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This article presents a multiscale, non-linear and directional statistical characterization of images based on the estimation of the skewness, flatness, entropy and distance from Gaussianity of the spatial increments. These increments are…
Density Estimation is one of the central areas of statistics whose purpose is to estimate the probability density function underlying the observed data. It serves as a building block for many tasks in statistical inference, visualization,…
Structure identification in cosmological simulations plays an important role in analysing simulation outputs. The definition of these structures directly impacts the inferred properties derived from these simulations. This paper proposes a…
We present a first procedure that can estimate -- with statistical consistency guarantees -- any local-maxima of a density, under benign distributional conditions. The procedure estimates all such local maxima, or $\textit{modal-sets}$, of…
There has been growing interest in the AI community for precise uncertainty quantification. Conditional density models f(y|x), where x represents potentially high-dimensional features, are an integral part of uncertainty quantification in…
Rapidly growing data sizes of scientific simulations pose significant challenges for interactive visualization and analysis techniques. In this work, we propose a compact probabilistic representation to interactively visualize large…
The concept of statistical convergence based on asymptotic density is introduced in this article through nets. Some possible extensions of classical results for statistical convergence of sequences are obtained in this article, with…
This paper establishes a precise high-dimensional asymptotic theory for boosting on separable data, taking statistical and computational perspectives. We consider a high-dimensional setting where the number of features (weak learners) $p$…
We obtain quantitative estimates for the asymptotic density of subsets of the two-dimensional integer lattice which contain only trivial solutions to an additive equation involving binary forms. In the process we develop an analogue of…
In this paper, we propose a general framework for the asymptotic analysis of node-based verification-based algorithms. In our analysis we tend the signal length $n$ to infinity. We also let the number of non-zero elements of the signal $k$…
The problem of quantifying uncertainty about the locations of multiple change points by means of confidence intervals is addressed. The asymptotic distribution of the change point estimators obtained as the local maximisers of moving sum…
We present a method that allows us to find asymptotic form of various characteristics of disordered systems in the strong localization regime, i.e., when either the random potential is big enough or the energy is close enough to the…
We present a new technique for visualizing high-dimensional data called cluster MDS (cl-MDS), which addresses a common difficulty of dimensionality reduction methods: preserving both local and global structures of the original sample in a…
Visualizing high-dimensional data is essential for understanding biomedical data and deep learning models. Neighbor embedding methods, such as t-SNE and UMAP, are widely used but can introduce misleading visual artifacts. We find that the…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…
In this work we give new density estimators by averaging classical density estimators such as the histogram, the frequency polygon and the kernel density estimators obtained over different bootstrap samples of the original data. We prove…
We present an abstract framework for asymptotic analysis of convergence based on the notions of eventual families of sets that we define. A family of subsets of a given set is called here an "eventual family" if it is upper hereditary with…
The paper establishes the central limit theorems and proposes how to perform valid inference in factor models. We consider a setting where many counties/regions/assets are observed for many time periods, and when estimation of a global…
For the spherical symmetric case, all quantities describing the relaxed dark matter halo can be expressed as functions of the gravitational potential $\Phi$. Decomposing the radial velocity dispersion $\sigma_r$ with respect to $\Phi$ at…
This article examines density estimation by combining a parametric approach with a nonparametric factor. The plug-in parametric estimator is seen as a crude estimator of the true density and is adjusted by a nonparametric factor. The…