scholarly journals How to define relative approximation error of an interval estimate: a proposal

2013 ◽  
Vol 7 ◽  
pp. 211-216 ◽  
Author(s):  
V. Kreinovich
Keyword(s):  
Approximation Error ◽  
Interval Estimate ◽  
Relative Approximation

Complexity issues for the symmetric interval eigenvalue problem

2014 ◽  
Vol 13 (1) ◽  
Author(s):  
Milan Hladík
Keyword(s):  
Computational Complexity ◽  
Eigenvalue Problem ◽  
Relative Error ◽  
Symmetric Matrix ◽  
Approximation Error ◽  
Np Hard ◽  
Approximation Errors ◽  
The Matrix ◽  
Polynomially Solvable ◽  
Relative Approximation

AbstractWe study the problem of computing the maximal and minimal possible eigenvalues of a symmetric matrix when the matrix entries vary within compact intervals. In particular, we focus on computational complexity of determining these extremal eigenvalues with some approximation error. Besides the classical absolute and relative approximation errors, which turn out not to be suitable for this problem, we adapt a less known one related to the relative error, and also propose a novel approximation error. We show in which error factors the problem is polynomially solvable and in which factors it becomes NP-hard.

scholarly journals MERACLE: Constructive Layer-Wise Conversion of a Tensor Train into a MERA

2020 ◽  
Author(s):  
Kim Batselier ◽  
Andrzej Cichocki ◽  
Ngai Wong
Keyword(s):  
Approximation Error ◽  
Low Rank ◽  
Multi Scale ◽  
Crucial Component ◽  
Procrustes Problem ◽  
First Time ◽  
And Storage ◽  
Relative Approximation ◽  
Matrix Factors ◽  
New Algorithms

Abstract In this article, two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglement renormalization ansatz (MERA). The Tucker core tensor is never explicitly computed but stored as a tensor train instead, resulting in both computationally and storage efficient algorithms. Both the multilinear Tucker-ranks as well as the MERA-ranks are automatically determined by the algorithm for a given upper bound on the relative approximation error. In addition, an iterative algorithm with low computational complexity based on solving an orthogonal Procrustes problem is proposed for the first time to retrieve optimal rank-lowering disentangler tensors, which are a crucial component in the construction of a low-rank MERA. Numerical experiments demonstrate the effectiveness of the proposed algorithms together with the potential storage benefit of a low-rank MERA over a tensor train.

How to Correct for Chance Agreement in the Estimation of Sensitivity and Specificity of Diagnostic Tests

1994 ◽  
Vol 33 (02) ◽  
pp. 180-186 ◽  
Author(s):  
H. Brenner ◽  
O. Gefeller
Keyword(s):  
Sensitivity And Specificity ◽  
Disease Status ◽  
Disease Prevalence ◽  
Small Sample ◽  
Small Samples ◽  
Interval Estimate ◽  
Traditional Concept ◽  
Interval Estimates ◽  
Major Disadvantage ◽  
Test Result

Abstract:The traditional concept of describing the validity of a diagnostic test neglects the presence of chance agreement between test result and true (disease) status. Sensitivity and specificity, as the fundamental measures of validity, can thus only be considered in conjunction with each other to provide an appropriate basis for the evaluation of the capacity of the test to discriminate truly diseased from truly undiseased subjects. In this paper, chance-corrected analogues of sensitivity and specificity are presented as supplemental measures of validity, which pay attention to the problem of chance agreement and offer the opportunity to be interpreted separately. While recent proposals of chance-correction techniques, suggested by several authors in this context, lead to measures which are dependent on disease prevalence, our method does not share this major disadvantage. We discuss the extension of the conventional ROC-curve approach to chance-corrected measures of sensitivity and specificity. Furthermore, point and asymptotic interval estimates of the parameters of interest are derived under different sampling frameworks for validation studies. The small sample behavior of the estimates is investigated in a simulation study, leading to a logarithmic modification of the interval estimate in order to hold the nominal confidence level for small samples.

GRAM: A True Null Model for Relative Binding Affinity Predictions

2019 ◽  
Author(s):  
Guanglei Cui ◽  
Alan P. Graves ◽  
Eric S. Manas
Keyword(s):  
Binding Affinity ◽  
Performance Metrics ◽  
Null Model ◽  
Performance Measure ◽  
Interval Estimate ◽  
Empirical Observation ◽  
Binding Affinity Prediction ◽  
Affinity Prediction ◽  
Relative Binding Affinity ◽  
Relative Binding

