Related papers: On Some Generalisations of Gauss Sequences
In the Bayesian literature on model comparison, Bayes factors play the leading role. In the classical statistical literature, model selection criteria are often devised used cross-validation ideas. Amalgamating the ideas of Bayes factor and…
This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…
We introduce the notions of sub Gaussian random variables in sub-linear expectation spaces. To avoid the problem caused by the existence of two different expectations, i.e., the upper expectation and the lower expectation, we divide the…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
The notion of the orbifold Euler characteristic came from physics at the end of 80's. There were defined higher order versions of the orbifold Euler characteristic and generalized ("motivic") versions of them. In a previous paper the…
Non-Gaussian quantum states of light are essential resources for quantum information processing and precision metrology. Among them, generalized coherent states (GCS), which naturally arise from the evolution of a coherent state with a…
In this paper we consider probabilistic analogues of some classical integral geometric formulae: Weyl--Steiner tube formulae and the Chern--Federer kinematic fundamental formula. The probabilistic building blocks are smooth, real-valued…
Gaussian process (GP) methods have been widely studied recently, especially for large-scale systems with big data and even more extreme cases when data is sparse. Key advantages of these methods consist in: 1) the ability to provide…
In this note, we explore two families of sequences associated to a suitable integer sequence: the gap-sum sequence and the gap-product sequence. These are the sums and the products of consecutive numbers not in the original sequence. We…
Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. We provide Gaussian process models based on pseudo-likelihood approximation to perform sequence labeling. Gaussian…
A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the…
The metric $D_\alpha (q,q')$ on the set $Q$ of particle locations of a homogeneous Poisson process on $R^d$, defined as the infimum of $(\sum_i |q_i - q_{i+1}|^\alpha)^{1/\alpha}$ over sequences in $Q$ starting with $q$ and ending with $q'$…
Let X=(X^0,\mu,T) be an ergodic measure preserving system. For a natural number k we consider the averages (*) 1/N \sum_{n=1}^N \prod_{j=1}^k f_j(T^{n a_j}x) where the functions f_j are bounded, and a_j are integers. A factor of X is…
The cross number of a sequence over a finite abelian group $G$ is the sum of the inverse orders of the terms of that sequence. We study two group invariants, the maximal cross number of a zero-sum free sequence over $G$, called…
In this article we consider a new derivation mode for generalized communicating P systems (GCPS) corresponding to the functioning of population protocols (PP) and based on the sequential derivation mode and a fairness condition. We show…
In this article we outline a rather general construction of diffeomorphism covariant coherent states for quantum gauge theories. By this we mean states $\psi_{(A,E)}$, labelled by a point (A,E) in the classical phase space, consisting of…
In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…
Recently a non-perturbative formula for the RG flow between UV and IR fixed points of the coefficient in the trace of the energy momentum tensor of the Euler density has been obtained for N=1 SUSY gauge theories by relating the trace and…
The ruler function or the Gros sequence is a classical infinite integer sequence that is underlying some interesting mathematical problems. In this paper, we provide four new problems containing this type of sequence: (i) a demographic…
Graph-structured data appears frequently in domains including chemistry, natural language semantics, social networks, and knowledge bases. In this work, we study feature learning techniques for graph-structured inputs. Our starting point is…