Related papers: Diffusion maps for changing data
One of the fundamental problems within the field of machine learning is dimensionality reduction. Dimensionality reduction methods make it possible to combat the so-called curse of dimensionality, visualize high-dimensional data and, in…
Diffusion models have emerged from various theoretical and methodological perspectives, each offering unique insights into their underlying principles. In this work, we provide an overview of the most prominent approaches, drawing attention…
We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…
Real-world data generation often involves certain geometries (e.g., graphs) that induce instance-level interdependence. This characteristic makes the generalization of learning models more difficult due to the intricate interdependent…
Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and…
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
Diffusion describes the motion of microscopic entities from regions of high concentration to regions of low concentration. In multiplex networks, flows can occur both within and across layers, and super-diffusion, a regime where the time…
We introduce a data-driven dynamic factor framework for modeling the joint evolution of high-dimensional covariates and responses without parametric assumptions. Standard factor models applied to covariates alone often lose explanatory…
Normal and anomalous diffusion are ubiquitous in many complex systems [1] . Here, we define a time and space generalized diffusion equation (GDE), which uses fractional-time derivatives and transformed d-path Laplacian operators on…
The analysis of data sometimes requires fitting many free parameters in a theory to a large number of data points. Questions naturally arise about the compatibility of specific subsets of the data, such as those from a particular experiment…
Compositional diffusion models offer a promising route to long-horizon planning by denoising multiple overlapping sub-trajectories while ensuring that together they constitute a global solution. However, enforcing local behavior over long…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
As a class of generative artificial intelligence frameworks inspired by statistical physics, diffusion models have shown extraordinary performance in synthesizing complicated data distributions through a denoising process gradually guided…
Graphs are widespread data structures used to model a wide variety of problems. The sheer amount of data to be processed has prompted the creation of a myriad of systems that help us cope with massive scale graphs. The pressure to deliver…
We analyze information diffusion using empirical data that tracks online communication around two instances of mass political mobilization, including the year that lapsed in-between the protests. We compare the global properties of the…
Homology-based invariants can be used to characterize the geometry of datasets and thereby gain some understanding of the processes generating those datasets. In this work we investigate how the geometry of a dataset changes when it is…
Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which…
The diffusion maps embedding of data lying on a manifold has shown success in tasks such as dimensionality reduction, clustering, and data visualization. In this work, we consider embedding data sets that were sampled from a manifold which…
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…