# Hadamard Extensions and the Identification of Mixtures of Product Distributions

arXiv: https://arxiv.org/abs/2101.11688 · HTML: https://mlsanity.com/paper/2101.11688/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 18 references that are in the map.
- First posted on arXiv 27 Jan 2021.

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

- [Beyond the Low-Degree Algorithm: Mixtures of Subcubes and Their Applications](https://mlsanity.com/paper/1803.06521/) (2018)
- [Source Identification for Mixtures of Product Distributions](https://mlsanity.com/paper/2012.14540/) (2020)
- [Learning Arbitrary Statistical Mixtures of Discrete Distributions](https://mlsanity.com/paper/1504.02526/) (2015)

## Built on by (most cited first, 4 of 4)

- [Learning latent causal graphs via mixture oracles](https://mlsanity.com/paper/2106.15563/) (2021)
- [Causal Inference Despite Limited Global Confounding via Mixture Models](https://mlsanity.com/paper/2112.11602/) (2021)
- [Identification of Mixtures of Discrete Product Distributions in Near-Optimal Sample and Time Complexity](https://mlsanity.com/paper/2309.13993/) (2023)
- [Tight Bounds on the Hardness of Learning Simple Nonparametric Mixtures](https://mlsanity.com/paper/2203.15150/) (2022)

## Abstract (arXiv)

The Hadamard Extension of a matrix is the matrix consisting of all Hadamard products of subsets of its rows. This construction arises in the context of identifying a mixture of product distributions on binary random variables: full column rank of such extensions is a necessary ingredient of identification algorithms. We provide several results concerning when a Hadamard Extension has full column rank.