# Beyond Black Box Densities: Parameter Learning for the Deviated Components

arXiv: https://arxiv.org/abs/2202.02651 · HTML: https://mlsanity.com/paper/2202.02651/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 48 references that are in the map.
- First posted on arXiv 5 Feb 2022.

## Builds on (most cited first, 3 of 3)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Singularity structures and impacts on parameter estimation in finite mixtures of distributions](https://mlsanity.com/paper/1609.02655/) (2016)
- [Decontamination of Mutual Contamination Models](https://mlsanity.com/paper/1710.01167/) (2017)

## Built on by (most cited first, 1 of 1)

- [Strong identifiability and parameter learning in regression with heterogeneous response](https://mlsanity.com/paper/2212.04091/) (2022)

## Abstract (arXiv)

As we collect additional samples from a data population for which a known density function estimate may have been previously obtained by a black box method, the increased complexity of the data set may result in the true density being deviated from the known estimate by a mixture distribution. To model this phenomenon, we consider the deviating mixture model (1-λ*)h0 + λ* (sumi = 1k pi* f(x|θi*)), where h0 is a known density function, while the deviated proportion λ* and latent mixing measure G* = sumi = 1k pi* δ_θi* associated with the mixture distribution are unknown. Via a novel notion of distinguishability between the known density h0 and the deviated mixture distribution, we establish rates of convergence for the maximum likelihood estimates of λ* and G* under Wasserstein metric. Simulation studies are carried out to illustrate the theory.