Summary of A Fourier Approach to the Parameter Estimation Problem For One-dimensional Gaussian Mixture Models, by Xinyu Liu et al.
A Fourier Approach to the Parameter Estimation Problem for One-dimensional Gaussian Mixture Models
by Xinyu Liu, Hai Zhang
First submitted to arxiv on: 19 Apr 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Signal Processing (eess.SP); 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 algorithm for estimating parameters in one-dimensional Gaussian mixture models (GMMs) leverages the Hankel structure inherent in Fourier data from independent and identically distributed (i.i.d) samples of the mixture. This novel approach resolves variance and component number simultaneously without requiring prior knowledge of the number of Gaussian components or good initial guesses. The consistency of the estimator is derived, and numerical experiments demonstrate superior performance in estimation accuracy and computational cost compared to classic algorithms like method of moments and maximum likelihood method. Additionally, the paper reveals a fundamental limit to estimating model order in GMMs if the number of i.i.d samples is finite, with a phase transition phenomenon depending on minimum separation distance between component means. Our algorithm achieves better scores in likelihood, AIC, and BIC compared to EM algorithm. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper proposes a new way to estimate parameters in Gaussian mixture models using special properties of Fourier data. This makes it easier to get the right answers without knowing beforehand how many different types of data there are or what their starting points should be. The method is tested on examples and shown to work better than other approaches. The paper also finds that there’s a limit to how well we can do this estimation if we only have a certain amount of data, but our algorithm does better than others in estimating model order. |
Keywords
* Artificial intelligence * Likelihood
