Summary of Breaking the Curse Of Dimensionality in Structured Density Estimation, by Robert A. Vandermeulen et al.
Breaking the curse of dimensionality in structured density estimation
by Robert A. Vandermeulen, Wai Ming Tai, Bryon Aragam
First submitted to arxiv on: 10 Oct 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG); Statistics Theory (math.ST)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper addresses the problem of estimating a structured multivariate density under Markov conditions implied by an undirected graph. The authors show that without these assumptions, the curse of dimensionality is present, making it challenging to solve this problem. However, they introduce a new graphical quantity called “graph resilience” and demonstrate how it controls the sample complexity. This allows them to circumvent the curse of dimensionality in density estimation, with notable improvements in sequential, hierarchical, and spatial data. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about finding patterns in complex data sets that follow rules. Imagine you have a big family tree and you want to know what’s common among all the people on it. The problem is that as the tree gets bigger, it becomes harder to find these patterns. But what if there was a way to make it easier? That’s what this paper is about. It shows how to avoid getting stuck in a “curse of dimensionality” by using special rules called Markov conditions. This helps us understand complex data better and can be useful for things like predicting weather or understanding how people move around a city. |
Keywords
» Artificial intelligence » Density estimation
