Related papers: Cluster Random Fields and Random-Shift Representat…
Bipartite field theories (BFTs) are a new class of 4d N=1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces. In this paper we derive, purely in terms of the gauge theory, the cluster transformations of face…
Random Forests (RFs) are strong machine learning tools for classification and regression. However, they remain supervised algorithms, and no extension of RFs to the one-class setting has been proposed, except for techniques based on…
Gaussian random fields (GRFs) constitute an important part of spatial modelling, but can be computationally infeasible for general covariance structures. An efficient approach is to specify GRFs via stochastic partial differential equations…
Recent work on approximating ground states of Heisenberg spin clusters by projected Hartree-Fock theory (PHF) is extended to a cluster-based ansatz (cPHF). Whereas PHF variationally optimizes a site-spin product state for the restoration of…
The extremal tail probabilities of moving sums in a marked Poisson random field is examined here. These sums are computed by adding up the weighted occurrences of events lying within a scanning set of fixed shape and size. Change of measure…
We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter…
Reinforcement learning (RL) has become the de facto method for achieving locomotion on humanoid robots in practice, yet stability analysis of the corresponding control policies is lacking. Recent work has attempted to merge control…
We present a catalog of 1921 spectroscopic redshifts measured in the fields of the massive galaxy clusters MACSJ0416.1--2403 ($z=0.397$), MACSJ0717.5+3745 ($z=0.546$), and MACSJ1149.5+2223 ($z=0.544$), i.e., three of the four clusters…
Classical clustering methods usually return either a finite partition of the observed data or a finite dendrogram over it. This finite-sample view is inadequate when the hierarchy of interest is a recursive geometric object with fine-scale…
Neural Radiance Fields (NeRF) have demonstrated very impressive performance in novel view synthesis via implicitly modelling 3D representations from multi-view 2D images. However, most existing studies train NeRF models with either…
In this paper, we consider a classic problem concerning the high excursion probabilities of a Gaussian random field $f$ living on a compact set $T$. We develop efficient computational methods for the tail probabilities $P(\sup_T f(t) > b)$…
Radiance Fields (RFs) have shown great potential to represent scenes from casually captured discrete views. Compositing parts or whole of multiple captured scenes could greatly interest several XR applications. Prior works can generate new…
Neural Radiance Field (NeRF), capable of synthesizing high-quality novel viewpoint images, suffers from issues like artifact occurrence due to its fixed sampling points during rendering. This study proposes a method that optimizes sampling…
Cluster variables have recently revolutionized numerical work in certain models involving fermionic variables. This novel representation of fermionic partition functions is continuing to find new applications. After describing results from…
Exact results for product-form stationary distributions of Markov chains are of interest in different fields. In stochastic reaction networks (CRNs), stationary distributions are mostly known in special cases where they are of product-form.…
We introduce in this paper the mechanism of graph random features (GRFs). GRFs can be used to construct unbiased randomized estimators of several important kernels defined on graphs' nodes, in particular the regularized Laplacian kernel. As…
Continuous-time random walks (CTRW) play important role in understanding of a wide range of phenomena. However, most theoretical studies of these models concentrate only on stationary-state dynamics. We present a new theoretical approach,…
Clustered sampling is prevalent in empirical regression discontinuity (RD) designs, but it has not received much attention in the theoretical literature. In this paper, we introduce a general model-based framework for such settings and…
Relativistic scalar fields are ubiquitous in modified theories of gravity. An important tool in understanding their impact on structure formation, especially in the context of N-body simulations, is the quasi-static approximation in which…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…