Related papers: On Generalization and Computation of Tukey's Depth…

Merging the two cultures of deep and statistical learning provides insights into structured high-dimensional data. Traditional statistical modeling is still a dominant strategy for structured tabular data. Deep learning can be viewed…

Depth estimation attracts widespread attention in the computer vision community. However, it is still quite difficult to recover an accurate depth map using only one RGB image. We observe a phenomenon that existing methods tend to fail in…

Among their competitors, projection depth and its induced estimators are very favorable because they can enjoy very high breakdown point robustness without having to pay the price of low efficiency, meanwhile providing a promising…

Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…

Empirical Bayes methods are widely used for large-scale inference, yet most classical approaches assume homoscedastic observations and focus primarily on posterior mean estimation. We develop a nonparametric empirical Bayes framework for…

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing…

The rapid emergence of massive datasets in various fields poses a serious challenge to traditional statistical methods. Meanwhile, it provides opportunities for researchers to develop novel algorithms. Inspired by the idea of…

The analysis of multidimensional data is becoming a more and more relevant topic in statistical and machine learning research. Given their complexity, such data objects are usually reshaped into matrices or vectors and then analysed.…

In regression analysis, we employ contour projection (CP) to develop a new dimension reduction theory. Accordingly, we introduce the notions of the central contour subspace and generalized contour subspace. We show that both of their…

Density estimation plays a crucial role in many data analysis tasks, as it infers a continuous probability density function (PDF) from discrete samples. Thus, it is used in tasks as diverse as analyzing population data, spatial locations in…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…

Scientific computer simulations cannot represent all scales in realistic applications. To bridge this model-data gap, parameters are injected into models and constrained with noisy data using Bayesian inversion. To reduce the number of…

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or…

We study the problem of space and time efficient evaluation of a nonparametric estimator that approximates an unknown density. In the regime where consistent estimation is possible, we use a piecewise multivariate polynomial interpolation…

Envelope methods offer targeted dimension reduction for various models. The overarching goal is to improve efficiency in multivariate parameter estimation by projecting the data onto a lower-dimensional subspace known as the envelope.…

We propose MaskingDepth, a novel semi-supervised learning framework for monocular depth estimation to mitigate the reliance on large ground-truth depth quantities. MaskingDepth is designed to enforce consistency between the…

We develop a rigorous theoretical framework for principal manifold estimation that recovers a latent low-dimensional manifold from a point cloud observed in a high-dimensional ambient space. Our framework accommodates manifolds with…

Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…

This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of…

A problem that is frequently encountered in a variety of mathematical contexts, is to find the common invariant subspaces of a single, or set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea…