Scalable sparse covariance estimation via self-concordance

We consider the class of convex minimization problems, composed of a self-concordant function, such as the $\log\det$ metric, a convex data fidelity term $h(\cdot)$ and, a regularizing -- possibly non-smooth -- function $g(\cdot)$. This type of problems have recently attracted a great deal of interest, mainly due to their omnipresence in top-notch applications. Under this \emph{locally} Lipschitz continuous gradient setting, we analyze the convergence behavior of proximal Newton schemes with the added twist of a probable presence of inexact evaluations. We prove attractive convergence rate guarantees and enhance state-of-the-art optimization schemes to accommodate such developments. Experimental results on sparse covariance estimation show the merits of our algorithm, both in terms of recovery efficiency and complexity.Comment: 7 pages, 1 figure, Accepted at AAAI-1

A Learning-Based Framework for Quantized Compressed Sensing

Sparse recovery from undersampled random quan- tization measurements is a recent active research topic. Previous work asserts that stable recovery can be guaranteed via the basis pursuit dequantizer (BPDQ) if the measurements number is large enough, considering random sampling patterns. In this paper, we study a learning-based method for optimizing the sampling pattern, within the framework of sparse recovery via BPDQ from their uniformly quantized measurements. Given a set of representative training signals, the method finds the sampling pattern that performs the best on average over these signals. We compare our approach with the random sampling and other state-of-the-art sampling methods, which shows that it achieves superior reconstruction performance. We demonstrate that proper accounting for sampling and careful sampler de- sign has a significant impact on the performance of quantized compressive sensing methods

Real-time DCT Learning-based Reconstruction of Neural Signals

Wearable and implantable body sensor network systems are one of the key technologies for continuous monitoring of patient’s vital health status such as temperature and blood pressure, and brain activity. Such devices are critical for early detection of emergency conditions of people at risk and offer a wide range of medical facilities and services. Despite continuous advances in the field of wearable and implantable medical devices, it still faces major challenges such as energy-efficient and low-latency reconstruction of signals. This work presents a power-efficient real-time system for recovering neural signals. Such systems are of high interest for implantable medical devices, where reconstruction of neural signals needs to be done in realtime with low energy consumption. We combine a deep network and DCT-learning based compressive sensing framework to propose a novel and efficient compression-decompression system for neural signals.We compare our approach with state-of-the-art compressive sensing methods and show that it achieves superior reconstruction performance with significantly less computing time

A Non-Euclidean Gradient Descent Framework for Non-Convex Matrix Factorization

We study convex optimization problems that feature low-rank matrix solutions. In such scenarios, non-convex methods offer significant advantages over convex methods due to their lower space complexity as well as faster convergence speed. Moreover, many of these methods feature rigorous approximation guarantees. Non-convex algorithms are simple to analyze and implement as they perform Euclidean gradient descent on matrix factors. In contrast, this paper derives non-Euclidean optimization frame- work in the non-convex setting that takes nonlinear gradient steps on the factors. We prove convergence rates to the global minimum under appropriate assumptions. We provide numerical evidence with Fourier Ptychography and FastText applications using real data that shows our approach can significantly enhance solution qualit

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