Abstract-Quantization is an important but often ignored consideration in discussions about compressed sensing. This paper studies the design of quantizers for random measurements of sparse signals that are optimal with respect to mean-squared error of the lasso reconstruction. We utilize recent results in high-resolution functional scalar quantization and homotopy continuation to approximate the optimal quantizer. Experimental results compare this quantizer to other practical designs and show a noticeable improvement in the operational distortion-rate performance.

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Matrix factorization from a small number of observed entries has recently garnered much attention as the key ingredient of successful recommendation systems. One unresolved problem in this area is how to adapt current methods to handle changing user preferences over time. Recent proposals to address this issue are heuristic in nature and do not fully exploit the time-dependent structure of the problem. As a principled and general temporal formulation, we propose a dynamical state space model of matrix factorization. Our proposal builds upon probabilistic matrix factorization, a Bayesian model with Gaussian priors. We utilize results in state tracking, i.e. the Kalman filter, to provide accurate recommendations in the presence of both process and measurement noise. We show how system parameters can be learned via expectation-maximization and provide comparisons to current published techniques.

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