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Related Concept Videos

Forgetting01:21

Forgetting

156
Forgetting is an intrinsic aspect of human memory, characterized by the gradual loss or inaccessibility of information over time. Hermann Ebbinghaus, a pioneering psychologist, extensively studied this phenomenon and formulated the forgetting curve. This curve illustrates that memory loss occurs rapidly immediately after learning and then decelerates over time. Several mechanisms contribute to forgetting, including encoding failure, storage decay, retrieval failure, and interference.
Encoding...
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Interference and Decay01:16

Interference and Decay

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Forgetting is a complex cognitive phenomenon influenced by several factors, among which interference and decay are particularly prominent. These processes explain why individuals often struggle to retrieve specific information from memory, leading to lapses in recall that can be observed in everyday situations.
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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
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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...
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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...
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Identification of the ARX Model with Random Impulse Noise Based on Forgetting Factor Multi-error Information Entropy.

Shaoxue Jing1

  • 1School of Physics and Electronic Electrical Engineering, Huaiyin Normal University, Huaian, 223300 Jiangsu China.

Circuits, Systems, and Signal Processing
|August 18, 2021
PubMed
Summary

A new stochastic gradient algorithm using minimum Shannon entropy enhances system identification. This novel approach offers faster convergence and more accurate parameter estimation for ARX models compared to traditional methods.

Keywords:
ARX modelForgetting factorInformation gradientMinimum error entropyMulti-errorParameter estimation

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Area of Science:

  • Control Systems
  • Signal Processing
  • Information Theory

Background:

  • Entropy is increasingly used in system identification.
  • Traditional stochastic gradient algorithms converge slowly.
  • Mean square error algorithms require more computation.

Purpose of the Study:

  • Propose a novel stochastic gradient algorithm based on minimum Shannon entropy.
  • Enhance the convergence speed of traditional stochastic gradient algorithms.
  • Improve the accuracy of parameter estimation in system identification.

Main Methods:

  • Implemented a multi-error method by stacking errors into a vector.
  • Integrated a forgetting factor to adjust the step size.
  • Applied the algorithm to estimate parameters of an ARX model with random impulse noise.

Main Results:

  • The proposed algorithm demonstrates faster convergence than traditional gradient methods.
  • Achieved more accurate parameter estimates compared to the traditional gradient algorithm.
  • Validated through numerical simulations and a case study.

Conclusions:

  • The novel minimum Shannon entropy-based stochastic gradient algorithm is effective.
  • The integration of a multi-error method and forgetting factor accelerates convergence.
  • The algorithm provides superior accuracy for ARX model parameter estimation in noisy environments.