Related papers: Functional data analysis for density functions by …

We consider nonparametric functional regression when both predictors and responses are functions. More specifically, we let $(X_1,Y_1),...,(X_n,Y_n)$ be random elements in $\mathcal{F}\times\mathcal{H}$ where $\mathcal{F}$ is a semi-metric…

Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected with measurement errors on discretized grids. In order to accurately smooth noisy functional…

We describe how density-functional theory, well-known for its many uses in ab initio calculations of electronic structure, can be used to study the ground state of inhomogeneous model Hamiltonians. The basic ideas and concepts are discussed…

Functional data analysis is a growing research field as more and more practical applications involve functional data. In this paper, we focus on the problem of regression and classification with functional predictors: the model suggested…

We propose a novel Bayesian nonparametric method for hierarchical modelling on a set of related density functions, where grouped data in the form of samples from each density function are available. Borrowing strength across the groups is a…

Important information concerning a multivariate data set, such as clusters and modal regions, is contained in the derivatives of the probability density function. Despite this importance, nonparametric estimation of higher order derivatives…

Functional data analysis, FDA, is now a well established discipline of statistics, with its core concepts and perspectives in place. Despite this, there are still fundamental statistical questions which have received relatively little…

Any explicit functional representation $f$ of a density is hampered by two main obstacles when we wish to use it as a generative model: designing $f$ so that sampling is fast, and estimating $Z = \int f$ so that $Z^{-1}f$ integrates to 1.…

Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…

Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…

Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices…

We consider centralized and distributed mirror descent algorithms over a finite-dimensional Hilbert space, and prove that the problem variables converge to an optimizer of a possibly nonsmooth function when the step sizes are square…

We propose a way of transforming the problem of conditional density estimation into a single nonparametric regression task via the introduction of auxiliary samples. This allows leveraging regression methods that work well in high…

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…

The computation of integrals is a fundamental task in the analysis of functional data, which are typically considered as random elements in a space of squared integrable functions. Borrowing ideas from recent advances in the Monte Carlo…

We propose the density ratio permutation test, a hypothesis test that assesses whether the ratio between two densities is proportional to a known function based on independent samples from each distribution. The test uses an efficient…

We reexamine the recently introduced basis-set correction theory based on density-functional theory consisting in correcting the basis-set incompleteness error of wave-function methods using a density functional. We use a one-dimensional…

Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of non-interacting fermions in 1d, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with…

In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…