Related papers: Probabilistic Learning on Manifolds
Although current semi-supervised medical segmentation methods can achieve decent performance, they are still affected by the uncertainty in unlabeled data and model predictions, and there is currently a lack of effective strategies that can…
Unsupervised discretization is a crucial step in many knowledge discovery tasks. The state-of-the-art method for one-dimensional data infers locally adaptive histograms using the minimum description length (MDL) principle, but the…
Dataset distillation aims to synthesize a compact subset of the original data, enabling models trained on it to achieve performance comparable to those trained on the original large dataset. Existing distribution-matching methods are…
The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution $P$ to another distribution $Q$…
For many interesting tasks, such as medical diagnosis and web page classification, a learner only has access to some positively labeled examples and many unlabeled examples. Learning from this type of data requires making assumptions about…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
This paper introduces a new probabilistic model for online learning which dynamically incorporates information from stochastic gradients of an arbitrary loss function. Similar to probabilistic filtering, the model maintains a Gaussian…
A fundamental problem in manifold learning is to approximate a functional relationship in a data chosen randomly from a probability distribution supported on a low dimensional sub-manifold of a high dimensional ambient Euclidean space. The…
When deploying a trained machine learning model in the real world, it is inevitable to receive inputs from out-of-distribution (OOD) sources. For instance, in continual learning settings, it is common to encounter OOD samples due to the…
Interpreting EEG signals linked to spoken language presents a complex challenge, given the data's intricate temporal and spatial attributes, as well as the various noise factors. Denoising diffusion probabilistic models (DDPMs), which have…
A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional…
We propose Riemannian Denoising Diffusion Probabilistic Models (RDDPMs) for learning distributions on submanifolds of Euclidean space that are level sets of functions, including most of the manifolds relevant to applications. Existing…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
This article presents a novel approach to construct Intrinsic Gaussian Processes for regression on unknown manifolds with probabilistic metrics (GPUM) in point clouds. In many real world applications, one often encounters high dimensional…
This paper proposes and analyzes a novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation. The proposed method is suitable for data generated from mixtures of…
The Minimal Learning Machine (MLM) is a nonlinear supervised approach based on learning a linear mapping between distance matrices computed in the input and output data spaces, where distances are calculated using a subset of points called…
Deep clustering, which learns representation and semantic clustering without labels information, poses a great challenge for deep learning-based approaches. Despite significant progress in recent years, most existing methods focus on…
This paper presents a nonlinear reduced-order modeling (ROM) framework that leverages deep learning and manifold learning to predict compressible flow fields with complex nonlinear features, including shock waves. The proposed DeepManifold…
In this work, we propose a novel framework for estimating the dimension of the data manifold using a trained diffusion model. A diffusion model approximates the score function i.e. the gradient of the log density of a noise-corrupted…
In the first part of this paper, we consider a family of continuous-time dynamical systems coupled with diffusion-transmutation processes. Under certain conditions, such randomly perturbed dynamical systems can be interpreted as an averaged…