Summary of Estimating a Function and Its Derivatives Under a Smoothness Condition, by Eunji Lim
Estimating a Function and Its Derivatives Under a Smoothness Condition
by Eunji Lim
First submitted to arxiv on: 16 May 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: 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 proposes novel methods for estimating an unknown function f* and its partial derivatives from noisy data sets. It considers a scenario where no assumptions are made about f, except that it is smooth in the sense that it has square integrable partial derivatives of order m. Two natural candidates for the estimator of f are discussed: the best fit to the data set satisfying a certain smoothness condition, and the one minimizing the degree of smoothness subject to an upper bound on the average of squared errors. The authors prove that these estimators can be computed as solutions to quadratic programs, establish their consistency and convergence rate, and illustrate their effectiveness numerically in a setting where stock option values and derivatives are estimated. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us better understand how to find unknown functions from noisy data. It’s like trying to figure out what shape something is by looking at blurry pictures. The researchers develop two new methods for doing this, which they show can be used to estimate things like the value of a stock option and its second derivative (which is important in finance). They prove that these methods work and get better as you have more data. |
