Related papers: Probabilistic Learning on Manifolds
Understanding the geometry of learned distributions is fundamental to improving and interpreting diffusion models, yet systematic tools for exploring their landscape remain limited. Standard latent-space interpolations fail to respect the…
A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally…
One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…
Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that is routinely generated. In applications that are constrained by memory and computational intensity, excessively large…
Choice behavior and preferences typically involve numerous and subjective aspects that are difficult to be identified and quantified. For this reason, their exploration is frequently conducted through the collection of ordinal evidence in…
Research on the distribution of prime numbers has revealed a dual character: deterministic in definition yet exhibiting statistical behavior reminiscent of random processes. In this paper we show that it is possible to use an image-focused…
Characterizing and controlling nonlinear, multi-scale phenomena play important roles in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex…
Diffusion models form an important class of generative models today, accounting for much of the state of the art in cutting edge AI research. While numerous extensions beyond image and video generation exist, few of such approaches address…
We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…
In the manifold learning problem one seeks to discover a smooth low dimensional surface, i.e., a manifold embedded in a higher dimensional linear vector space, based on a set of measured sample points on the surface. In this paper we…
Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent…
High-dimensional data are often assumed to lie on lower-dimensional manifolds. We study how to construct diffusion processes on this data manifold using only point cloud samples and without access to charts, projections, or other geometric…
Understanding the macroscopic characteristics of biological complexes demands precision and specificity in statistical ensemble modeling. One of the primary challenges in this domain lies in sampling from particular subsets of the…
This paper examines some methods and ideas underlying the author's successful probabilistic learning systems(PLS), which have proven uniquely effective and efficient in generalization learning or induction. While the emerging principles are…
The paper presents a Projection-Based Reduced-Order Model for simulations of high Reynolds turbulent flows. The PBROM are enhanced by incorporating various models of turbulent viscosity and residual closures to model the effects of…
Most work on supervised learning research has focused on marginal predictions. In decision problems, joint predictive distributions are essential for good performance. Previous work has developed methods for assessing low-order predictive…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
Recent years have witnessed increasing interests in prompt-based learning in which models can be trained on only a few annotated instances, making them suitable in low-resource settings. When using prompt-based learning for text…
Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…
In this paper, we propose a novel approach for manifold learning that combines the Earthmover's distance (EMD) with the diffusion maps method for dimensionality reduction. We demonstrate the potential benefits of this approach for learning…