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In this work, we address the problem of polynomial interpolation of non-pointwise data. More specifically, we assume that our input information comes from measurements obtained on diffuse compact domains. Although the nodal and the diffused…

Numerical Analysis · Mathematics 2025-09-22 Ludovico Bruni Bruno , Stefano De Marchi , Giacomo Elefante

The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…

Chemical Physics · Physics 2016-08-24 Markus Kowalewski , Elisabeth Larsson , Alfa Heryudono

Mixup is an efficient data augmentation approach that improves the generalization of neural networks by smoothing the decision boundary with mixed data. Recently, dynamic mixup methods have improved previous static policies effectively…

Machine Learning · Computer Science 2023-10-24 Zicheng Liu , Siyuan Li , Ge Wang , Cheng Tan , Lirong Wu , Stan Z. Li

Recent advances in semi-supervised learning have shown tremendous potential in overcoming a major barrier to the success of modern machine learning algorithms: access to vast amounts of human-labeled training data. Previous algorithms based…

Machine Learning · Computer Science 2019-11-22 Phi Vu Tran

Recently, flow-based methods have achieved promising success in video frame interpolation. However, electron microscopic (EM) images suffer from unstable image quality, low PSNR, and disorderly deformation. Existing flow-based interpolation…

Computer Vision and Pattern Recognition · Computer Science 2021-01-19 Zejin Wang , Guodong Sun , Lina Zhang , Guoqing Li , Hua Han

As an effective data augmentation method, Mixup synthesizes an extra amount of samples through linear interpolations. Despite its theoretical dependency on data properties, Mixup reportedly performs well as a regularizer and calibrator…

Machine Learning · Computer Science 2023-11-01 Aiyang Han , Chuanxing Geng , Songcan Chen

We propose a new nonconforming \(P_1\) finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of…

Numerical Analysis · Mathematics 2025-10-08 Chenchen Geng , Hua Wang , Qichen Zhang

The mutual information (MI) between two random variables is an important correlation measure in data analysis. The Shannon entropy of a joint probability distribution is the variable part under fixed marginals. We aim to minimize and…

Optimization and Control · Mathematics 2025-09-08 Paula Franke , Kay Hamacher , Paul Manns

We introduce Noisy Feature Mixup (NFM), an inexpensive yet effective method for data augmentation that combines the best of interpolation based training and noise injection schemes. Rather than training with convex combinations of pairs of…

Machine Learning · Computer Science 2023-05-23 Soon Hoe Lim , N. Benjamin Erichson , Francisco Utrera , Winnie Xu , Michael W. Mahoney

We propose a randomized multiplicative weight update (MWU) algorithm for $\ell_{\infty}$ regression that runs in $\widetilde{O}\left(n^{2+1/22.5} \text{poly}(1/\epsilon)\right)$ time when $\omega = 2+o(1)$, improving upon the previous best…

Data Structures and Algorithms · Computer Science 2025-04-29 Deeksha Adil , Shunhua Jiang , Rasmus Kyng

We introduce Interpolation Consistency Training (ICT), a simple and computation efficient algorithm for training Deep Neural Networks in the semi-supervised learning paradigm. ICT encourages the prediction at an interpolation of unlabeled…

Machine Learning · Statistics 2022-10-20 Vikas Verma , Kenji Kawaguchi , Alex Lamb , Juho Kannala , Arno Solin , Yoshua Bengio , David Lopez-Paz

Multimodal recommendation aims to integrate collaborative signals with heterogeneous content such as visual and textual information, but remains challenged by modality-specific noise, semantic inconsistency, and unstable propagation over…

Information Retrieval · Computer Science 2026-02-02 Wei Yang , Rui Zhong , Yiqun Chen , Chi Lu , Peng Jiang

Data augmentation by mixing samples, such as Mixup, has widely been used typically for classification tasks. However, this strategy is not always effective due to the gap between augmented samples for training and original samples for…

Machine Learning · Computer Science 2019-06-21 Takuya Shimada , Shoichiro Yamaguchi , Kohei Hayashi , Sosuke Kobayashi

Presently the most successful approaches to semi-supervised learning are based on consistency regularization, whereby a model is trained to be robust to small perturbations of its inputs and parameters. To understand consistency…

Machine Learning · Computer Science 2019-02-22 Ben Athiwaratkun , Marc Finzi , Pavel Izmailov , Andrew Gordon Wilson

Cross-modal hashing is an important approach for multimodal data management and application. Existing unsupervised cross-modal hashing algorithms mainly rely on data features in pre-trained models to mine their similarity relationships.…

Information Retrieval · Computer Science 2022-07-12 Liang Li , Baihua Zheng , Weiwei Sun

Image interpolation is a special case of image super-resolution, where the low-resolution image is directly down-sampled from its high-resolution counterpart without blurring and noise. Therefore, assumptions adopted in super-resolution…

Image and Video Processing · Electrical Eng. & Systems 2020-10-28 Junchao Zhang

Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…

Numerical Analysis · Mathematics 2024-12-16 Bosu Choi , Jihun Han , Yoonsang Lee

When selecting data to build machine learning models in practical applications, factors such as availability, acquisition cost, and discriminatory power are crucial considerations. Different data modalities often capture unique aspects of…

Machine Learning · Computer Science 2024-10-31 Chang Liu , Jieshi Chen , Lee H. Harrison , Artur Dubrawski

Many recent semi-supervised learning (SSL) studies build teacher-student architecture and train the student network by the generated supervisory signal from the teacher. Data augmentation strategy plays a significant role in the SSL…

Computer Vision and Pattern Recognition · Computer Science 2022-03-16 JongMok Kim , Jooyoung Jang , Seunghyeon Seo , Jisoo Jeong , Jongkeun Na , Nojun Kwak

Finding well-defined clusters in data represents a fundamental challenge for many data-driven applications, and largely depends on good data representation. Drawing on literature regarding representation learning, studies suggest that one…

Machine Learning · Computer Science 2020-11-05 Daniel Lutscher , Ali el Hassouni , Maarten Stol , Mark Hoogendoorn
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