# A Binarizing NUV Prior and its Use for M-Level Control and Digital-to-Analog Conversion

arXiv: https://arxiv.org/abs/2105.02599 · HTML: https://mlsanity.com/paper/2105.02599/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 May 2021.

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

- [Half-Space and Box Constraints as NUV Priors: First Results](https://mlsanity.com/paper/2109.00036/) (2021)

## Abstract (arXiv)

Priors with a NUV representation (normal with unknown variance) have mostly been used for sparsity. In this paper, a novel NUV prior is proposed that effectively binarizes. While such a prior may have many uses, in this paper, we explore its use for discrete-level control (with M ≥ 2 levels) including, in particular, a practical scheme for digital-to-analog conversion. The resulting computations, for each planning period, amount to iterating forward-backward Gaussian message passing recursions (similar to Kalman smoothing), with a complexity (per iteration) that is linear in the planning horizon. In consequence, the proposed method is not limited to a short planning horizon and can therefore outperform "optimal" methods. A preference for sparse level switches can easily be incorporated.