Summary of Conditional Regression For the Nonlinear Single-variable Model, by Yantao Wu et al.
Conditional regression for the Nonlinear Single-Variable Model
by Yantao Wu, Mauro Maggioni
First submitted to arxiv on: 14 Nov 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 This paper explores compositional models that regress a function F on Rd without suffering from dimensionality. By assuming a geometric structure on the data’s support or imposing smoothness on F, several existing statistical models circumvent the curse of dimensionality. Compositional models assume F = f ∘ g, where g maps to Rr with r << d, and have been studied for linear g. However, when g is nonlinear, understanding which g’s allow estimating F without dimensionality issues is lacking. This paper proposes a new model, F(X) = f(ΠγX), where Πγ is the closest-point projection onto a regular curve γ. The input data X is not low-dimensional and is conditioned on Πγ(X) being well-defined. A nonparametric estimator based on conditional regression is proposed, which achieves the optimal min-max rate for non-parametric regression under suitable assumptions. The computational complexity is O(d^2nlogn), with all constants being at most low-order polynomials in d. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at a new way to understand how data relates to each other, without getting lost in the huge amount of information. By assuming certain patterns or smoothness in the data, we can use existing statistical models to find relationships. The authors explore a new type of model that maps data onto a curve and show that it’s possible to learn about this relationship quickly and accurately. |
Keywords
* Artificial intelligence * Regression
