Related papers: Just Previsions
This paper discusses predictive inference and feature selection for generalized linear models with scarce but high-dimensional data. We argue that in many cases one can benefit from a decision theoretically justified two-stage approach:…
We introduce the concept of a prenormed model of a particular kind of finitary single-sorted first-order theories, interpreted over a category with finite products. These are referred to as prealgebraic theories, for the fact that their…
We introduce a novel projection depth for data lying in a general Hilbert space, called the regularized projection depth, with a focus on functional data. By regularizing projection directions, the proposed depth does not suffer from the…
It is understood now that all projective (and conformal) invariants of Riemannian metrics can be found by a transparent construction based on representation theory. So this article with a partial and quite cumbersome construction of…
The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a…
A wide array of graphical models can be parametrised to have atomic probabilities represented by monomial functions. Such monomial structure has proven very useful when studying robustness under the assumption of a multilinear model where…
Parity is ubiquitous, but not always identified as a simplifying tool for computations. Using parity, having in mind the example of the bosonic/fermionic Fock space, and the framework of Z_2-graded (super) algebra, we clarify relationships…
We give a complete characterization of invariant integrable complex structures on principal bundles defined over hermitian symmetric spaces, using the Jordan algebraic approach for the curvature computations. In view of possible…
We discuss representations of monogenic functions over very regular groups.
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…
This paper investigates positive harmonic functions on a domain which contains an infinite cylinder, and whose boundary is contained in the union of parallel hyperplanes. (In the plane its boundary consists of two sets of vertical…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minmalistic set of operations on…
We provide a self-contained introduction to the classical theory of universal-homogeneous models (also known as generic structures, rich models, or Fra\"iss\'e limits). In the literature, most treatments restrict consideration to embeddings…
Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…
Any representational enterprise must omit variation in order to function. NASA still uses Newtonian mechanics, though Einstein superseded Newton, and the standard picture of scientific progress cannot explain how. A description that omitted…
The nonzero level sets of a homogeneous, logarithmically homogeneous, or translationally homogeneous function are affine spheres if and only if the Hessian determinant of the function is a multiple of a power or an exponential of the…
We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…
By studying the theory of rational curves, we introduce a notion of rational simple connectedness for projective homogeneous spaces. As an application, we prove that over a function field of an algebraic surface, a projective homogeneous…
We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…