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Related Concept Videos

Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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Variation01:19

Variation

An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation, which is the square root of variance.
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Empirical Method to Interpret Standard Deviation01:09

Empirical Method to Interpret Standard Deviation

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Standard Error of the Mean01:13

Standard Error of the Mean

The sampling variability of a statistic is defined as how much the statistic varies from one sample to another. The sampling variability of a statistic is typically measured by measuring its standard error.The standard error of the mean is an example of a standard error. It is a unique standard deviation known as the standard deviation of the sampling distribution of the mean. The standard error of the mean is a statistic that calculates how correctly a sample distribution represents a...
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...

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Related Experiment Videos

Linear dependency between /spl epsi/ and the input noise in /spl epsi/-support vector regression.

J T Kwok1, I W Tsang

  • 1Dept. of Comput. Sci., Hong Kong Univ. of Sci. and Technol., China.

IEEE Transactions on Neural Networks
|February 2, 2008
PubMed
Summary

Choosing the optimal insensitivity parameter (epsilon) for epsilon-support vector regression (epsilon-SVR) is crucial. This study refines theoretical predictions for epsilon, aligning them more closely with experimental findings for Gaussian noise.

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Area of Science:

  • Machine Learning
  • Statistical Modeling
  • Computational Statistics

Background:

  • The epsilon-support vector regression (epsilon-SVR) algorithm requires careful selection of the insensitivity parameter, epsilon.
  • Previous theoretical work by Smola et al. predicted a linear relationship between optimal epsilon and data noise, but showed discrepancies with experimental results for Gaussian noise.

Purpose of the Study:

  • To investigate the discrepancy between theoretically predicted and experimentally observed optimal epsilon values in epsilon-SVR, particularly for Gaussian noise.
  • To develop a more accurate theoretical prediction for the optimal epsilon parameter by analyzing the regression problem directly.

Main Methods:

  • Analysis of the epsilon-support vector regression problem.
  • Theoretical prediction of the optimal epsilon parameter based on the regression formulation.
  • Comparison of theoretical predictions with experimental observations.

Main Results:

  • The refined theoretical prediction for the optimal epsilon parameter shows significantly closer agreement with experimentally observed values compared to previous models.
  • The study confirms a linear scaling relationship between the optimal epsilon and the noise level in the input data.
  • The proposed approach provides a better explanation for experimental results in the context of Gaussian noise.

Conclusions:

  • The direct analysis of the regression problem offers a more accurate method for determining the optimal epsilon parameter in epsilon-SVR.
  • The findings improve the practical application of epsilon-SVR by providing a more reliable guideline for parameter selection.
  • This work bridges the gap between theoretical expectations and empirical performance of epsilon-SVR with respect to its key parameter.