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A low-complexity model for signal quality prediction in a nonlinear fiber-optical network is developed. The model, which builds on the Gaussian noise model, takes into account the signal degradation caused by a combination of chromatic…
We consider problem of signal detection in Gaussian white noise. Test statistics are linear combinations of squares of estimators of Fourier coefficients or $\mathbb{L}_2$-norms of kernel estimators. We point out necessary and sufficient…
Neural recordings, returns from radars and sonars, images in astronomy and single-molecule microscopy can be modeled as a linear superposition of a small number of scaled and delayed copies of a band-limited or diffraction-limited point…
In computational physics, machine learning has now emerged as a powerful complementary tool to explore efficiently candidate designs in engineering studies. Outputs in such supervised problems are signals defined on meshes, and a natural…
Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…
We consider a matrix-valued Gaussian sequence model, that is, we observe a sequence of high-dimensional $M \times N$ matrices of heterogeneous Gaussian random variables $x_{ij,k}$ for $i \in\{1,...,M\}$, $j \in \{1,...,N\}$ and $k \in…
We consider the problem of detecting the presence of a spatially correlated multichannel signal corrupted by additive Gaussian noise (i.i.d across sensors). No prior knowledge is assumed about the system parameters such as the noise…
Detection of sparse signals arises in a wide range of modern scientific studies. The focus so far has been mainly on Gaussian mixture models. In this paper, we consider the detection problem under a general sparse mixture model and obtain…
Models with many signals, high-dimensional models, often impose structures on the signal strengths. The common assumption is that only a few signals are strong and most of the signals are zero or close (collectively) to zero. However, such…
This paper studies recursive composite hypothesis testing in a network of sparsely connected agents. The network objective is to test a simple null hypothesis against a composite alternative concerning the state of the field, modeled as a…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
We consider the problem of super-resolving the line spectrum of a multisinusoidal signal from a finite number of samples, some of which may be completely corrupted. Measurements of this form can be modeled as an additive mixture of a…
Higher criticism is a method for detecting signals that are both sparse and weak. Although first proposed in cases where the noise variables are independent, higher criticism also has reasonable performance in settings where those variables…
In the near future, the Internet of Things will interconnect billions of devices, forming a vast network where users sporadically transmit short messages through multi-path wireless channels. These channels are characterized by the…
In this paper, we focus on the following testing problem: assume that we are given observations of a real-valued signal along the grid $0,1,\ldots,N-1$, corrupted by white Gaussian noise. We want to distinguish between two hypotheses: (a)…
The problem of detecting a wide-sense stationary Gaussian signal process embedded in white Gaussian noise, where the power spectral density of the signal process exhibits uncertainty, is investigated. The performance of minimax robust…
Detecting test samples drawn sufficiently far away from the training distribution statistically or adversarially is a fundamental requirement for deploying a good classifier in many real-world machine learning applications. However, deep…
We study estimation of an $s$-sparse signal in the $p$-dimensional Gaussian sequence model with equicorrelated observations and derive the minimax rate. A new phenomenon emerges from correlation, namely the rate scales with respect to…
We consider noisy observations of a distribution with unknown support. In the deconvolution model, it has been proved recently [19] that, under very mild assumptions, it is possible to solve the deconvolution problem without knowing the…
Correlation analysis is a fundamental step in uncovering meaningful insights from complex datasets. In this paper, we study the problem of detecting correlations between two random graphs following the Gaussian Wigner model with unlabeled…