Related papers: Revisiting Functional Derivatives in Multi-object …

Applicative functors are a generalisation of monads. Both allow the expression of effectful computations into an otherwise pure language, like Haskell. Applicative functors are to be preferred to monads when the structure of a computation…

We propose a simpler derivation of the probability density function of Feller Diffusion using the Fourier Transform and solving the resulting equation via the Method of Characteristics. We also discuss simulation algorithms and confirm key…

We pose a new algebraic formalism for studying differential calculus in vector bundles. This is achieved by studying various functors of differential calculus over arbitrary graded commutative algebras (DCGCA) and applying this language to…

We propose a novel procedure for outlier detection in functional data, in a semi-supervised framework. As the data is functional, we consider the coefficients obtained after projecting the observations onto orthonormal bases (wavelet, PCA).…

Using movement primitive libraries is an effective means to enable robots to solve more complex tasks. In order to build these movement libraries, current algorithms require a prior segmentation of the demonstration trajectories. A…

Function is defined as the ensemble of tasks that enable the product to complete the designed purpose. Functional tools, such as functional modeling, offer decision guidance in the early phase of product design, where explicit design…

In a world blessed with a great diversity of loss functions, we argue that that choice between them is not a matter of taste or pragmatics, but of model. Probabilistic depencency graphs (PDGs) are probabilistic models that come equipped…

A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…

A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…

Mathematical models are sometime given as functions of independent input variables and equations or inequations connecting the input variables. A probabilistic characterization of such models results in treating them as functions with…

A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…

We initiate the study of active learning polynomial threshold functions (PTFs). While traditional lower bounds imply that even univariate quadratics cannot be non-trivially actively learned, we show that allowing the learner basic access to…

While precise data observation is essential for the learning processes of predictive models, it can be challenging owing to factors such as insufficient observation accuracy, high collection costs, and privacy constraints. In this paper, we…

In this manuscript, we generalize F-calculus to apply it on fractal Tartan spaces. The generalized standard F-calculus is used to obtain the integral and derivative of the functions on the fractal Tartan with different dimensions. The…

Despite of various similar features, Functional Data Analysis and High-Dimensional Data Analysis are two major fields in Statistics that grew up recently almost independently one from each other. The aim of this paper is to propose a survey…

Dimensionality reduction is one of the key issues in the design of effective machine learning methods for automatic induction. In this work, we introduce recursive maxima hunting (RMH) for variable selection in classification problems with…

Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the…

Derivative of a function can be expressed in terms of integration over a small neighborhood of the point of differentiation, so-called differentiation by integration method. In this text a maximal generalization of existing results which…

Additive models form a widely popular class of regression models which represent the relation between covariates and response variables as the sum of low-dimensional transfer functions. Besides flexibility and accuracy, a key benefit of…

This paper presents a versatile technique for the purpose of feature selection and extraction - Class Dependent Features (CDFs). We use CDFs to improve the accuracy of classification and at the same time control computational expense by…