Summary of Hound: High-order Universal Numerical Differentiator For a Parameter-free Polynomial Online Approximation, by Igor Katrichek
HOUND: High-Order Universal Numerical Differentiator for a Parameter-free Polynomial Online Approximation
by Igor Katrichek
First submitted to arxiv on: 18 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Methodology (stat.ME)
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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 proposed scalar numerical differentiator is represented by a system of nonlinear differential equations of arbitrary high order. The explicit solution for this system is derived, demonstrating that with suitable choice of differentiator order, error converges to zero for polynomial signals with additive white noise. In more general cases, the error remains bounded if the highest estimated derivative is also bounded. Notably, this numerical differentiation method does not require tuning parameters based on signal characteristics. A discretization method for the equations implements a cumulative smoothing algorithm for time series, operating online without data accumulation and solving interpolation and extrapolation problems without coefficient fitting. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper introduces a new way to differentiate signals using mathematical equations. It works by solving these equations to get an answer that gets closer to the correct result as you go higher in order. This method is good for finding the derivative of a signal, especially when there’s noise added. What’s cool about this approach is it doesn’t need any special settings based on the type of signal being differentiated. The team also came up with a way to turn these equations into code that can be used to analyze data in real-time. |
Keywords
» Artificial intelligence » Time series
