Related papers: Spatial Coupling as a Proof Technique
In a series of papers (Lombardi & Schneider 2001, 2002) we studied in detail the statistical properties of an interpolation technique widely used in astronomy. In particular, we considered the average interpolated map and its covariance…
Mixup refers to interpolation-based data augmentation, originally motivated as a way to go beyond empirical risk minimization (ERM). Its extensions mostly focus on the definition of interpolation and the space (input or feature) where it…
Linear nested codes, where two or more sub-codes are nested in a global code, have been proposed as candidates for reliable multi-terminal communication. In this paper, we consider nested array-based spatially coupled low-density…
We prove an $l^p$ decoupling inequality for hypersurfaces with nonzero Gaussian curvature and use it to derive a corresponding $l^p$ decoupling for curves not contained in a hyperplane. This extends our earlier work from [2]
Spectral Method is a commonly used scheme to cluster data points lying close to Union of Subspaces by first constructing a Random Geometry Graph, called Subspace Clustering. This paper establishes a theory to analyze this method. Based on…
We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…
The coupled entropy, $H_\kappa,$ is proven to uniquely satisfy the requirement that a generalized entropy be a measure of the uncertainty at the scale, $\sigma,$ for a class of non-exponential distributions. The coupled stretched…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
Spatial pattern formation is a key feature of many natural systems in physics, chemistry and biology. The essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo…
We present a method for finding cross-modal space-time correspondences. Given two images from different visual modalities, such as an RGB image and a depth map, our model identifies which pairs of pixels correspond to the same physical…
We show that a simple telescoping sum trick, together with the triangle inequality and a tensorisation property of expected-contractive coefficients of random channels, allow us to achieve general simultaneous decoupling for multiple users…
Multimodal data is a precious asset enabling a variety of downstream tasks in machine learning. However, real-world data collected across different modalities is often not paired, which is a significant challenge to learn a joint…
This paper offers an expository overview of the field of spatial econometrics. It first justifies the necessity of special statistical procedures for the analysis of spatial data and then proceeds to describe the fundamentals of these…
We present angle-uniform parallel coordinates, a data-independent technique that deforms the image plane of parallel coordinates so that the angles of linear relationships between two variables are linearly mapped along the horizontal axis…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional relationship between the dimension (say, $p$) and the sample size (say,…
Contrastive language--audio pretraining (CLAP) has achieved remarkable success as an audio--text embedding framework, but existing approaches are limited to monaural or single-source conditions and cannot fully capture spatial information.…
As the interference in PPP based wireless networks exhibit spatial correlation, any joint analysis involving multiple spatial points either end up with numerical integrations over $\mathbb{R}^2$ or become analytically too intractable. To…
Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…
Estimating spatially distributed information through the interpolation of scattered observation datasets often overlooks the critical role of domain knowledge in understanding spatial dependencies. Additionally, the features of these data…