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Priors with a NUV representation (normal with unknown variance) have mostlybeen used for sparsity. In this paper, a novel NUV prior is proposed thateffectively binarizes. While such a prior may have many uses, in this paper, weexplore its use for discrete-level control (with M $\geq$ 2 levels) including,in particular, a practical scheme for digital-to-analog conversion. Theresulting computations, for each planning period, amount to iteratingforward-backward Gaussian message passing recursions (similar to Kalmansmoothing), with a complexity (per iteration) that is linear in the planninghorizon. In consequence, the proposed method is not limited to a short planninghorizon and can therefore outperform "optimal" methods. A preference for sparselevel switches can easily be incorporated.

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