# Multiscale Blind Source Separation

arXiv: https://arxiv.org/abs/1608.07173 · HTML: https://mlsanity.com/paper/1608.07173/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Aug 2016.

## Built on by (most cited first, 3 of 3)

- [Causal Discovery in Linear Latent Variable Models Subject to Measurement Error](https://mlsanity.com/paper/2211.03984/) (2022)
- [Causal Discovery in Linear Structural Causal Models with Deterministic Relations](https://mlsanity.com/paper/2111.00341/) (2021)
- [Causal Discovery in Linear Models with Unobserved Variables and Measurement Error](https://mlsanity.com/paper/2407.19426/) (2024)

## Abstract (arXiv)

We provide a new methodology for statistical recovery of single linear mixtures of piecewise constant signals (sources) with unknown mixing weights and change points in a multiscale fashion. We show exact recovery within an ε-neighborhood of the mixture when the sources take only values in a known finite alphabet. Based on this we provide the SLAM (Separates Linear Alphabet Mixtures) estimators for the mixing weights and sources. For Gaussian error, we obtain uniform confidence sets and optimal rates (up to log-factors) for all quantities. SLAM is efficiently computed as a nonconvex optimization problem by a dynamic program tailored to the finite alphabet assumption. Its performance is investigated in a simulation study. Finally, it is applied to assign copy-number aberrations from genetic sequencing data to different clones and to estimate their proportions.