Hagit Messer

Hai Victor Habi, Hagit Messer, Yoram Bresler

The Cramér-Rao bound (CRB), a well-known lower bound on the performance of any unbiased parameter estimator, has been used to study a wide variety of problems. However, to obtain the CRB, requires an analytical expression for the likelihood of the measurements given the parameters, or equivalently a precise and explicit statistical model for the data. In many applications, such a model is not available. Instead, this work introduces a novel approach to approximate the CRB using data-driven methods, which removes the requirement for an analytical statistical model. This approach is based on the recent success of deep generative models in modeling complex, high-dimensional distributions. Using a learned normalizing flow model, we model the distribution of the measurements and obtain an approximation of the CRB, which we call Generative Cramér-Rao Bound (GCRB). Numerical experiments on simple problems validate this approach, and experiments on two image processing tasks of image denoising and edge detection with a learned camera noise model demonstrate its power and benefits.

Dror Jacoby, Yanzhi Li, Shuyue Yu et al.

Millimeter-wave (mmWave) links are increasingly utilized in wireless x-haul transport to meet growing service demands. However, the inherent susceptibility of mmWave links to weather-related attenuation creates uncertainty about future network capacity which can significantly affect Quality of Service (QoS). This creates a critical challenge: how to make admission control decisions for slices with QoS requirements, balancing acceptance rewards against the risk of future QoS-violation penalties due to capacity uncertainty? To address this, we develop a proactive slice admission control framework that tightly integrates: (i) a predictor that leverages historical link measurements to forecast short-term attenuation and quantify uncertainty; and (ii) an admission control algorithm that incorporates both the predictions and uncertainties to maximize rewards and minimize QoS-violation penalties. We compare our framework against baseline, state-of-the-art, and idealized oracle algorithms using real-world mmWave x-haul data and residential traffic traces. Simulations suggest that our framework can achieve revenues that are 250% larger than baseline algorithms and 75% larger than state-of-the-art algorithms.

Hai Victor Habi, Hagit Messer, Yoram Bresler

The Bayesian Cramér-Rao bound (BCRB) is a crucial tool in signal processing for assessing the fundamental limitations of any estimation problem as well as benchmarking within a Bayesian frameworks. However, the BCRB cannot be computed without full knowledge of the prior and the measurement distributions. In this work, we propose a fully learned Bayesian Cramér-Rao bound (LBCRB) that learns both the prior and the measurement distributions. Specifically, we suggest two approaches to obtain the LBCRB: the Posterior Approach and the Measurement-Prior Approach. The Posterior Approach provides a simple method to obtain the LBCRB, whereas the Measurement-Prior Approach enables us to incorporate domain knowledge to improve the sample complexity and {interpretability}. To achieve this, we introduce a Physics-encoded score neural network which enables us to easily incorporate such domain knowledge into a neural network. We {study the learning} errors of the two suggested approaches theoretically, and validate them numerically. We demonstrate the two approaches on several signal processing examples, including a linear measurement problem with unknown mixing and Gaussian noise covariance matrices, frequency estimation, and quantized measurement. In addition, we test our approach on a nonlinear signal processing problem of frequency estimation with real-world underwater ambient noise.