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During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…

Numerical Analysis · Mathematics 2023-02-07 Michael J. Byrne , Rosemary A. Renaut

Conventional regularization is designed to control variance, but in small-data regression it can also aggravate underfitting when predictive signal is concentrated in weak directions of a restricted representation. We study a…

Machine Learning · Computer Science 2026-04-21 Dongseok Kim , Gisung Oh

Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty…

Machine Learning · Statistics 2025-12-01 Eliot Wong-Toi , Alex Boyd , Vincent Fortuin , Stephan Mandt

Closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have…

Numerical Analysis · Mathematics 2024-09-13 Benjamin Sanderse , Panos Stinis , Romit Maulik , Shady E. Ahmed

Fairness is a popular research topic in recent years. A research topic closely related to fairness is bias and debiasing. Among different types of bias problems, position bias is one of the most widely encountered symptoms. Position bias…

Information Retrieval · Computer Science 2024-01-31 Hao Wang

This paper studies $\ell_1$ regularization with high-dimensional features for support vector machines with a built-in reject option (meaning that the decision of classifying an observation can be withheld at a cost lower than that of…

Statistics Theory · Mathematics 2012-01-06 Marten Wegkamp , Ming Yuan

Regularization plays an important role in generalization of deep neural networks, which are often prone to overfitting with their numerous parameters. L1 and L2 regularizers are common regularization tools in machine learning with their…

Machine Learning · Computer Science 2019-10-21 Dae Hoon Park , Chiu Man Ho , Yi Chang , Huaqing Zhang

Time series forecasting is at the core of important application domains posing significant challenges to machine learning algorithms. Recently neural network architectures have been widely applied to the problem of time series forecasting.…

Machine Learning · Computer Science 2022-07-28 Chrysoula Kosma , Giannis Nikolentzos , Nancy Xu , Michalis Vazirgiannis

Dropout is a very effective way of regularizing neural networks. Stochastically "dropping out" units with a certain probability discourages over-specific co-adaptations of feature detectors, preventing overfitting and improving network…

Neural and Evolutionary Computing · Computer Science 2017-08-04 Pietro Morerio , Jacopo Cavazza , Riccardo Volpi , Rene Vidal , Vittorio Murino

Neural networks are more expressive when they have multiple layers. In turn, conventional training methods are only successful if the depth does not lead to numerical issues such as exploding or vanishing gradients, which occur less…

Machine Learning · Computer Science 2022-06-07 Carles Riera , Camilo Rey , Thiago Serra , Eloi Puertas , Oriol Pujol

Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…

Numerical Analysis · Mathematics 2007-05-23 Alexandre J. Chorin , Panagiotis Stinis

Ensemble methods are known for enhancing the accuracy and robustness of machine learning models by combining multiple base learners. However, standard approaches like greedy or random ensembling often fall short, as they assume a constant…

Machine Learning · Computer Science 2025-06-24 Sebastian Pineda Arango , Maciej Janowski , Lennart Purucker , Arber Zela , Frank Hutter , Josif Grabocka

Generalization is a central problem in Machine Learning. Indeed most prediction methods require careful calibration of hyperparameters usually carried out on a hold-out \textit{validation} dataset to achieve generalization. The main goal of…

Machine Learning · Statistics 2021-02-18 Karim Lounici , Katia Meziani , Benjamin Riu

In many real world applications of machine learning, models have to meet certain domain-based requirements that can be expressed as constraints (e.g., safety-critical constraints in autonomous driving systems). Such constraints are often…

Machine Learning · Computer Science 2022-06-20 Kshitij Goyal , Sebastijan Dumancic , Hendrik Blockeel

This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…

Machine Learning · Computer Science 2021-12-10 Martin Burger

Reinforcement learning with evaluation metrics as rewards is widely used to enhance specific capabilities of language models. However, for tasks such as factually consistent summarisation, existing metrics remain underdeveloped, limiting…

Computation and Language · Computer Science 2026-05-27 Yuxuan Ye , Raul Santos-Rodriguez , Edwin Simpson

We investigate different methods for regularizing quantile regression when predicting either a subset of quantiles or the full inverse CDF. We show that minimizing an expected pinball loss over a continuous distribution of quantiles is a…

Machine Learning · Statistics 2021-02-11 Taman Narayan , Serena Wang , Kevin Canini , Maya Gupta

This paper describes a new approach on optimization of constraint satisfaction problems (CSPs) by means of substituting sub-CSPs with locally consistent regular membership constraints. The purpose of this approach is to reduce the number of…

Artificial Intelligence · Computer Science 2019-08-19 Sven Löffler , Ke Liu , Petra Hofstedt

In this paper we explore the relation between distributionally robust learning and different forms of regularization to enforce robustness of deep neural networks. In particular, starting from a concrete min-max distributionally robust…

Optimization and Control · Mathematics 2022-03-29 Camilo Garcia Trillos , Nicolas Garcia Trillos

With the growing attention on learning-to-learn new tasks using only a few examples, meta-learning has been widely used in numerous problems such as few-shot classification, reinforcement learning, and domain generalization. However,…

Computer Vision and Pattern Recognition · Computer Science 2020-04-14 Hung-Yu Tseng , Yi-Wen Chen , Yi-Hsuan Tsai , Sifei Liu , Yen-Yu Lin , Ming-Hsuan Yang