On Measure Concentration of Random Maximum A-Posteriori Perturbations

The maximum a-posteriori (MAP) perturbation framework has emerged as a useful approach for inference and learning in high dimensional complex models. By maximizing a randomly perturbed potential function, MAP perturbations generate unbiased samples from the Gibbs distribution. Unfortunately, the computational cost of generating so many high-dimensional random variables can be prohibitive. More efficient algorithms use sequential sampling strategies based on the expected value of low dimensional MAP perturbations. This paper develops new measure concentration inequalities that bound the number of samples needed to estimate such expected values. Applying the general result to MAP perturbations can yield a more efficient algorithm to approximate sampling from the Gibbs distribution. The measure concentration result is of general interest and may be applicable to other areas involving expected estimations

Asymptotic Task-Based Quantization with Application to Massive MIMO

Quantizers take part in nearly every digital signal processing system which operates on physical signals. They are commonly designed to accurately represent the underlying signal, regardless of the specific task to be performed on the quantized data. In systems working with high-dimensional signals, such as massive multiple-input multiple-output (MIMO) systems, it is beneficial to utilize low-resolution quantizers, due to cost, power, and memory constraints. In this work we study quantization of high-dimensional inputs, aiming at improving performance under resolution constraints by accounting for the system task in the quantizers design. We focus on the task of recovering a desired signal statistically related to the high-dimensional input, and analyze two quantization approaches: We first consider vector quantization, which is typically computationally infeasible, and characterize the optimal performance achievable with this approach. Next, we focus on practical systems which utilize hardware-limited scalar uniform analog-to-digital converters (ADCs), and design a task-based quantizer under this model. The resulting system accounts for the task by linearly combining the observed signal into a lower dimension prior to quantization. We then apply our proposed technique to channel estimation in massive MIMO networks. Our results demonstrate that a system utilizing low-resolution scalar ADCs can approach the optimal channel estimation performance by properly accounting for the task in the system design