Robust 1-Bit Compressed Sensing via Hinge Loss Minimization

This work theoretically studies the problem of estimating a structured high-dimensional signal $x_0 \in \mathbb{R}^n$ from noisy $1$-bit Gaussian measurements. Our recovery approach is based on a simple convex program which uses the hinge loss function as data fidelity term. While such a risk minimization strategy is very natural to learn binary output models, such as in classification, its capacity to estimate a specific signal vector is largely unexplored. A major difficulty is that the hinge loss is just piecewise linear, so that its "curvature energy" is concentrated in a single point. This is substantially different from other popular loss functions considered in signal estimation, e.g., the square or logistic loss, which are at least locally strongly convex. It is therefore somewhat unexpected that we can still prove very similar types of recovery guarantees for the hinge loss estimator, even in the presence of strong noise. More specifically, our non-asymptotic error bounds show that stable and robust reconstruction of $x_0$ can be achieved with the optimal oversampling rate $O(m^{-1/2})$ in terms of the number of measurements $m$. Moreover, we permit a wide class of structural assumptions on the ground truth signal, in the sense that $x_0$ can belong to an arbitrary bounded convex set $K \subset \mathbb{R}^n$. The proofs of our main results rely on some recent advances in statistical learning theory due to Mendelson. In particular, we invoke an adapted version of Mendelson's small ball method that allows us to establish a quadratic lower bound on the error of the first order Taylor approximation of the empirical hinge loss function

Theory of Curie temperature enhancement in electron-doped EuO

We present a comparative, theoretical study of the doping dependence of the critical temperature $T_C$ of the ferromagnetic insulator-metal transition in Gd-doped and O-deficient EuO, respectively. The strong $T_C$ enhancement in Eu$_{1-x}$Gd$_x$O is due to Kondo-like spin fluctuations on the Gd sites, which are absent in EuO$_{1-x}$. Moreover, we find that the $T_C$ saturation in Eu$_{1-x}$Gd$_x$O for large $x$ is due to a reduced activation of dopant electrons into the conduction band, in agreement with experiments, rather than antiferromagnetic long-range contributions of the RKKY interaction. The results shed light on possibilities for further increasing $T_C$.Comment: Published version; 3 references adde

A fresh look at paralytics in the critically ill: real promise and real concern.

Neuromuscular blocking agents (NMBAs), or "paralytics," often are deployed in the sickest patients in the intensive care unit (ICU) when usual care fails. Despite the publication of guidelines on the use of NMBAs in the ICU in 2002, clinicians have needed more direction to determine which patients would benefit from NMBAs and which patients would be harmed. Recently, new evidence has shown that paralytics hold more promise when used in carefully selected lung injury patients for brief periods of time. When used in early acute respiratory distress syndrome (ARDS), NMBAs assist to establish a lung protective strategy, which leads to improved oxygenation, decreased pulmonary and systemic inflammation, and potentially improved mortality. It also is increasingly recognized that NMBAs can cause harm, particularly critical illness polyneuromyopathy (CIPM), when used for prolonged periods or in septic shock. In this review, we address several practical considerations for clinicians who use NMBAs in their practice. Ultimately, we conclude that NMBAs should be considered a lung protective adjuvant in early ARDS and that clinicians should consider using an alternative NMBA to the aminosteroids in septic shock with less severe lung injury pending further studies

Modelling and Forecasting of Realized Covariance Matrices

In this thesis, we use observation-driven models for time-series of daily RCs. That is, we assume a matrix-variate probability distribution for the daily RCs, whose parameters are updated based on the RC realizations from previous days. In particular, Chapter 2 looks at different matrix-variate probability distributions for the RCs and their theoretical and empirical properties. Chapter 3 proposes a flexible observation-driven model to update all distribution-specific time-varying parameters, not just the expected value matrix as is done in the literature so far. Chapter 4 introduces an observation-driven updating mechanism that is applicable to high-dimensional time-series of RCs. Each of these three chapters is a self-contained paper