Summary of Estimation Of Multiple Mean Vectors in High Dimension, by Gilles Blanchard (lmo et al.
Estimation of multiple mean vectors in high dimension
by Gilles Blanchard, Jean-Baptiste Fermanian, Hannah Marienwald
First submitted to arxiv on: 22 Mar 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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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 The paper proposes new methods for estimating multi-dimensional means of probability distributions based on independent samples. The approach involves combining empirical means using convex combinations, with weights determined by a testing procedure or minimization of an upper confidence bound on the quadratic risk. Theoretical analysis shows that these methods asymptotically approach an oracle improvement in quadratic risk as the effective dimension of the data increases. Experimental results demonstrate the effectiveness of the proposed methods in estimating multiple kernel mean embeddings using simulated and real-world datasets. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper is about finding a way to estimate many different types of probability distributions based on some given samples. The authors combine the sample means together using special weights, which they find using two different methods. They show that these methods work better than just taking the average of the sample means, especially when there are a lot of dimensions in the data. They test their methods using fake and real-world data sets. |
Keywords
* Artificial intelligence * Probability
