The performance of (OR-PCA) technique heavily depends on the optimum tuning of the explicit regularizers. This tuning is dataset-sensitive and often impractical to optimize in real-world scenarios. We aim to remove the dependency on these tuning parameters by using implicit regularization. To this end, we develop an approach that integrates implicit regularization properties of various gradient descent methods to estimate sparse outliers and low-dimensional representations in a streaming setting—a non-trivial extension of existing techniques. A key novelty lies in the design of a new parameterization for matrix estimation in OR-PCA. Our method incorporates three different versions of modified gradient descent that separate but naturally encourage sparsity and low-rank structures in the data. Experimental results on synthetic and real-world video datasets demonstrate that the proposed method, namely, OR-PCA (TF-ORPCA), outperforms existing OR-PCA methods. TF-ORPCA makes it more scalable for large datasets.

Conventionally, in a differentially private additive noise mechanism, independent and identically distributed (i.i.d.) noise samples are added to each coordinate of the response. In this work, we formally present the addition of noise that is independent but not identically distributed (i.n.i.d.) across the coordinates to achieve tighter privacy-accuracy trade-off by exploiting coordinate-wise disparity in privacy leakage. In particular, we study the i.n.i.d. Gaussian and Laplace mechanisms and obtain the conditions under which these mechanisms guarantee privacy. The optimal choice of parameters that ensure these conditions are derived considering (weighted) mean squared and$\ell _{ p}^{ p}$-errors as measures of accuracy. Theoretical analyses and numerical simulations demonstrate that the i.n.i.d. mechanisms achieve higher utility for the given privacy requirements compared to their i.i.d. counterparts. One of the interesting observations is that the Laplace mechanism outperforms Gaussian even in high dimensions, as opposed to the popular belief, if the irregularity in coordinate-wise sensitivities is exploited. We also demonstrate how the i.n.i.d. noise can improve the performance in private (a) coordinate descent, (b) principal component analysis, and (c) deep learning with group clipping.

MassiveMIMO (mMIMO) enables users with different requirements to get connected to the same base station (BS) on the same set of resources. In the uplink of Multi-user massive MIMO (MU-mMIMO), while such heterogeneous users are served, decoupling facilitates the use of user-specific detection schemes. In this paper, we propose a low-complexity linear decoupling scheme called Sequential Decoupler (SD), which aids in the parallel detection of each user's data stream. The proposed algorithm shows significant complexity reduction. Simulations reveal that the complexity of the proposed scheme is only 0.15% of the conventional Singular Value Decomposition (SVD) based decoupling and is about 47% of the pseudo-inverse based decoupling schemes when 80 users with two antennas each are served by the BS. Also, the proposed scheme is scalable when new users are added to the system and requires fewer operations than computing the decoupler all over again. Further numerical analyses indicate that the proposed scheme achieves significant complexity reduction without any degradation in performance and is a promising low-complex alternative to the existing decoupling schemes.

The framework of differential privacy protects an individual’s privacy while publishing query responses on congregated data. In this work, a new noise addition mechanism for differential privacy is introduced where the noise added is sampled from a hybrid density that resembles Laplace in the centre and Gaussian in the tail. With a sharper centre and light, sub-Gaussian tail, this density has the best characteristics of both distributions. We theoretically analyze the proposed mechanism, and we derive the necessary and sufficient condition in one dimension and a sufficient condition in high dimensions for the mechanism to guarantee (ϵ, δ)-differential privacy. Numerical simulations corroborate the efficacy of the proposed mechanism compared to other existing mechanisms in achieving a better trade-off between privacy and accuracy.