Related papers: Statistical Inference for Ultrahigh Dimensional Lo…
This paper proposes a new test for a change point in the mean of high-dimensional data based on the spatial sign and self-normalization. The test is easy to implement with no tuning parameters, robust to heavy-tailedness and theoretically…
We establish a strong Gaussian approximation for high-dimensional non-degenerate U-statistics with diverging dimension. Under mild assumptions, we construct, on a sufficiently rich probability space, a Gaussian process that uniformly…
We consider optimal sensor placement for hyper-parameterized linear Bayesian inverse problems, where the hyper-parameter characterizes nonlinear flexibilities in the forward model, and is considered for a range of possible values. This…
Bayesian change-point detection, together with latent variable models, allows to perform segmentation over high-dimensional time-series. We assume that change-points lie on a lower-dimensional manifold where we aim to infer subsets of…
Recent developments in extreme value statistics have established the so-called geometric approach as a powerful modelling tool for multivariate extremes. We tailor these methods to the case of spatial modelling and examine their efficacy at…
We consider the problem of robust mean and location estimation w.r.t. any pseudo-norm of the form $x\in\mathbb{R}^d\to ||x||_S = \sup_{v\in S}<v,x>$ where $S$ is any symmetric subset of $\mathbb{R}^d$. We show that the deviation-optimal…
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…
We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The…
Traditional methods for spatial inference estimate smooth interpolating fields based on features measured at well-located points. When the spatial locations of some observations are missing, joint inference of the fields and locations is…
The geometric median, a notion of center for multivariate distributions, has gained recent attention in robust statistics and machine learning. Although conceptually distinct from the mean (i.e., expectation), we demonstrate that both are…
We consider in this paper the problem of sampling a high-dimensional probability distribution $\pi$ having a density with respect to the Lebesgue measure on $\mathbb{R}^d$, known up to a normalization constant $x \mapsto \pi(x)=…
Additive spatial statistical models with weakly stationary process assumptions have become standard in spatial statistics. However, one disadvantage of such models is the computation time, which rapidly increases with the number of data…
We consider the problem of approximating sums of high-dimensional stationary time series by Gaussian vectors, using the framework of functional dependence measure. The validity of the Gaussian approximation depends on the sample size $n$,…
To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…
Datasets containing both categorical and continuous variables are frequently encountered in many areas, and with the rapid development of modern measurement technologies, the dimensions of these variables can be very high. Despite the…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their…
We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing…
Statisticians increasingly face the problem to reconsider the adaptability of classical inference techniques. In particular, divers types of high-dimensional data structures are observed in various research areas; disclosing the boundaries…
The problem of identifying regions of spatially interesting, different or adversarial behavior is inherent to many practical applications involving distributed multisensor systems. In this work, we develop a general framework stemming from…