Related papers: Revisiting Functional Derivatives in Multi-object …
Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…
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…
In probabilistic coherence spaces, a denotational model of probabilistic functional languages, mor-phisms are analytic and therefore smooth. We explore two related applications of the corresponding derivatives. First we show how derivatives…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
Multi-target tracking is an important problem in civilian and military applications. This paper investigates multi-target tracking in distributed sensor networks. Data association, which arises particularly in multi-object scenarios, can be…
Probability-generating function (PGF) kernels are introduced, which constitute a class of kernels supported on the unit hypersphere, for the purposes of spherical data analysis. PGF kernels generalize RBF kernels in the context of spherical…
In many applications of computer vision it is important to accurately estimate the trajectory of an object over time by fusing data from a number of sources, of which 2D and 3D imagery is only one. In this paper, we show how to use a deep…
It is a significant challenge to design probabilistic programming systems that can accommodate a wide variety of inference strategies within a unified framework. Noting that the versatility of modern automatic differentiation frameworks is…
We present a modelling framework for multi-target tracking based on possibility theory and illustrate its ability to account for the general lack of knowledge that the target-tracking practitioner must deal with when working with real data.…
We propose a framework for performing differentiable geometric modeling based on the Function Representation (FRep). The framework is built on top of modern libraries for performing automatic differentiation allowing us to obtain…
For classification problems, feature extraction is a crucial process which aims to find a suitable data representation that increases the performance of the machine learning algorithm. According to the curse of dimensionality theorem, the…
Learning about density functional approximations (DFAs), or approximations for the exchange-correlation functional, can be intimidating. Density Functional Theory is now one of the primary simulation tools for the practicing chemist or…
Existing approaches for derivative estimation are restricted to univariate functional data. We propose two methods to estimate the principal components and scores for the derivatives of multivariate functional data. As a result, the…
When tracking a large number of targets, it is often computationally expensive to represent the full joint distribution over target states. In cases where the targets move independently, each target can instead be tracked with a separate…
How do we take repeated derivatives of composed multivariate functions? for one-dimensional functions, the common tools consist of the Fa\'a di Bruno formula with Bell polynomials; while there are extensions of the Fa\'a di Bruno formula,…
The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…
Classification is a core topic in functional data analysis. A large number of functional classifiers have been proposed in the literature, most of which are based on functional principal component analysis or functional regression. In…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
Gradient-based techniques are becoming increasingly critical in quantitative fields, notably in statistics and computer science. The utility of these techniques, however, ultimately depends on how efficiently we can evaluate the derivatives…