Related papers: Diffusion-based method for producing density equal…
When auditing a redistricting plan, a persuasive method is to compare the plan with an ensemble of neutrally drawn redistricting plans. Ensembles are generated via algorithms that sample distributions on balanced graph partitions. To audit…
We present an algorithm for creating contiguous cartograms using meshes. We use numerical optimization to minimize cartographic error and distortion by transforming the mesh vertices. The vertices can either be optimized in the plane or…
Graph generation addresses the problem of generating new graphs that have a data distribution similar to real-world graphs. While previous diffusion-based graph generation methods have shown promising results, they often struggle to scale…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
The Diffusion Map is a nonlinear dimensionality reduction technique used to analyze high-dimensional data, with recent applications extending to datasets from the social sciences. Previous research has given little attention to how the…
Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology,…
Global visual geolocation predicts where an image was captured on Earth. Since images vary in how precisely they can be localized, this task inherently involves a significant degree of ambiguity. However, existing approaches are…
Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are…
Mapper, a topological algorithm, is frequently used as an exploratory tool to build a graphical representation of data. This representation can help to gain a better understanding of the intrinsic shape of high-dimensional genomic data and…
Our work focuses on addressing sample deficiency from low-density regions of data manifold in common image datasets. We leverage diffusion process based generative models to synthesize novel images from low-density regions. We observe that…
In this paper, we present a new statistical approach to automatically identify cancer regions in pathological images. The proposed method is built from statistical theory in line with evidence-based medicine. The two core technologies are…
The construction of deprivation indices is complicated by the inherent ambiguity in defining deprivation as well as the potential for partisan manipulation. Nevertheless, deprivation indices provide an essential tool for mitigating the…
State-of-the-art diffusion models can generate highly realistic images based on various conditioning like text, segmentation, and depth. However, an essential aspect often overlooked is the specific camera geometry used during image…
We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional datasets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other…
We propose a fast and scalable algorithm to project a given density on a set of structured measures defined over a compact 2D domain. The measures can be discrete or supported on curves for instance. The proposed principle and algorithm are…
We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding…
Density ratio estimation serves as an important technique in the unsupervised machine learning toolbox. However, such ratios are difficult to estimate for complex, high-dimensional data, particularly when the densities of interest are…
For an artist or a graphic designer, the spatial layout of a scene is a critical design choice. However, existing text-to-image diffusion models provide limited support for incorporating spatial information. This paper introduces Composite…
Diffusion maps (DM) constitute a classic dimension reduction technique, for data lying on or close to a (relatively) low-dimensional manifold embedded in a much larger dimensional space. The DM procedure consists in constructing a spectral…
The perception of high-definition maps is an integral component of environmental perception in autonomous driving systems. Existing research have often focused on online construction of high-definition maps. For instance, the Maptr[9]…