相关论文: Cluster Random Fields and Random-Shift Representat…

We study the extremes of multivariate regularly varying random fields. The crucial tools in our study are the tail field and the spectral field, notions that extend the tail and spectral processes of Basrak and Segers (2009). The spatial…

Given an $R^d$-valued random field (rf) $Z(t),t\in T$ and an $\alpha$-homogeneous mapping $\kappa$ we define the corresponding equivalent class of rf's (denoted by $K_\alpha$) which include representers of the same tail measure $\nu_Z$.…

Statistical Relational Learning (SRL) models have attracted significant attention due to their ability to model complex data while handling uncertainty. However, most of these models have been limited to discrete domains due to their…

The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…

Often we wish to predict a large number of variables that depend on each other as well as on other observed variables. Structured prediction methods are essentially a combination of classification and graphical modeling, combining the…

Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…

Conditional random fields (CRFs) have been shown to be one of the most successful approaches to sequence labeling. Various linear-chain neural CRFs (NCRFs) are developed to implement the non-linear node potentials in CRFs, but still keeping…

This paper presents a focused review of Markov random fields (MRFs)--commonly used probabilistic representations of spatial dependence in discrete spatial domains--for categorical data, with an emphasis on models for binary-valued…

Max-stable random fields provide canonical models for the dependence of multivariate extremes. Inference with such models has been challenging due to the lack of tractable likelihoods. In contrast, the finite dimensional cumulative…

We introduce chefs' random tables (CRTs), a new class of non-trigonometric random features (RFs) to approximate Gaussian and softmax kernels. CRTs are an alternative to standard random kitchen sink (RKS) methods, which inherently rely on…

Markov Random Fields (MRFs), a formulation widely used in generative image modeling, have long been plagued by the lack of expressive power. This issue is primarily due to the fact that conventional MRFs formulations tend to use simplistic…

We consider the clustering of extremes for stationary regularly varying random fields over arbitrary growing index sets. We study sufficient assumptions on the index set such that the limit of the point random fields of the exceedances…

Neural radiance fields (NeRFs) are a powerful tool for implicit scene representations, allowing for differentiable rendering and the ability to make predictions about unseen viewpoints. There has been growing interest in object and…

The cranked relativistic mean field (CRMF) theory is applied for the description of superdeformed (SD) rotational bands observed in $^{153}$Ho. The question of the structure of the so-called SD band in $^{154}$Er is also addressed and a…

Despite successful applications across a broad range of NLP tasks, conditional random fields ("CRFs"), in particular the linear-chain variant, are only able to model local features. While this has important benefits in terms of inference…

Random Forest (RF) is an ensemble supervised machine learning technique that was developed by Breiman over a decade ago. Compared with other ensemble techniques, it has proved its accuracy and superiority. Many researchers, however, believe…

Max-stable random fields are very appropriate for the statistical modelling of spatial extremes. Hence, integrals of functions of max-stable random fields over a given region can play a key role in the assessment of the risk of natural…

Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…

While LLMs have grown popular in sequence labeling, linear-chain conditional random fields (CRFs) remain a popular alternative with the ability to directly model interactions between labels. However, the Markov assumption limits them to %…

We consider a stationary random field indexed by an increasing sequence of subsets of $\mathbb{Z}^d$ obeying a very broad geometrical assumption on how the sequence expands. Under certain mixing and local conditions, we show how the tail…