Summary of On Adaptivity and Minimax Optimality Of Two-sided Nearest Neighbors, by Tathagata Sadhukhan et al.
On adaptivity and minimax optimality of two-sided nearest neighbors
by Tathagata Sadhukhan, Manit Paul, Raaz Dwivedi
First submitted to arxiv on: 20 Nov 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Statistics Theory (math.ST); Methodology (stat.ME)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| 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 research paper presents an analysis of nearest neighbor (NN) algorithms in recommender systems and sequential decision-making systems when dealing with non-smooth, non-linear functions and vast amounts of missingness. The authors focus on matrix completion settings where the underlying data follows a latent non-linear factor model. They establish three key properties for a suitable two-sided NN: it adapts to the smoothness of the non-linearity, its error rate matches an oracle’s rate with knowledge of both row and column latent factors, and its mean squared error (MSE) is non-trivial even when multiple matrix entries are missing deterministically. The findings are supported by numerical simulations and a case study using data from the HeartSteps mobile health study. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper studies how to use nearest neighbor algorithms when some of the data is missing, which happens often in recommender systems and decision-making systems. The researchers look at a special kind of non-linear relationship between the variables and show that their algorithm can work well even with a lot of missing data. They test their ideas on real-world data from a mobile health study called HeartSteps. |
Keywords
» Artificial intelligence » Mse » Nearest neighbor
