proposes an internal iteration scalar-innovation gradient estimation method based on multi-innovation theory for a nonlinear sandwich system subject to a quantized sensor and friction nonlinearity. Different from the existing multi-innovation gradient method (MISG ), the proposed method is designed to resolve the existing shortages of the conventional MISG. First, the decomposing method is applied to derive the identification model, and the redundant parameter estimation problem is avoided. Then, an adaptive filter based on the prior knowledge of the system is proposed to obtain the helpful identification data. Second, to solve the multi-innovation length problem in MISG, the internal iteration principle is presented to convert the multi-innovation updating to scalar-innovation updating under a given innovation length, where the positive estimation performance can be achieved. Subsequently, the trigger mechanism is used to produce the suboptimal initial estimate value when the next parameter adaptive law is updated. Then, the fast convergence rate is obtained. Finally, the proposed estimation strategy is verified by conducting a numerical example and an experiment on a practical electromechanical system test bench. </div>
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S. Ch, Rx Q T B · 2008
Estimation of unknowns in the presence of noise and uncertainty is an active area of study, because no method handles all cases well, or even satisfactorily. The basic problem considered is the linear system, Ax ≈ b, where A and b are given matrices with noise and uncertainty from measurements or modeling. The goal is to get the ”best ” estimate of x. The problem is useful in a wide variety of situations since it covers how to invert a matrix that contains uncertainty. Mainstream methods like least squares and total least squares fail dramatically when A is ill-conditioned. Other methods like Tikhonov regression, ridge regression, and min max (bounded data uncertainty) provide robustness at the cost of fine details (by reducing �x�). This paper presents a new family of regression methods based off the backward error criteria which can add robustness and when possible enhances fine details (by increasing �x�). This paper covers the motivation, proof, and application of backward error estimation. The resulting algorithms are compared against existing methods in numerical examples from image processing. This paper is concerned with the estimation of unknowns that are related to some measurements by a linear model that is subject to uncertainty. Consider the set of linear equations, Ax = b, where A ∈ R m×n and b ∈ R m are given. The goal is to calculate the value of x ∈ R n. If the equation is exact and A is not singular, the solution can be readily found by a variety of techniques, such as taking the QR factorization
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Morena Raiola (22439390), Isaac Esteban (20445935), Kenzo Ivanovitch (246056) et al. · Figshare · 2025
(A), The error made in continuous registration of landmarks belonging to different cardiac layers from images at 25% resolution. There is no statistically significant difference between the error made on myocardial cells, splanchnic mesodermal cells, and endodermal cells. (B), x-y-z decomposition of the continuous mean error, related to a 25% rescaled image (e01, e02, e05, e06, e15, e16, e24, e26, e27) is reported. (C) Number of landmarks in two-hours video interval for which the error was estimated. (TIF)
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Kazamarande, Evariste (Louvain Univ. Catholique, Louvain-la-Neuve (Belgium).) · OpenGrey (Institut de l'Information Scientifique et Technique) · 1984
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Zhengbin Li (14259417), Lijun Ma (207865), Yongqiang Wang (211682) · Figshare · 2022
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Ernst Hairer, Michel Roche, Christian Lubich · Lecture notes in mathematics · 1989
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Martin Weiser · Spark · 2018
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Roos, Matts · CERN Document Server (European Organization for Nuclear Research) · 1984
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John R. Dormand · 2018
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Daniel Kahneman, Linnea Gandhi · OSF Preprints (OSF Preprints) · 2020
We are interested in studying error in numeric judgments made by collections of independent individuals. When error emerges, how much is attributable to systematic versus random causes, or bias versus noise? How can we explain, predict or otherwise influence these sources of error, in particular noise? In this study we will conduct an extension of Jacowitz &amp; Kahneman 1995 to explore the ratio of bias to noise in estimation error. We will run a study 1 where we provide no anchor. We will run a study 2 where for each participant we vary randomly by participant whether a given trivia question has a low or a high anchor presented. (The anchors are generated by study 1.) We will also explore the relationship between estimation error and (a) CRT scores as well as (b) self-reported confidence in responses. Finally we will ask about predictions of how close others will be to one's own score, expecting (over)estimations of others' agreement. The stimuli are trivia estimation problems with “right” answers, directly from Jacowitz &amp; Kahneman 1995 or slightly modified to take into account present culture. The domains will cover general trivia (e.g., the length of a river, top speed of a house cat) that is primarily US-based. We chose this narrow set of stimuli to not only replicate the original study but also remove elements of value judgment or preference from the study, which would artificially inflate noise.
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