Related papers: Probabilistic Learning on Manifolds
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…
Generative models such as diffusion models, excel at capturing high-dimensional distributions with diverse input modalities, e.g. robot trajectories, but are less effective at multi-step constraint reasoning. Task and Motion Planning (TAMP)…
Normalizing flows are invertible neural networks with tractable change-of-volume terms, which allow optimization of their parameters to be efficiently performed via maximum likelihood. However, data of interest are typically assumed to live…
We develop an Euler-type method to predict the evolution of a time-dependent probability measure without explicitly learning an operator that governs its evolution. We use linearized optimal transport theory to prove that the measure-valued…
Few-shot learning is a rapidly evolving area of research in machine learning where the goal is to classify unlabeled data with only one or "a few" labeled exemplary samples. Neural networks are typically trained to minimize a distance…
Sampling from learned high-dimensional distributions is a foundational computational problem. We introduce U-turn chains: Markov chains obtained by iterating short forward-backward steps of a diffusion model, in which each step proposes a…
DIPLODOCUS (Distribution-In-PLateaux methODOlogy for the CompUtation of transport equationS) is a novel framework being developed for the mesoscopic modelling of astrophysical systems via the transport of particle distribution functions…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…
Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($\sigma \to 0$). In this work, we propose an alternative perspective: their success…
A key element in transfer learning is representation learning; if representations can be developed that expose the relevant factors underlying the data, then new tasks and domains can be learned readily based on mappings of these salient…
In the absence of prior knowledge, ordinal embedding methods obtain new representation for items in a low-dimensional Euclidean space via a set of quadruple-wise comparisons. These ordinal comparisons often come from human annotators, and…
Foundation models enable prompt-based classifiers for zero-shot and few-shot learning. Nonetheless, the conventional method of employing fixed prompts suffers from distributional shifts that negatively impact generalizability to unseen…
Manifold learning seeks a low dimensional representation that faithfully captures the essence of data. Current methods can successfully learn such representations, but do not provide a meaningful set of operations that are associated with…
Learning from point sets is an essential component in many computer vision and machine learning applications. Native, unordered, and permutation invariant set structure space is challenging to model, particularly for point set…
In this paper, a novel diffusion estimation algorithm is proposed from a probabilistic perspective by combining diffusion strategy and the probabilistic least-mean-squares (PLMS) at all agents. The proposed method diffusion probabilistic…
Diffusion models are increasingly used as powerful conditional generators, yet real deployments often involve multiple target distributions arising from different tasks, e.g., diverse prompt domains in text-to-image generation, or multiple…
This paper tackles the challenge presented by small-data to the task of Bayesian inference. A novel methodology, based on manifold learning and manifold sampling, is proposed for solving this computational statistics problem under the…
Machine learning (ML) has become a versatile tool for analyzing anomalous diffusion trajectories, yet most existing pipelines are trained on large collections of simulated data. In contrast, experimental trajectories, such as those from…
Generally, reduced order models of fluid flows are obtained by projecting the Navier-Stokes equations onto a reduced subspace spanned by vector functions that carry the meaningful information of the dynamics. A common method to generate…