Relative binding affinity prediction is a critical component in computer aided drug design. Significant amount of effort has been dedicated to developing rapid and reliable in silico methods. However, robust assessment of their performance is still a complicated issue, as it requires a performance measure applicable in the prospective setting and more importantly a true null model that defines the expected performance of random in an objective manner. Although many performance metrics, such as correlation coefficient (r2), mean unsigned error (MUE), and room mean square error (RMSE), are frequently used in the literature, a true and non-trivial null model has yet been identified. To address this problem, here we introduce an interval estimate as an additional measure, namely prediction interval (PI), which can be estimated from the error distribution of the predictions. The benefits of using the interval estimate are 1) it provides the uncertainty range in the predicted activities, which is important in prospective applications; 2) a true null model with well-defined PI can be established. We provide one such example termed Gaussian Random Affinity Model (GRAM), which is based on the empirical observation that the affinity change in a typical lead optimization effort has the tendency to distribute normally N (0, s). Having an analytically defined PI that only depends on the variation in the activities, GRAM should in principle allow us to compare the performance of relative binding affinity prediction methods in a standard way, ultimately critical to measuring the progress made in algorithm development.<br>

THE MODEL FOR MANAGING INVESTMENTS IN THE MOSCOW ENVIRONMENT BASED ON A POWER REGRESSION EQUATION

2020 ◽  
Vol 2 (7) ◽  
pp. 91-99
Author(s):  
E. V. KOSTYRIN ◽  
◽  
M. S. SINODSKAYA ◽  
Keyword(s):  
Solid Waste ◽  
Influencing Factors ◽  
Pair Correlation ◽  
Approximation Error ◽  
Regression Equation ◽  
Regression Equations ◽  
The Impact ◽  
The Relationship ◽  
Average Approximation ◽  
Average Approximation Error

The article analyzes the impact of certain factors on the volume of investments in the environment. Regression equations describing the relationship between the volume of investment in the environment and each of the influencing factors are constructed, the coefficients of the Pearson pair correlation between the dependent variable and the influencing factors, as well as pairwise between the influencing factors, are calculated. The average approximation error for each regression equation is determined. A correlation matrix is constructed and a conclusion is made. The developed econometric model is implemented in the program of separate collection of municipal solid waste (MSW) in Moscow. The efficiency of the model of investment management in the environment is evaluated on the example of the growth of planned investments in the activities of companies specializing in the export and processing of solid waste.

POLYGONAL APPROXIMATION OF DIGITAL CURVE BASED ON REVERSE ENGINEERING CONCEPT

2013 ◽  
Vol 13 (04) ◽  
pp. 1350017 ◽  
Author(s):  
KUMAR S. RAY ◽  
BIMAL KUMAR RAY
Keyword(s):  
Reverse Engineering ◽  
Linear Time ◽  
Line Drawing ◽  
Approximation Error ◽  
Zero Approximation ◽  
Polygonal Approximation ◽  
Digital Curve ◽  
Symmetric Approximation ◽  
Engineering Concept ◽  
Automatic Algorithm

This paper applies reverse engineering on the Bresenham's line drawing algorithm [J. E. Bresenham, IBM System Journal, 4, 106–111 (1965)] for polygonal approximation of digital curve. The proposed method has a number of features, namely, it is sequential and runs in linear time, produces symmetric approximation from symmetric digital curve, is an automatic algorithm and the approximating polygon has the least non-zero approximation error as compared to other algorithms.

scholarly journals Two-stage segment linearization as part of the thermocouple measurement chain

2021 ◽  
Vol 54 (1-2) ◽  
pp. 141-151
Author(s):  
Dragan Živanović ◽  
Milan Simić
Keyword(s):  
Transfer Functions ◽  
Approximation Error ◽  
Linearization Method ◽  
Linear Segment ◽  
Virtual Instrumentation ◽  
Memory Consumption ◽  
Thermocouple Measurement ◽  
Two Stage ◽  
Approximation Errors ◽  
Input Range

An implementation of a two-stage piece-wise linearization method for reduction of the thermocouple approximation error is presented in the paper. First, the whole thermocouple measurement chain of a transducer is described, and possible error is analysed to define the required level of accuracy for linearization of the transfer characteristics. Evaluation of linearization functions and analysis of approximation errors are performed by the virtual instrumentation software package LabVIEW. The method is appropriate for thermocouples and other sensors where nonlinearity varies a lot over the range of input values. The basic principle of this method is to first transform the abscissa of the transfer function by a linear segment look-up table in such a way that significantly nonlinear parts of the input range are expanded before a standard piece-wise linearization. In this way, applying equal-segment linearization two times has a similar effect to non-equal-segment linearization. For a given examples of the thermocouple transfer functions, the suggested method provides significantly better reduction of the approximation error, than the standard segment linearization, with equal memory consumption for look-up tables. The simple software implementation of this two-stage linearization method allows it to be applied in low calculation power microcontroller measurement transducers, as a replacement of the standard piece-wise linear approximation method.

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