Related papers: Generalized level measure based on a family of con…
We present a generalized information-theoretic measure of synchronization in quantum systems. This measure is applicable to dynamics of anharmonic oscillators, few-level atoms, and coupled oscillator networks. Furthermore, the new measure…
This paper develops a generalized (quasi-) Bayes framework for conditional moment restriction models, where the parameter of interest is a nonparametric structural function of endogenous variables. We establish contraction rates for a class…
The technique known as group averaging provides powerful machinery for the study of constrained systems. However, it is likely to be well defined only in a limited set of cases. Here, we investigate the possibility of using a `renormalized'…
Researchers have developed ways to generalize the mean and variance to situations in which a data metric is available. We apply the tools developed in Pennec (2006) to categorical data, and show the generality of this approach by…
Generalization is at the core of machine learning models. However, the definition of generalization is not entirely clear. We employ set theory to introduce the concepts of algorithms, hypotheses, and dataset generalization. We analyze the…
A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.
In this paper we deal with conditional aggregation-based survival functions recently introduced by Boczek et al. (2020). The concept is worth to study because of its possible implementation in real-life situations and mathematical theory as…
Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous…
Databases in domains such as healthcare are routinely released to the public in aggregated form. Unfortunately, naive modeling with aggregated data may significantly diminish the accuracy of inferences at the individual level. This paper…
Generally, the measurement process consists in coupling a system to a detector that can give a continuous output. However, it may be interesting to use as a detector a system with a discrete spectrum, especially in view of applications to…
Parametric Gr\"obner bases have been studied for more than 15 years and are now a further developed subject. Here we propose a general study of parametric standard bases, that is with local orders. We mainly focus on the commutative case…
Let $\mu$ be a positive Borel measure on the interval $[0,1)$. For $\alpha>0$, the generalized Hankel matrix $\mathcal{H}_{\mu, \alpha}=(\mu_{n, k, \alpha})_{n, k \geq 0}$ with entries $\mu_{n, k, \alpha}=\int_{[0,1)}…
We generalize the measurement using an expanded concept of cover, in order to provide a new approach to size of set other than cardinality. The generalized measurement has application backgrounds such as a generalized problem in dimension…
Concentration of measure is studied, and obtained, for stable and related random vectors.
Density aggregation is a central problem in machine learning, for instance when combining predictions from a Deep Ensemble. The choice of aggregation remains an open question with two commonly proposed approaches being linear pooling…
We consider an empirical likelihood framework for inference for a statistical model based on an informative sampling design and population-level information. The population-level information is summarized in the form of estimating equations…
We introduce a framework of layered subsets, and give a sufficient condition for when a set system supports an agreement test. Agreement testing is a certain type of property testing that generalizes PCP tests such as the plane vs. plane…
Estimating the level set of a signal from measurements is a task that arises in a variety of fields, including medical imaging, astronomy, and digital elevation mapping. Motivated by scenarios where accurate and complete measurements of the…
In the present work we show that the local generalized monotonicity of a lower semicontinuous set-valued operator on some certain type of dense sets ensures the global generalized monotonicity of that operator. We achieve this goal…
Generalized contextuality is a possible indicator of non-classical behaviour in quantum information theory. In finite-dimensional systems, this is justified by the fact that noncontextual theories can be embedded into some simplex, i.e.…