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Expected Value01:15

Expected Value

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The expected value is known as the "long-term" average or mean. This means that over the long term of experimenting over and over, you would expect this average. The expected average is represented by the symbol μ. It is calculated as follows:
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The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
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E. C. Tolman emphasized the purposiveness of behavior — the idea that much of our behavior is goal-directed. For instance, employees who aim for a promotion work diligently to meet their targets. Tolman argued that when classical conditioning and operant conditioning occur, the organism acquires certain expectations. In classical conditioning, a child might fear a dog because they expect it to bite. In operant conditioning, a person might consistently work overtime because they expect a...
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Expectation maximisation pseudo labels.

Moucheng Xu1, Yukun Zhou2, Chen Jin3

  • 1UCL Centre for Medical Image Computing (CMIC), University College London, 90 High Holborn, London, WC1V 6LJ, UK; UCL Department of Medical Physics and Biomedical Engineering, University College London, Gower Street, London, WC1E 6BT, UK; Satsuma Lab, University College Londo, 90 High Holborn, WC1V 6LJ, UK.

Medical Image Analysis
|March 1, 2024
PubMed
Summary
This summary is machine-generated.

This study links pseudo-labelling to Expectation Maximisation, introducing Bayesian Pseudo Labels for improved semi-supervised medical image segmentation. This method enhances model robustness and accuracy in segmenting various anatomical structures.

Keywords:
Bayesian deep learningExpectation–maximisationGenerative modelsPseudo labelsRobustnessSegmentationSemi-supervised learning

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Area of Science:

  • Machine Learning
  • Medical Image Analysis
  • Computer Vision

Background:

  • Pseudo-labelling is a self-training technique using model predictions on unlabeled data.
  • Its empirical success is evident but lacks a strong theoretical foundation.
  • Existing methods may not fully leverage unlabeled data for robust model training.

Purpose of the Study:

  • To establish a theoretical link between pseudo-labelling and the Expectation Maximisation (EM) algorithm.
  • To introduce a generalized framework for pseudo-labelling, termed Bayesian Pseudo Labels (BPL).
  • To demonstrate the effectiveness of BPL in semi-supervised medical image segmentation tasks.

Main Methods:

  • Connecting pseudo-labelling to the EM algorithm to understand its underlying principles.
  • Generalizing pseudo-labelling using Bayes' theorem to derive Bayesian Pseudo Labels.
  • Developing a variational approach with adaptive thresholding for generating high-quality BPLs.
  • Applying pseudo-labelling and BPL to semi-supervised segmentation of medical images (CT, MRI).

Main Results:

  • Empirical successes of pseudo-labelling are explained through its connection to EM.
  • Bayesian Pseudo Labels offer a theoretically grounded generalization.
  • The proposed variational approach effectively generates high-quality pseudo-labels.
  • Significant improvements shown in semi-supervised segmentation of lung vessels, brain tumors, and prostate MRI.
  • Demonstrated enhancement of learned representation robustness using pseudo-labels.

Conclusions:

  • Pseudo-labelling is an empirical estimation of a more comprehensive EM-based formulation.
  • Bayesian Pseudo Labels provide a robust and theoretically sound extension.
  • The method significantly advances semi-supervised medical image segmentation accuracy and robustness.
  • The framework is applicable to diverse medical imaging modalities and segmentation tasks.