相关论文: A note on non-classical Nonstandard Arithmetic

Given a directed graph, the Minimal Feedback Arc Set (FAS) problem asks for a minimal set of arcs which, when removed, results in an acyclic graph. Equivalently, the FAS problem asks to find an ordering of the vertices that minimizes the…

For statistical decision problems with finite parameter space, it is well-known that the upper value (minimax value) agrees with the lower value (maximin value). Only under a generalized notion of prior does such an equivalence carry over…

In this paper, we study properties of sensitivity, transitivity and chaos for non-autonomous discrete systems(NDS). Firstly, we present some different sufficient conditions for NDS to be chaotic. Then, we relate the transitivity with the…

Humans can observe a single, imperfect demonstration and immediately generalize to very different problem settings. Robots, in contrast, often require hundreds of examples and still struggle to generalize beyond the training conditions. We…

We study the problem of learning directed acyclic graphs from continuous observational data, generated according to a linear Gaussian structural equation model. State-of-the-art structure learning methods for this setting have at least one…

In this article, we show that R.H. Bing's pseudo-circle admits a minimal non-invertible map. This resolves a problem raised by Bruin, Kolyada and Snoha in the negative. The main tool is the Denjoy-Rees technique, further developed by…

In real-world recommender systems, implicitly collected user feedback, while abundant, often includes noisy false-positive and false-negative interactions. The possible misinterpretations of the user-item interactions pose a significant…

A new proof of the equivalence of the Taut String Algorithm and the one-dimensional Rudin-Osher-Fatemi model is presented. Based on duality and the projection theorem in Hilbert space, the proof is strictly elementary. Existence and…

This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…

Physical systems may couple to other systems through variables that are not gauge invariant. When we split a gauge system into two subsystems, the gauge-invariant variables of the two subsystems have less information than the gauge…

In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…

A system is invariant with respect to an input transformation if we can transform any dynamic input by this function and obtain the same output dynamics after adjusting the initial conditions appropriately. Often, the set of all such input…

We consider a class of tempered subordinators, namely a class of subordinators with one-dimensional marginal tempered distributions which belong to a family studied in [3]. The main contribution in this paper is a non-central moderate…

Adaptive data analysis is frequently criticized for its pessimistic generalization guarantees. The source of these pessimistic bounds is a model that permits arbitrary, possibly adversarial analysts that optimally use information to bias…

We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We are guided by the theory of sparse stochastic processes,…

Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…

We investigate and compare the fundamental performance of several distributed learning methods that have been proposed recently. We do this in the context of a distributed version of the classical signal-in-Gaussian-white-noise model, which…

Multi-output Gaussian process (MGP) has been attracting increasing attention as a transfer learning method to model multiple outputs. Despite its high flexibility and generality, MGP still faces two critical challenges when applied to…

Restricting the chain-antichain principle CAC to partially ordered sets which respect the natural ordering of the integers is a trivial distinction in the sense of classical reverse mathematics. We utilize computability-theoretic reductions…

We present the basic theory of central subsets of semigroups from the nonstandard perspective. A key feature of this perspective is the replacement of the algebra of ultrafilters with the algebra of elements of iterated hyperextensions, a…