Related papers: Statistical Depth for Big Functional Data with App…

Hyperspectral imaging provides detailed information about the scanned objects, as it captures their spectral characteristics within a large number of wavelength bands. Classification of such data has become an active research topic due to…

We consider the problem of estimating the difference between two undirected functional graphical models with shared structures. In many applications, data are naturally regarded as a vector of random functions rather than as a vector of…

Aggregating multi-subject functional magnetic resonance imaging (fMRI) data is indispensable for generating valid and general inferences from patterns distributed across human brains. The disparities in anatomical structures and functional…

Statistical shape modeling (SSM) is an enabling quantitative tool to study anatomical shapes in various medical applications. However, directly using 3D images in these applications still has a long way to go. Recent deep learning methods…

Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace…

We describe recent progress in the statistical mechanical description of many-body systems via machine learning combined with concepts from density functional theory and many-body simulations. We argue that the neural functional theory by…

Background: Deep neural networks have proven to be powerful computational tools for modeling, prediction, and generation. However, the workings of these models have generally been opaque. Recent work has shown that the performance of some…

Quantification of sputter depth profiles is frequently done by fitting the convolution integral over concentration and depth resolution function. For a thin delta layer, there exist analytical solutions. The analytical depth resolution…

Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…

In this paper, we show how convolutional neural networks (CNN) can be used in regression and classification learning problems of noisy and non-noisy functional data. The main idea is to transform the functional data into a 28 by 28 image.…

The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…

We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…

Set function learning has emerged as a crucial area in machine learning, addressing the challenge of modeling functions that take sets as inputs. Unlike traditional machine learning that involves fixed-size input vectors where the order of…

We propose a framework for descriptively analyzing sets of partial orders based on the concept of depth functions. Despite intensive studies in linear and metric spaces, there is very little discussion on depth functions for non-standard…

We propose learning a depth covariance function with applications to geometric vision tasks. Given RGB images as input, the covariance function can be flexibly used to define priors over depth functions, predictive distributions given…

Multi-dimensional functional data arises in numerous modern scientific experimental and observational studies. In this paper we focus on longitudinal functional data, a structured form of multidimensional functional data. Operating within a…

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…

Depth is one of the keys that make neural networks succeed in the task of large-scale image recognition. The state-of-the-art network architectures usually increase the depths by cascading convolutional layers or building blocks. In this…

This work presents Depth Anything, a highly practical solution for robust monocular depth estimation. Without pursuing novel technical modules, we aim to build a simple yet powerful foundation model dealing with any images under any…

Graph matching is an important and persistent problem in computer vision and pattern recognition for finding node-to-node correspondence between graph-structured data. However, as widely used, graph matching that incorporates pairwise…