Cramer Rao-Type Bounds for Sparse Bayesian Learning

In this paper, we derive Hybrid, Bayesian and Marginalized Cram\'{e}r-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their prior distribution parameters. We assume the unknown vector to be drawn from a compressible Student-t prior distribution. We derive CRBs that encompass the deterministic or random nature of the unknown parameters of the prior distribution and the regression noise variance. We extend the MCRB to the case where the compressible vector is distributed according to a general compressible prior distribution, of which the generalized Pareto distribution is a special case. We use the derived bounds to uncover the relationship between the compressibility and Mean Square Error (MSE) in the estimates. Further, we illustrate the tightness and utility of the bounds through simulations, by comparing them with the MSE performance of two popular SBL-based estimators. It is found that the MCRB is generally the tightest among the bounds derived and that the MSE performance of the Expectation-Maximization (EM) algorithm coincides with the MCRB for the compressible vector. Through simulations, we demonstrate the dependence of the MSE performance of SBL based estimators on the compressibility of the vector for several values of the number of observations and at different signal powers.Comment: Accepted for publication in the IEEE Transactions on Signal Processing, 11 pages, 10 figure

Variational Student: Learning Compact and Sparser Networks in Knowledge Distillation Framework

The holy grail in deep neural network research is porting the memory- and computation-intensive network models on embedded platforms with a minimal compromise in model accuracy. To this end, we propose a novel approach, termed as Variational Student, where we reap the benefits of compressibility of the knowledge distillation (KD) framework, and sparsity inducing abilities of variational inference (VI) techniques. Essentially, we build a sparse student network, whose sparsity is induced by the variational parameters found via optimizing a loss function based on VI, leveraging the knowledge learnt by an accurate but complex pre-trained teacher network. Further, for sparsity enhancement, we also employ a Block Sparse Regularizer on a concatenated tensor of teacher and student network weights. We demonstrate that the marriage of KD and the VI techniques inherits compression properties from the KD framework, and enhances levels of sparsity from the VI approach, with minimal compromise in the model accuracy. We benchmark our results on LeNet MLP and VGGNet (CNN) and illustrate a memory footprint reduction of 64x and 213x on these MLP and CNN variants, respectively, without a need to retrain the teacher network. Furthermore, in the low data regime, we observed that our method outperforms state-of-the-art Bayesian techniques in terms of accuracy

Over-The-Air Clustered Wireless Federated Learning

Privacy, security, and bandwidth constraints have led to federated learning (FL) in wireless systems, where training a machine learning (ML) model is accomplished collaboratively without sharing raw data. Often, such collaborative FL strategies necessitate model aggregation at a server. On the other hand, decentralized FL necessitates that participating clients reach a consensus ML model by exchanging parameter updates. In this work, we propose the over-the-air clustered wireless FL (CWFL) strategy, which eliminates the need for a strong central server and yet achieves an accuracy similar to the server-based strategy while using fewer channel uses as compared to decentralized FL. We theoretically show that the convergence rate of CWFL per cluster is O(1/T) while mitigating the impact of noise. Using the MNIST and CIFAR datasets, we demonstrate the accuracy performance of CWFL for the different number of clusters across communication rounds.Comment: Under review at ICASSP 202

Seeing is Believing: A Federated Learning Based Prototype to Detect Wireless Injection Attacks

Reactive injection attacks are a class of security threats in wireless networks wherein adversaries opportunistically inject spoofing packets in the frequency band of a client thereby forcing the base-station to deploy impersonation-detection methods. Towards circumventing such threats, we implement secret-key based physical-layer signalling methods at the clients which allow the base-stations to deploy machine learning (ML) models on their in-phase and quadrature samples at the baseband for attack detection. Using Adalm Pluto based software defined radios to implement the secret-key based signalling methods, we show that robust ML models can be designed at the base-stations. However, we also point out that, in practice, insufficient availability of training datasets at the base-stations can make these methods ineffective. Thus, we use a federated learning framework in the backhaul network, wherein a group of base-stations that need to protect their clients against reactive injection threats collaborate to refine their ML models by ensuring privacy on their datasets. Using a network of XBee devices to implement the backhaul network, experimental results on our federated learning setup shows significant enhancements in the detection accuracy, thus presenting wireless security as an excellent use-case for federated learning in 6G networks and beyond.Comment: 6 pages with 8 figure