相关论文: Transient anisotropic kernel for probabilistic lea…

This paper presents mathematical results in support of the methodology of the probabilistic learning on manifolds (PLoM) recently introduced by the authors, which has been used with success for analyzing complex engineering systems. The…

We present a generative learning framework for probabilistic sampling based on an extension of the Probabilistic Learning on Manifolds (PLoM) approach, which is designed to generate statistically consistent realizations of a random vector…

A novel extension of the Probabilistic Learning on Manifolds (PLoM) is presented. It makes it possible to synthesize solutions to a wide range of nonlinear stochastic boundary value problems described by partial differential equations…

In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…

Nonlinear manifold learning (ML) based reduced-order models (ROMs) can substantially improve the quality of nonlinear flow-field modeling. However, noise and the lack of physical information often distort the dimensionality-reduction…

Imitation Learning (IL) is a promising paradigm for teaching robots to perform novel tasks using demonstrations. Most existing approaches for IL utilize neural networks (NN), however, these methods suffer from several well-known…

Inertial algorithms for minimizing nonsmooth and nonconvex functions as the inertial proximal alternating linearized minimization algorithm (iPALM) have demonstrated their superiority with respect to computation time over their non inertial…

Diffusion Probabilistic Models (DPMs) have achieved strong generative performance, yet their inductive biases remain largely implicit. In this work, we aim to build inductive biases into the training and sampling of diffusion models to…

Streaming adaptations of manifold learning based dimensionality reduction methods, such as Isomap, are based on the assumption that a small initial batch of observations is enough for exact learning of the manifold, while remaining…

Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…

The performance of Visio-Language Transformers drops sharply when an input modality (e.g., image) is missing, because the model is forced to make predictions using incomplete information. Existing missing-aware prompt methods help reduce…

Masked Image Modeling (MIM) is a powerful self-supervised strategy for visual pre-training without the use of labels. MIM applies random crops to input images, processes them with an encoder, and then recovers the masked inputs with a…

This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that…

In this paper we study nonconvex and nonsmooth optimization problems with semi-algebraic data, where the variables vector is split into several blocks of variables. The problem consists of one smooth function of the entire variables vector…

Prototype-based methods are of the particular interest for domain specialists and practitioners as they summarize a dataset by a small set of representatives. Therefore, in a classification setting, interpretability of the prototypes is as…

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…

Multimodal learning seeks to combine data from multiple input sources to enhance the performance of different downstream tasks. In real-world scenarios, performance can degrade substantially if some input modalities are missing. Existing…

Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case.…

Transductive few-shot learning algorithms have showed substantially superior performance over their inductive counterparts by leveraging the unlabeled queries. However, the vast majority of such methods are evaluated on perfectly…

Wide accessibility of imaging and profile sensors in modern industrial systems created an abundance of high-dimensional sensing variables. This led to a a growing interest in the research of high-dimensional process monitoring. However,…