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In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...
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Image transformations and blurring.

IEEE transactions on pattern analysis and machine intelligence·2009
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Related Experiment Video

Updated: May 8, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Learning graphical model parameters with approximate marginal inference.

Justin Domke1

  • 1NICTA and Australia National University, Canberra, Australia. justin.domke@nicta.com.au

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 24, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces marginalization-based learning for graphical models, outperforming traditional likelihood methods. This approach improves accuracy, especially when models are approximate, addressing computational challenges in machine learning.

Related Experiment Videos

Last Updated: May 8, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

  • Machine Learning
  • Statistical Modeling
  • Computer Vision

Background:

  • Likelihood-based learning for graphical models is computationally complex and sensitive to incorrect model assumptions.
  • Existing methods struggle with both computational demands and robustness when the underlying model is not perfectly specified.

Purpose of the Study:

  • To investigate alternative learning methods for graphical models that bypass the limitations of likelihood-based approaches.
  • To develop and evaluate parameter fitting strategies that directly optimize the accuracy of predicted marginal distributions.

Main Methods:

  • Developed and applied parameter fitting techniques that directly maximize the accuracy of predicted marginals.
  • Incorporated approximations in both the model structure and the inference process during training.
  • Conducted experiments on imaging problems to compare performance against traditional methods.

Main Results:

  • Marginalization-based learning demonstrated superior performance compared to likelihood-based approximations in experimental settings.
  • The proposed methods showed particular advantage on challenging imaging problems where the fitted model was inherently approximate.
  • The approach effectively handles model and inference approximations during the learning phase.

Conclusions:

  • Marginalization-based learning offers a more robust and accurate alternative to likelihood-based methods for graphical models.
  • This approach is particularly beneficial for complex, real-world problems where model misspecification is common.
  • The findings suggest a promising direction for improving the practical application of graphical models in machine learning.