Related papers: Bump detection in heterogeneous Gaussian regressio…
Necessary and sufficient conditions of uniform consistency are explored. A hypothesis is simple. Nonparametric sets of alternatives are bounded convex sets in $\mathbb{L}_p$, $p >1$ with "small" balls deleted. The "small" balls have the…
The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. The pre-change observations are assumed to be stationary with a known distribution, while the post-change…
We study the hardness of classically simulating Gaussian boson sampling at nonzero photon distinguishability. We find that similar to regular boson sampling, distinguishability causes exponential attenuation of the many-photon interference…
This paper deals with adaptive radar detection of a subspace signal competing with two sources of interference. The former is Gaussian with unknown covariance matrix and accounts for the joint presence of clutter plus thermal noise. The…
We introduce a bottleneck method for learning data representations based on information deficiency, rather than the more traditional information sufficiency. A variational upper bound allows us to implement this method efficiently. The…
Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…
In certain situations that shall be undoubtedly more and more common in the Big Data era, the datasets available are so massive that computing statistics over the full sample is hardly feasible, if not unfeasible. A natural approach in this…
Let $Y$ be a Gaussian vector whose components are independent with a common unknown variance. We consider the problem of estimating the mean $\mu$ of $Y$ by model selection. More precisely, we start with a collection…
In this paper, we study sequential testing problems with \emph{overlapping} hypotheses. We first focus on the simple problem of assessing if the mean $\mu$ of a Gaussian distribution is smaller or larger than a fixed $\epsilon>0$; if…
The effect of measurement errors in discriminant analysis is investigated. Given observations $Z=X+\epsilon$, where $\epsilon$ denotes a random noise, the goal is to predict the density of $X$ among two possible candidates $f$ and $g$. We…
We study the problem of learning latent variables in Gaussian graphical models. Existing methods for this problem assume that the precision matrix of the observed variables is the superposition of a sparse and a low-rank component. In this…
In high-dimensional regression, we attempt to estimate a parameter vector $\beta_0\in\mathbb{R}^p$ from $n\lesssim p$ observations $\{(y_i,x_i)\}_{i\leq n}$ where $x_i\in\mathbb{R}^p$ is a vector of predictors and $y_i$ is a response…
Quantum state discrimination plays a central role in quantum information and communication. For the discrimination of optical quantum states, the two most widely adopted measurement techniques are photon detection, which produces discrete…
We derive novel anti-concentration bounds for the difference between the maximal values of two Gaussian random vectors across various settings. Our bounds are dimension-free, scaling with the dimension of the Gaussian vectors only through…
Destructive interference between signal and background processes poses a fundamental challenge in searches for top-philic scalar resonances, significantly reducing experimental sensitivity to well-motivated extensions of the Higgs sector.…
Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with 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…
High-dimensional linear regression has been thoroughly studied in the context of independent and identically distributed data. We propose to investigate high-dimensional regression models for independent but non-identically distributed…
A distributed inference scheme which uses bounded transmission functions over a Gaussian multiple access channel is considered. When the sensor measurements are decreasingly reliable as a function of the sensor index, the conditions on the…