Related papers: Revisiting Functional Derivatives in Multi-object …
Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…
High-dimensional functional data are becoming increasingly common in fields such as environmental monitoring and neuroimaging. This paper studies high-dimensional functional linear regression models that relate a scalar response to…
The smooth function reconstruction needs to use derivatives. In 2010, we used the gradually varied derivatives to successfully constructed smooth surfaces for real data. We also briefly explained why the gradually varied derivatives are…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
Identifying and quantifying spatial correlation are important aspects of studying the collective behaviour of multi-agent systems. Pair correlation functions (PCFs) are powerful statistical tools which can provide qualitative and…
A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
The cumulative distribution function (CDF) is fundamental for characterizing random variables, making it essential in applications that require privacy-preserving data analysis. This paper introduces a novel framework for constructing…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
Particle probability hypothesis density filtering has become a promising means for multi-target tracking due to its capability of handling an unknown and time-varying number of targets in non-linear non-Gaussian system. However, its…
The generalized Fermi-Dirac functions and their derivatives are important in evaluating the thermodynamic quantities of partially degenerate electrons in hot dense stellar plasmas. New recursion relations of the generalized Fermi-Dirac…
Density-potential functional theory (DPFT) is an alternative formulation of orbital-free density functional theory that may be suitable for modeling the electronic structure of large systems. To date, DPFT has been applied mainly to quantum…
This paper provides a unifying view of a wide range of problems of interest in machine learning by framing them as the minimization of functionals defined on the space of probability measures. In particular, we show that generative…
Particle filters flexibly represent multiple posterior modes nonparametrically, via a collection of weighted samples, but have classically been applied to tracking problems with known dynamics and observation likelihoods. Such generative…
In the seminal work [9], several macroscopic market observables have been introduced, in an attempt to find characteristics capturing the diversity of a financial market. Despite the crucial importance of such observables for investment…
Model diagnostics is an indispensable component of regression analysis, yet it is not well addressed in standard textbooks on generalized linear models. The lack of exposition is attributed to the fact that when outcome data are discrete,…
Density functional theory (DFT) is an essential building block for modern theoretical physics, chemistry, and engineering, especially those concerning electronic properties. Through decades of development, various program packages for…
Dependency functions of dependent variables are relevant for i) performing uncertainty quantification and sensitivity analysis in presence of dependent variables and/or correlated variables, and ii) simulating random dependent variables. In…
Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…
In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of…