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Maximum margin binary classification is one of the most fundamental algorithms in machine learning, yet the role of featurization maps and the high-dimensional asymptotics of the misclassification error for non-Gaussian features are still…

Statistics Theory · Mathematics 2023-10-03 Andrea Montanari , Feng Ruan , Basil Saeed , Youngtak Sohn

In this paper, we study the accuracy of values aggregated over classes predicted by a classification algorithm. The problem is that the resulting aggregates (e.g., sums of a variable) are known to be biased. The bias can be large even for…

Machine Learning · Statistics 2019-12-02 Q. A. Meertens , C. G. H. Diks , H. J. van den Herik , F W Takes

We consider two problems of estimation in high-dimensional Gaussian models. The first problem is that of estimating a linear functional of the means of $n$ independent $p$-dimensional Gaussian vectors, under the assumption that most of…

Statistics Theory · Mathematics 2018-11-12 Olivier Collier , Arnak S. Dalalyan

In this paper we provide an analytical framework for investigating the efficiency of a consensus-based model for tackling global optimization problems. This work justifies the optimization algorithm in the mean-field sense showing the…

Analysis of PDEs · Mathematics 2018-02-08 José A. Carrillo , Young-Pil Choi , Claudia Totzeck , Oliver Tse

We analyze statistical features of the ``optimization landscape'' in a random version of one of the simplest constrained optimization problems of the least-square type: finding the best approximation for the solution of an overcomplete…

Mathematical Physics · Physics 2022-06-08 Yan V. Fyodorov , Rashel Tublin

Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this…

Machine Learning · Computer Science 2017-09-15 John Lipor , Laura Balzano

We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…

Optimization and Control · Mathematics 2025-11-24 Shibshankar Dey , Sanjay Mehrotra , Anirudh Subramanyam

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

Statistics Theory · Mathematics 2021-02-08 Rungang Han , Rebecca Willett , Anru R. Zhang

We consider the weighted least squares spline approximation of a noisy dataset. By interpreting the weights as a probability distribution, we maximize the associated entropy subject to the constraint that the mean squared error is…

Numerical Analysis · Mathematics 2024-01-19 Luigi Brugnano , Domenico Giordano , Felice Iavernaro , Giorgia Rubino

We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the…

Computation · Statistics 2023-01-24 He Jiang , Ery Arias-Castro

Non-Gaussian and multimodal distributions are an important part of many recent robust sensor fusion algorithms. In difference to robust cost functions, they are probabilistically founded and have good convergence properties. Since their…

Robotics · Computer Science 2020-01-14 Tim Pfeifer , Peter Protzel

Nonparametric estimation using uniform-width binning is a standard approach for evaluating the calibration performance of machine learning models. However, existing theoretical analyses of the bias induced by binning are limited to binary…

Machine Learning · Computer Science 2025-07-14 Masahiro Fujisawa , Futoshi Futami

We propose a Bayesian approach for model-based clustering of multivariate categorical data where variables are allowed to be associated within clusters and the number of clusters is unknown. The approach uses a two-layer mixture of finite…

Methodology · Statistics 2024-07-09 Gertraud Malsiner-Walli , Bettina Grün , Sylvia Frühwirth-Schnatter

Self-training is a classical approach in semi-supervised learning which is successfully applied to a variety of machine learning problems. Self-training algorithm generates pseudo-labels for the unlabeled examples and progressively refines…

Machine Learning · Computer Science 2020-06-22 Samet Oymak , Talha Cihad Gulcu

This paper deals with uncertainty quantification and out-of-distribution detection in deep learning using Bayesian and ensemble methods. It proposes a practical solution to the lack of prediction diversity observed recently for standard…

Machine Learning · Computer Science 2025-02-03 Antoine de Mathelin , François Deheeger , Mathilde Mougeot , Nicolas Vayatis

Finding parameters that minimise a loss function is at the core of many machine learning methods. The Stochastic Gradient Descent algorithm is widely used and delivers state of the art results for many problems. Nonetheless, Stochastic…

Machine Learning · Computer Science 2018-09-26 Yao Zhang , Andrew M. Saxe , Madhu S. Advani , Alpha A. Lee

We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…

Statistics Theory · Mathematics 2019-07-09 Ankit Pensia , Varun Jog , Po-Ling Loh

In order to cluster or partition data, we often use Expectation-and-Maximization (EM) or Variational approximation with a Gaussian Mixture Model (GMM), which is a parametric probability density function represented as a weighted sum of…

Machine Learning · Computer Science 2013-07-04 Ji Won Yoon

Finite mixture models are a useful statistical model class for clustering and density approximation. In the Bayesian framework finite mixture models require the specification of suitable priors in addition to the data model. These priors…

Methodology · Statistics 2024-07-09 Bettina Grün , Gertraud Malsiner-Walli

Minimization of the (regularized) entropy of classification probabilities is a versatile class of discriminative clustering methods. The classification probabilities are usually defined through the use of some classical losses from…

Statistics Theory · Mathematics 2021-12-17 Edouard Genetay , Adrien Saumard , Rémi Coulaud