# A maximum-likelihood and moment-matching density estimator for crowd-sourcing label prediction

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## Abstract

We deal with the parameter estimation problem for probability density models with latent variables. For this problem traditionally the expectation maximization (EM) algorithm has been broadly used. However, it suffers from bad local maxima, and the quality of the estimator is sensitive to the initial model choice. Recently, an alternative density estimator has been proposed that is based on matching the moments between sample averaged and model averaged. This moment matching estimator is typically used as the initial iterate for the EM algorithm for further refinement. However, there is actually no guarantee that the EM-refined estimator still yields the moments close enough to the sample-averaged one. Motivated by this issue, in this paper we propose a novel estimator that takes merits of both worlds: we do likelihood maximization, but the moment discrepancy score is used as a regularizer that prevents the model-averaged moments from straying away from those estimated from data. On some crowd-sourcing label prediction problems, we demonstrate that the proposed approach yields more accurate density estimates than the existing estimators.

### Keywords

Density estimation Expectation maximization Moment matching Crowd-sourcing label prediction problem## Notes

### Acknowledgements

This work is supported by National Research Foundation of Korea (NRF-2016R1A1A1A05921948)

### Compliance with Ethical Standards

### Conflict of interests

The authors have no conflict of interest.

### Consent for Publication

This research does not involve human participants nor animals. Consent to submit this manuscript has been received tacitly from the authors’ institution, Seoul National University of Science & Technology.

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