Foundations of Model Selection: Difference between revisions
Created page with "Title: Foundations of Model Selection Research Question: How can we determine the best model for explaining a given set of data, considering the complexity of the model and the amount of data? Methodology: The researchers proposed a method called "model selection," which involves minimizing a two-part code consisting of a model subject to complexity constraints, and a data-to-model code. This method is based on Kolmogorov complexity, which measures the minimal length o..." |
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Title: Foundations of Model Selection | Title: Foundations of Model Selection | ||
Research Question: How can we determine the best model for explaining a given set of data, considering | Research Question: How can we determine the best model for explaining a given set of data, especially when considering model complexity? | ||
Methodology: The | Methodology: The authors propose a new approach to model selection called Kolmogorov's structure function. This function measures the relationship between the individual data and its explanation (model), and can be expressed as a two-part code consisting of a model description and a data-to-model code. The authors also consider a one-part code consisting of just the data-to-model code. | ||
Results: The | Results: The main result of this study is that minimizing the two-part code or the one-part code always selects a model that is a "best explanation" of the data within given model-complexity constraints. This means that the best fit cannot be computationally monotonically approximated, but the two-part code or the one-part code can be monotonically minimized, allowing for an approximation of the best-fitting model. | ||
Implications: This research | Implications: This research has significant implications for the field of statistics and learning theory. It suggests that the traditional probabilistic approach to measuring goodness of selection may not always be relevant, especially in cases where the part of the support of the probability density function that will ever be observed has about zero measure. The authors' approach provides a more practical solution to selecting the best model for explaining a given set of data, especially considering model complexity. | ||
Link to Article: https://arxiv.org/abs/ | Link to Article: https://arxiv.org/abs/0204037v2 | ||
Authors: | Authors: | ||
arXiv ID: | arXiv ID: 0204037v2 | ||
[[Category:Computer Science]] | [[Category:Computer Science]] | ||
[[Category:Model]] | [[Category:Model]] | ||
[[Category:Code]] | |||
[[Category:Part]] | |||
[[Category:Data]] | [[Category:Data]] | ||
[[Category: | [[Category:Best]] | ||
Revision as of 05:02, 24 December 2023
Title: Foundations of Model Selection
Research Question: How can we determine the best model for explaining a given set of data, especially when considering model complexity?
Methodology: The authors propose a new approach to model selection called Kolmogorov's structure function. This function measures the relationship between the individual data and its explanation (model), and can be expressed as a two-part code consisting of a model description and a data-to-model code. The authors also consider a one-part code consisting of just the data-to-model code.
Results: The main result of this study is that minimizing the two-part code or the one-part code always selects a model that is a "best explanation" of the data within given model-complexity constraints. This means that the best fit cannot be computationally monotonically approximated, but the two-part code or the one-part code can be monotonically minimized, allowing for an approximation of the best-fitting model.
Implications: This research has significant implications for the field of statistics and learning theory. It suggests that the traditional probabilistic approach to measuring goodness of selection may not always be relevant, especially in cases where the part of the support of the probability density function that will ever be observed has about zero measure. The authors' approach provides a more practical solution to selecting the best model for explaining a given set of data, especially considering model complexity.
Link to Article: https://arxiv.org/abs/0204037v2 Authors: arXiv ID: 0204037v2