相关论文: Conditional supremum in Riesz spaces and applicati…
Recently, Forr\'e (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provides a unified framework for both random and non-stochastic variables. The original paper establishes…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
As society transitions towards an AI-based decision-making infrastructure, an ever-increasing number of decisions once under control of humans are now delegated to automated systems. Even though such developments make various parts of…
We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…
Many econometrics textbooks imply that under mean independence of the regressors and the error term, the OLS parameters have a causal interpretation. We show that even when this assumption is satisfied, OLS might identify a pseudo-parameter…
As in the cases of freeness and monotonic independence, the notion of conditional freeness is meaningful when complex-valued states are replaced by positive conditional expectations. In this framework, the paper presents several positivity…
We study the fractional maximal operator acting between Orlicz spaces. We characterise whether the operator is bounded between two given Orlicz spaces. Also a necessary and sufficient conditions for the existence of an optimal target and…
Hierarchies of conditional beliefs (Battigalli and Siniscalchi 1999) play a central role for the epistemic analysis of solution concepts in sequential games. They are practically modelled by type structures, which allow the analyst to…
We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…
This thesis presents a formalization of martingales in arbitrary Banach spaces using Isabelle/HOL. We begin by examining formalizations in prominent proof repositories and extend the definition of the conditional expectation operator from…
We introduce the notion of ideally supported achievement sets for a series of real numbers. We analize their complexity and topological properties. We compare the notion of ideal achievement sets with the notion of ideally supported sum…
We develop a design-based framework for causal inference that accommodates random potential outcomes without introducing outcome models, thereby extending the classical Neyman--Rubin paradigm in which outcomes are treated as fixed. By…
When the underlying conditional density is known, conditional expectations can be computed analytically or numerically. When, however, such knowledge is not available and instead we are given a collection of training data, the goal of this…
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of application are studied, in particular,…
This paper makes 3 contributions. First, it generalizes the Lindeberg\textendash Feller and Lyapunov Central Limit Theorems to Hilbert Spaces by way of $L^2$. Second, it generalizes these results to spaces in which sample failure and…
For a large class of supermodular integrands, we establish conditions under which balls are the unique (up to translations) maximizers of the Riesz-type functionals with constraints.
We introduce Riesz Logic, whose models are abelian lattice ordered groups, which generalise Riesz spaces (vector lattices), and show soundness and completeness. Our motivation is to provide a logic for distributional semantics of natural…
The Bessel point process is a rigid point process on the positive real line and its conditional measure on a bounded interval $[0,R]$ is almost surely an orthogonal polynomial ensemble. In this article, we show that if $R$ tends to…
In operator algebra theory, a conditional expectation is usually assumed to be a projection map onto a sub-algebra. In the paper, a further type of conditional expectation and an extension of the Lueders - von Neumann measurement to…
For any fixed $p>2$, a necessary and sufficient condition is obtained for the boundedness of the Riesz transforms associated with second order elliptic operators with real, symmetric, bounded measurable coefficients.