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Learning intersections of halfspaces is a central problem in Computational Learning Theory. Even for just two halfspaces, it remains a major open question whether learning is possible in polynomial time with respect to the margin $\gamma$…

Machine Learning · Computer Science 2025-11-18 Ilias Diakonikolas , Mingchen Ma , Lisheng Ren , Christos Tzamos

We give a new algorithm for learning mixtures of $k$ Gaussians (with identity covariance in $\mathbb{R}^n$) to TV error $\varepsilon$, with quasi-polynomial ($O(n^{\text{poly\,log}\left(\frac{n+k}{\varepsilon}\right)})$) time and sample…

Machine Learning · Computer Science 2025-03-05 Khashayar Gatmiry , Jonathan Kelner , Holden Lee

We consider mixtures of $k\geq 2$ Gaussian components with unknown means and unknown covariance (identical for all components) that are well-separated, i.e., distinct components have statistical overlap at most $k^{-C}$ for a large enough…

Machine Learning · Computer Science 2023-06-09 Rares-Darius Buhai , David Steurer

Fair top-$k$ selection, which ensures appropriate proportional representation of members from minority or historically disadvantaged groups among the top-$k$ selected candidates, has drawn significant attention. We study the problem of…

Data Structures and Algorithms · Computer Science 2026-03-31 Guangya Cai

Multi-group agnostic learning is a formal learning criterion that is concerned with the conditional risks of predictors within subgroups of a population. The criterion addresses recent practical concerns such as subgroup fairness and hidden…

Machine Learning · Computer Science 2024-06-18 Christopher Tosh , Daniel Hsu

Attribute-efficient PAC learning of sparse halfspaces has been a fundamental problem in machine learning theory. In recent years, machine learning algorithms are faced with prevalent data corruptions or even malicious attacks. It is of…

Machine Learning · Computer Science 2026-03-06 Shiwei Zeng , Jie Shen

The study of fair algorithms has become mainstream in machine learning and artificial intelligence due to its increasing demand in dealing with biases and discrimination. Along this line, researchers have considered fair versions of…

Data Structures and Algorithms · Computer Science 2023-01-11 Sayan Bandyapadhyay , Fedor V. Fomin , Tanmay Inamdar , Kirill Simonov

We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…

Machine Learning · Computer Science 2023-07-18 Ilias Diakonikolas , Jelena Diakonikolas , Daniel M. Kane , Puqian Wang , Nikos Zarifis

The goal in thinning is to summarize a dataset using a small set of representative points. Remarkably, sub-Gaussian thinning algorithms like Kernel Halving and Compress can match the quality of uniform subsampling while substantially…

Machine Learning · Statistics 2026-03-03 Annabelle Michael Carrell , Albert Gong , Abhishek Shetty , Raaz Dwivedi , Lester Mackey

Algorithms are increasingly used to automate or aid human decisions, yet recent research shows that these algorithms may exhibit bias across legally protected demographic groups. However, data on these groups may be unavailable to…

Computers and Society · Computer Science 2026-02-17 Floris Holstege , Mackenzie Jorgensen , Kirtan Padh , Jurriaan Parie , Krsto Prorokovic , Joel Persson , Lukas Snoek

We consider the problem of boosting the accuracy of weak learning algorithms in the agnostic learning framework of Haussler (1992) and Kearns et al. (1992). Known algorithms for this problem (Ben-David et al., 2001; Gavinsky, 2002; Kalai et…

Machine Learning · Computer Science 2012-02-22 Vitaly Feldman

The problem of Non-Gaussian Component Analysis (NGCA) is about finding a maximal low-dimensional subspace $E$ in $\mathbb{R}^n$ so that data points projected onto $E$ follow a non-gaussian distribution. Although this is an appropriate model…

Machine Learning · Computer Science 2017-04-05 Yan Shuo Tan , Roman Vershynin

Fairness-aware classification models have gained increasing attention in recent years as concerns grow on discrimination against some demographic groups. Most existing models require full knowledge of the sensitive features, which can be…

Machine Learning · Computer Science 2025-05-02 Kaiqi Jiang , Wenzhe Fan , Mao Li , Xinhua Zhang

Group-fairness in classification aims for equality of a predictive utility across different sensitive sub-populations, e.g., race or gender. Equality or near-equality constraints in group-fairness often worsen not only the aggregate utility…

Machine Learning · Computer Science 2021-06-01 Kulin Shah , Pooja Gupta , Amit Deshpande , Chiranjib Bhattacharyya

The growing capability and accessibility of machine learning has led to its application to many real-world domains and data about people. Despite the benefits algorithmic systems may bring, models can reflect, inject, or exacerbate implicit…

Machine Learning · Computer Science 2021-10-28 Ángel Alexander Cabrera , Will Epperson , Fred Hohman , Minsuk Kahng , Jamie Morgenstern , Duen Horng Chau

Unsupervised anomaly detection is a critical task in many high-social-impact applications such as finance, healthcare, social media, and cybersecurity, where demographics involving age, gender, race, disease, etc, are used frequently. In…

Machine Learning · Computer Science 2025-05-19 Feng Xiao , Xiaoying Tang , Jicong Fan

In this work, we revisit the problem of estimating the mean and covariance of an unknown $d$-dimensional Gaussian distribution in the presence of an $\varepsilon$-fraction of adversarial outliers. The pioneering work of [DKK+16] gave a…

Data Structures and Algorithms · Computer Science 2021-10-25 Pravesh K. Kothari , Peter Manohar , Brian Hu Zhang

With the rapid development of quantum computers, quantum algorithms have been studied extensively. However, quantum algorithms tackling statistical problems are still lacking. In this paper, we propose a novel non-oracular quantum adaptive…

Methodology · Statistics 2021-07-20 Wenxuan Zhong , Yuan Ke , Ye Wang , Yongkai Chen , Jinyang Chen , Ping Ma

In distributional or average-case analysis, the goal is to design an algorithm with good-on-average performance with respect to a specific probability distribution. Distributional analysis can be useful for the study of general-purpose…

Data Structures and Algorithms · Computer Science 2020-07-28 Tim Roughgarden

In machine learning, training data often capture the behaviour of multiple subgroups of some underlying human population. When the amounts of training data for the subgroups are not controlled carefully, under-representation bias arises. We…

Machine Learning · Computer Science 2022-09-07 Quan Zhou , Jakub Marecek , Robert N. Shorten