Related papers: Perspective Functions: Properties, Constructions, …
This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, are also used in many…
The advent of high resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high resolution data require a functional approach. The starting point is a…
In this paper, we review Fisher information matrices properties in weighted version and discuss inequalities/bounds on it by using reduced weight functions. In particular, an extended form of the Fisher information inequality previously…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…
A promising theory of quaternion-valued functions of one quaternionic variable, now called slice regular functions, has been introduced in 2006. The basic examples of slice regular functions are power series centered at 0 on their balls of…
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…
A class of real functions, which is the generalization of a family of convex functions, is introduced; in this connection, we have defined $X$-convex, strictly $X$-convex, quasi-$X$-convex, strictly quasi-$X$-convex, and semi-strictly…
In discrete convex analysis, the scaling and proximity properties for the class of L$^\natural$-convex functions were established more than a decade ago and have been used to design efficient minimization algorithms. For the larger class of…
We introduce generalized notions of a divergence function and a Fisher information matrix. We propose to generalize the notion of an exponential family of models by reformulating it in terms of the Fisher information matrix. Our methods are…
A key question in many low-rank problems throughout optimization, machine learning, and statistics is to characterize the convex hulls of simple low-rank sets and judiciously apply these convex hulls to obtain strong yet computationally…
As a generalization of geodesic function, in the present paper, we introduce the notion of geodesic $\varphi$-convex function and deduce some basic properties of $\varphi$-convex function and geodesic $\varphi$-convex function. We also…
Archetype and archetypoid analysis can be extended to functional data. Each function is represented as a mixture of actual observations (functional archetypoids) or functional archetypes, which are a mixture of observations in the data set.…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
Statistical decision problems lie at the heart of statistical machine learning. The simplest problems are binary and multiclass classification and class probability estimation. Central to their definition is the choice of loss function,…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…
New perspectives, proofs, and some extensions of known results are presented concerning the behavior of the Fitzpatrick function of a monotone type operator in the general context of a locally convex space.
We extend classical analytic tools for finite-state statistical models to allow zero probabilities. Using methods from algebraic statistics and information geometry, we develop a framework in which a smooth statistical model could hit the…
We present a new piecewise linear regression methodology that utilizes fitting a difference of convex functions (DC functions) to the data. These are functions $f$ that may be represented as the difference $\phi_1 - \phi_2$ for a choice of…