We consider the problem of estimating a regularization parameter, or a shrinkage coefficient $α\in (0,1)$ for Regularized Tyler's M-estimator (RTME). In particular, we propose to estimate an optimal shrinkage coefficient by setting $α$ as the solution to a suitably chosen objective function; namely the leave-one-out cross-validated (LOOCV) log-likelihood loss. Since LOOCV is computationally prohibitive even for moderate sample size $n$, we propose a computationally efficient approximation for the LOOCV log-likelihood loss that eliminates the need for invoking the RTME procedure $n$ times for each sample left out during the LOOCV procedure. This approximation yields an $O(n)$ reduction in the running time complexity for the LOOCV procedure, which results in a significant speedup for computing the LOOCV estimate. We demonstrate the efficiency and accuracy of the proposed approach on synthetic high-dimensional data sampled from heavy-tailed elliptical distributions, as well as on real high-dimensional datasets for object recognition, face recognition, and handwritten digit's recognition. Our experiments show that the proposed approach is efficient and consistently more accurate than other methods in the literature for shrinkage coefficient estimation.

Parameterized mathematical models play a central role in understanding and design of complex information systems. However, they often cannot take into account the intricate interactions innate to such systems. On the contrary, purely data-driven approaches do not need explicit mathematical models for data generation and have a wider applicability at the cost of interpretability. In this paper, we consider the design of a one-bit compressive autoencoder, and propose a novel hybrid model-based and data-driven methodology that allows us to not only design the sensing matrix for one-bit data acquisition, but also allows for learning the latent-parameters of an iterative optimization algorithm specifically designed for the problem of one-bit sparse signal recovery. Our results demonstrate a significant improvement compared to state-of-the-art model-based algorithms.

Parameterized mathematical models play a central role in understanding and design of complex information systems. However, they often cannot take into account the intricate interactions innate to such systems. On the contrary, purely data-driven approaches do not need explicit mathematical models for data generation and have a wider applicability at the cost of interpretability. In this paper, we consider the design of a one-bit compressive variational autoencoder, and propose a novel hybrid model-based and data-driven methodology that allows us not only to design the sensing matrix and the quantization thresholds for one-bit data acquisition, but also allows for learning the latent-parameters of iterative optimization algorithms specifically designed for the problem of one-bit sparse signal recovery. In addition, the proposed method has the ability to adaptively learn the proper quantization thresholds, paving the way for amplitude recovery in one-bit compressive sensing. Our results demonstrate a significant improvement compared to state-of-the-art model-based algorithms.