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Finite-width fully connected neural networks with Gaussian-initialized weights deviate from their infinite-width Gaussian limit, exhibiting non-vanishing higher-order cumulants. We approximate these deviations, for a neural network…
The problem of known signal detection in Additive White Gaussian Noise is considered. In previous work, a new detection scheme was introduced by the authors, and it was demonstrated that optimum performance cannot be reached in a real…
We derive improved regression and classification rates for support vector machines using Gaussian kernels under the assumption that the data has some low-dimensional intrinsic structure that is described by the box-counting dimension. Under…
In genome-wide prediction, independence of marker allele substitution effects is typically assumed; however, since early stages of this technology it has been known that nature points to correlated effects. In statistics, graphical models…
We consider the Grassmann graph of $k$-dimensional subspaces of an $n$-dimensional vector space over the $q$-element field and its subgraph $\Gamma(n,k)_q$ formed by non-degenerate linear $[n,k]_q$ codes. We assume that $1<k<n-1$. It is…
We introduce a Bayesian solution to the problem of inferring the density profile of strong gravitational lenses when the lens galaxy may contain multiple dark or faint substructures. The source and lens models are based on a superposition…
In paper I (Yu et al. [1]), we show through N-body simulation that a local monotonic Gaussian transformation can significantly reduce non-Gaussianity in a noise-free lensing convergence field. This makes the Gaussianization a promising…
Most of the modern literature on robust mean estimation focuses on designing estimators which obtain optimal sub-Gaussian concentration bounds under minimal moment assumptions and sometimes also assuming contamination. This work looks at…
Weakly supervised semantic segmentation (WSSS) based on image-level labels is challenging since it is hard to obtain complete semantic regions. To address this issue, we propose a self-training method that utilizes fused multi-scale…
This paper presents generalizations of semidefinite programming formulations of 1-norm optimization problems over infinite dictionaries of vectors of complex exponentials, which were recently proposed for superresolution, gridless…
Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…
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…
We study the problem of detection of a p-dimensional sparse vector of parameters in the linear regression model with Gaussian noise. We establish the detection boundary, i.e., the necessary and sufficient conditions for the possibility of…
Vector quantization(VQ) is a lossy data compression technique from signal processing, which is restricted to feature vectors and therefore inapplicable for combinatorial structures. This contribution presents a theoretical foundation of…
Given a homogeneous component of an exterior algebra, we characterize those subspaces in which every nonzero element is decomposable. In geometric terms, this corresponds to characterizing the projective linear subvarieties of the Grassmann…
Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…
Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.
Weakly-Supervised Semantic Segmentation (WSSS) aims to train segmentation models by weak labels, which is receiving significant attention due to its low annotation cost. Existing approaches focus on generating pseudo labels for supervision…
This paper studies network information theory problems where the external noise is Gaussian distributed. In particular, the Gaussian broadcast channel with coherent fading and the Gaussian interference channel are investigated. It is shown…