In system identification, interval (and fuzzy) estimates can lead to much better accuracy than the traditional statistical ones: General algorithm and case study

Kumkov, Sergey S.; Kreinovich, Vladik; Pownuk, Andrzej

doi:10.1109/smc.2017.8122631

Cited by 5 publications

(2 citation statements)

References 15 publications

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“…For comparison, Table 1 shows estimates of parameters obtained for investigated chemical substances. Computation results and previous special investigation [11,12] confirm the fact that the interval approach and one on the basis of the standard statistical procedures can usefully complement each other even in the case of processing the experimental data under conditions of uncertainty.…”

Section: For Comparison With Equation By the Interval Estimation The Lsqm-equation Issupporting

confidence: 58%

Interval approach to processing the noised thermophysical data

Kumkov

Redkin

Першина

et al. 2020

International Conference of Numerical Analysis and Applied Mathematics Icnaam 2019

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The paper deals with application of numerical methods to processing the experimental data on the thermophysical properties of several chemical substances and their compounds (cryolites, rare earth compounds, and alkali halides). The main aim of investigations is in estimating the parameters of dependencies between the heat of fusion and the melting temperature of these chemical substances. The data are corrupted by the measuring errors. Procession is implemented under conditions of uncertainty: there is no any information on probabilistic properties of the corrupting factors, samples of measurements are short, and only approximate functions are known that describes mentioned dependencies. Under such conditions, the standard statistical methods can be applied formally. To obtain guarantied results in parameters estimation, the interval analysis methods and procedures are used.

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Section: For Comparison With Equation By the Interval Estimation The Lsqm-equation Issupporting

confidence: 58%

Interval approach to processing the noised thermophysical data

Kumkov

Redkin

Першина

et al. 2020

International Conference of Numerical Analysis and Applied Mathematics Icnaam 2019

Self Cite

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“…Over several decades various regression methods have been developed such as methods for linear regression models where the dependent variable has been either rounded or interval-censored [20,21], methods for models that have intervalvalued covariates and a precise dependent variable [22], interval-based algorithms for the data-fitting problem where measurement errors are supposed to be bounded and known [23,24], some probabilistic [25] and likelihood-based [26] methods, nonparametric methods [27,28], and others [29,30].…”

Section: Introductionmentioning

confidence: 99%

Neural network model for imprecise regression with interval dependent variables

Tretiak¹,

Schollmeyer²,

Ferson³

2022

Preprint

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We propose a new iterative method using machine learning algorithms to fit an imprecise regression model to data that consist of intervals rather than point values. The method is based on a single-layer interval neural network which can be trained to produce an interval prediction. It seeks parameters for the optimal model that minimize the mean squared error between the actual and predicted interval values of the dependent variable using a first-order gradient-based optimization and interval analysis computations to model the measurement imprecision of the data. The method captures the relationship between the explanatory variables and a dependent variable by fitting an imprecise regression model, which is linear with respect to unknown interval parameters even the regression model is nonlinear. We consider the explanatory variables to be precise point values, but the measured dependent values are characterized by interval bounds without any probabilistic information. Thus, the imprecision is modeled non-probabilistically even while the scatter of dependent values is modeled probabilistically by homoscedastic Gaussian distributions. The proposed iterative method estimates the lower and upper bounds of the expectation region, which is an envelope of all possible precise regression lines obtained by ordinary regression analysis based on any configuration of real-valued points from the respective intervals and their x-values.

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Comparison of Interval Analysis and Standard Statistical Methods for Estimating Experimental Data with Uncertainty

Kumkov

Jaulin

2019

Meas Tech

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In system identification, interval (and fuzzy) estimates can lead to much better accuracy than the traditional statistical ones: General algorithm and case study

Cited by 5 publications

References 15 publications

Interval approach to processing the noised thermophysical data

Interval approach to processing the noised thermophysical data

Neural network model for imprecise regression with interval dependent variables

Comparison of Interval Analysis and Standard Statistical Methods for Estimating Experimental Data with Uncertainty

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