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Optimization and generalization are two essential aspects of statistical machine learning. In this paper, we propose a framework to connect optimization with generalization by analyzing the generalization error based on the optimization…

Machine Learning · Statistics 2022-10-13 Fusheng Liu , Haizhao Yang , Soufiane Hayou , Qianxiao Li

We derive upper bounds on the generalization error of a learning algorithm in terms of the mutual information between its input and output. The bounds provide an information-theoretic understanding of generalization in learning problems,…

Machine Learning · Computer Science 2017-11-07 Aolin Xu , Maxim Raginsky

Diffusion models now generate high-quality, diverse samples, with an increasing focus on more powerful models. Although ensembling is a well-known way to improve supervised models, its application to unconditional score-based diffusion…

Machine Learning · Computer Science 2026-01-22 Raphaël Razafindralambo , Rémy Sun , Frédéric Precioso , Damien Garreau , Pierre-Alexandre Mattei

Modern deep neural networks can produce badly calibrated predictions, especially when train and test distributions are mismatched. Training an ensemble of models and averaging their predictions can help alleviate these issues. We propose a…

Machine Learning · Computer Science 2020-07-09 Asa Cooper Stickland , Iain Murray

Supervised online learning with an ensemble of students randomized by the choice of initial conditions is analyzed. For the case of the perceptron learning rule, asymptotically the same improvement in the generalization error of the…

Disordered Systems and Neural Networks · Physics 2009-10-31 R. Urbanczik

Existing generalization theories of supervised learning typically take a holistic approach and provide bounds for the expected generalization over the whole data distribution, which implicitly assumes that the model generalizes similarly…

Machine Learning · Computer Science 2024-01-08 Firas Laakom , Yuheng Bu , Moncef Gabbouj

Traditional machine learning approaches assume that data comes from a single generating mechanism, which may not hold for most real life data. In these cases, the single mechanism assumption can result in suboptimal performance. We…

Machine Learning · Computer Science 2025-01-31 Mehmet Efe Lorasdagi , Ahmet Berker Koc , Ali Taha Koc , Suleyman Serdar Kozat

Although being a crucial question for the development of machine learning algorithms, there is still no consensus on how to compare classifiers over multiple data sets with respect to several criteria. Every comparison framework is…

Machine Learning · Statistics 2023-07-06 Christoph Jansen , Malte Nalenz , Georg Schollmeyer , Thomas Augustin

Despite the ubiquitous use of stochastic optimization algorithms in machine learning, the precise impact of these algorithms and their dynamics on generalization performance in realistic non-convex settings is still poorly understood. While…

Machine Learning · Statistics 2022-07-12 Liam Hodgkinson , Umut Şimşekli , Rajiv Khanna , Michael W. Mahoney

Meta learning uses information from base learners (e.g. classifiers or estimators) as well as information about the learning problem to improve upon the performance of a single base learner. For example, the Bayes error rate of a given…

Machine Learning · Computer Science 2016-03-11 Kevin R. Moon , Veronique Delouille , Alfred O. Hero

One of the main open problems in the theory of multi-category margin classification is the form of the optimal dependency of a guaranteed risk on the number C of categories, the sample size m and the margin parameter gamma. From a practical…

Statistics Theory · Mathematics 2018-12-04 Khadija Musayeva , Fabien Lauer , Yann Guermeur

Recent work has focused on data-driven learning of the evolution of unknown systems via deep neural networks (DNNs), with the goal of conducting long time prediction of the evolution of the unknown system. Training a DNN with low…

Machine Learning · Computer Science 2022-12-28 Victor Churchill , Steve Manns , Zhen Chen , Dongbin Xiu

The choice of batch-size in a stochastic optimization algorithm plays a substantial role for both optimization and generalization. Increasing the batch-size used typically improves optimization but degrades generalization. To address the…

Machine Learning · Computer Science 2020-03-03 Yeming Wen , Kevin Luk , Maxime Gazeau , Guodong Zhang , Harris Chan , Jimmy Ba

Ensemble learning has gained success in machine learning with major advantages over other learning methods. Bagging is a prominent ensemble learning method that creates subgroups of data, known as bags, that are trained by individual…

Neural and Evolutionary Computing · Computer Science 2022-09-07 Giang Ngo , Rodney Beard , Rohitash Chandra

Highly overparametrized neural networks can display curiously strong generalization performance - a phenomenon that has recently garnered a wealth of theoretical and empirical research in order to better understand it. In contrast to most…

Machine Learning · Computer Science 2020-09-29 Jorg Bornschein , Francesco Visin , Simon Osindero

Experimental studies are a cornerstone of Machine Learning (ML) research. A common and often implicit assumption is that the study's results will generalize beyond the study itself, e.g., to new data. That is, repeating the same study under…

Machine Learning · Computer Science 2025-12-05 Federico Matteucci , Vadim Arzamasov , Jose Cribeiro-Ramallo , Marco Heyden , Konstantin Ntounas , Klemens Böhm

It has been recognized that the diversity of base learners is of utmost importance to a good ensemble. This paper defines a novel measurement of diversity, termed as exclusivity. With the designed exclusivity, we further propose an ensemble…

Machine Learning · Computer Science 2016-05-17 Xiaojie Guo

Deep learning models have lately shown great performance in various fields such as computer vision, speech recognition, speech translation, and natural language processing. However, alongside their state-of-the-art performance, it is still…

Machine Learning · Computer Science 2019-04-09 Daniel Jakubovitz , Raja Giryes , Miguel R. D. Rodrigues

The question why deep learning algorithms generalize so well has attracted increasing research interest. However, most of the well-established approaches, such as hypothesis capacity, stability or sparseness, have not provided complete…

Machine Learning · Computer Science 2017-11-07 Tom Zahavy , Bingyi Kang , Alex Sivak , Jiashi Feng , Huan Xu , Shie Mannor

Diversity or complementarity of experts in ensemble pattern recognition and information processing systems is widely-observed by researchers to be crucial for achieving performance improvement upon fusion. Understanding this link between…

Machine Learning · Statistics 2013-12-31 Kartik Audhkhasi , Abhinav Sethy , Bhuvana Ramabhadran , Shrikanth S. Narayanan