Related papers: Non-Gaussian Observations in Nonlinear Compressed …
Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…
In one-bit compressed sensing, previous results state that sparse signals may be robustly recovered when the measurements are taken using Gaussian random vectors. In contrast to standard compressed sensing, these results are not extendable…
This paper investigates the fundamental information-theoretic limits for the control and sensing of noiseless linear dynamical systems subject to a broad class of nonlinear observations. We analyze the interactions between the control and…
We provide theoretical and empirical evidence for a type of asymmetry between causes and effects that is present when these are related via linear models contaminated with additive non-Gaussian noise. Assuming that the causes and the…
We consider drawing statistical inferences based on data subject to non-Gaussian measurement error. Unlike most existing methods developed under the assumption of Gaussian measurement error, the proposed strategy exploits hypercomplex…
The well known metrological linear squeezing parameters (such as quadrature or spin squeezing) efficiently quantify the sensitivity of Gaussian states. Yet, these parameters are insufficient to characterize the much wider class of highly…
Gaussian random fields pervade all areas of science. However, it is often the departures from Gaussianity that carry the crucial signature of the nonlinear mechanisms at the heart of diverse phenomena, ranging from structure formation in…
Measures of the non-Gaussianity of a random field depend on how accurately one is able to measure the field. If a signal measured at a certain point is to be averaged with its surroundings, or coarse-grained, the magnitude of its…
We establish the large deviations asymptotic performance (error exponent) of consensus+innovations distributed detection over random networks with generic (non-Gaussian) sensor observations. At each time instant, sensors 1) combine theirs…
In an ensemble of two-level atoms that can be described in terms of a collective spin, entangled states can be used to enhance the sensitivity of interferometric precision measurements. While non-Gaussian spin states can produce larger…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
We consider estimation of a deterministic unknown parameter vector in a linear model with non-Gaussian noise. In the Gaussian case, dimensionality reduction via a linear matched filter provides a simple low dimensional sufficient statistic…
Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…
Nonparametric regression for massive numbers of samples (n) and features (p) is an increasingly important problem. In big n settings, a common strategy is to partition the feature space, and then separately apply simple models to each…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
We analyze the effect of lossy compression in the processing of sensor signals that must be used to detect anomalous events in the system under observation. The intuitive relationship between the quality loss at higher compression and the…
Multiple photon subtraction applied to a displaced phase-averaged coherent state, which is a non-Gaussian classical state, produces conditional states with a non trivial (positive) Glauber-Sudarshan $P$-representation. We theoretically and…
This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…