Related papers: New proofs to measurable, predictable and optional…

Recent advances in machine learning make it possible to design efficient prediction algorithms for data sets with huge numbers of parameters. This paper describes a new technique for "hedging" the predictions output by many such algorithms,…

We consider MAP estimators for structured prediction with exponential family models. In particular, we concentrate on the case that efficient algorithms for uniform sampling from the output space exist. We show that under this assumption…

We give an interpretation of the construction of torsors from preceding work (Bertram, Kinyon: Associative Geometries. I, J. Lie Theory 20) in terms of classical projective geometry. For the Desarguesian case, this leads to a reformulation…

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…

We give an elementary proof of the real section conjecture for quasi-projective hyperbolic curves and semi-abelian varieties. The underlying argument is essentially equivalent to the one given by J. Stix.

In classical geometry, there is no such well-known and much-studied topic as the construction of conic sections (or briefly conics) from its five points. Its importance in many applications of mechanical engineering, civil engineering and…

Conformal prediction has recently emerged as a promising strategy for quantifying the uncertainty of a predictive model; these algorithms modify the model to output sets of labels that are guaranteed to contain the true label with high…

We prove a convergence theorem for partial sums of sectorial forms with vertex zero and a common semi-angle. As an example we prove an absorption theorem for sectorial forms.

We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…

This paper reviews the growing field of Bayesian prediction. Bayes point and interval prediction are defined and exemplified and situated in statistical prediction more generally. Then, four general approaches to Bayes prediction are…

The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…

We examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and conduct a numerical study to analyze the behavior of the…

As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using It\^o's formula and on a new…

We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most…

We present projective descriptions of classical spaces of functions and distributions. More precisely, we provide descriptions of these spaces by semi-norms which are defined by a combination of classical norms and multiplication or…

In the theory of conditional sets, many classical theorems from areas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often to be applied in areas such as mathematical economics or…

The random measures on the space of continuous functions are considered. Stationary random measures are described. The weak solutions of the stochastic equations are substituted by the strong measure-valued solutions.

In semialgebraic geometry, projections play a prominent role. A definable choice is a semialgebraic selection of one point in every fiber of a projection. Definable choices exist by semialgebraic triviality, but their complexity depends…

We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not…

These expanded lecture notes are based on a tutorial on categorical proof theory presented at the summer school associated with the conference "Topology, Algebra, and Categories in Logic 2021-2022." The chapter delves into various…