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Model selection, via penalized likelihood type criteria, is a standard task in many statistical inference and machine learning problems. Progress has led to deriving criteria with asymptotic consistency results and an increasing emphasis on…

Statistics Theory · Mathematics 2022-05-13 TrungTin Nguyen , Faicel Chamroukhi , Hien Duy Nguyen , Florence Forbes

Mixture of Experts (MoE) models constitute a widely utilized class of ensemble learning approaches in statistics and machine learning, known for their flexibility and computational efficiency. They have become integral components in…

Machine Learning · Statistics 2025-05-26 Tuan Thai , TrungTin Nguyen , Dat Do , Nhat Ho , Christopher Drovandi

Mixtures-of-Experts (MoE) are conditional mixture models that have shown their performance in modeling heterogeneity in data in many statistical learning approaches for prediction, including regression and classification, as well as for…

Methodology · Statistics 2019-07-17 Bao Tuyen Huynh , Faicel Chamroukhi

Mixture of Experts (MoE) are successful models for modeling heterogeneous data in many statistical learning problems including regression, clustering and classification. Generally fitted by maximum likelihood estimation via the well-known…

Machine Learning · Statistics 2018-10-30 Faicel Chamroukhi , Bao-Tuyen Huynh

We investigate the estimation properties of the mixture of experts (MoE) model in a high-dimensional setting, where the number of predictors is much larger than the sample size, and for which the literature is particularly lacking in…

Statistics Theory · Mathematics 2024-07-03 TrungTin Nguyen , Hien D Nguyen , Faicel Chamroukhi , Geoffrey J McLachlan

Mixtures-of-Experts models and their maximum likelihood estimation (MLE) via the EM algorithm have been thoroughly studied in the statistics and machine learning literature. They are subject of a growing investigation in the context of…

Machine Learning · Statistics 2019-09-13 Faïcel Chamroukhi , Florian Lecocq , Hien D. Nguyen

Mixture of Experts (MoE) is a popular framework for modeling heterogeneity in data for regression, classification and clustering. For continuous data which we consider here in the context of regression and cluster analysis, MoE usually use…

Methodology · Statistics 2015-06-30 Faicel Chamroukhi

Originally introduced as a neural network for ensemble learning, mixture of experts (MoE) has recently become a fundamental building block of highly successful modern deep neural networks for heterogeneous data analysis in several…

Machine Learning · Statistics 2024-02-12 Huy Nguyen , TrungTin Nguyen , Khai Nguyen , Nhat Ho

Mixture of experts (MoE) model is a statistical machine learning design that aggregates multiple expert networks using a softmax gating function in order to form a more intricate and expressive model. Despite being commonly used in several…

Machine Learning · Statistics 2024-06-25 Huy Nguyen , Nhat Ho , Alessandro Rinaldo

Understanding consumer choice is fundamental to marketing and management research, as firms increasingly seek to personalize offerings and optimize customer engagement. Traditional choice modeling frameworks, such as multinomial logit (MNL)…

Machine Learning · Computer Science 2025-03-11 Diego Vallarino

Mixture-of-experts (MoE) model incorporates the power of multiple submodels via gating functions to achieve greater performance in numerous regression and classification applications. From a theoretical perspective, while there have been…

Machine Learning · Statistics 2024-06-25 Huy Nguyen , Pedram Akbarian , TrungTin Nguyen , Nhat Ho

Mixture-of-Experts (MoE) is a flexible framework that combines multiple specialized submodels (``experts''), by assigning covariate-dependent weights (``gating functions'') to each expert, and have been commonly used for analyzing…

Methodology · Statistics 2026-01-06 Qicheng Zhao , Celia M. T. Greenwood , Qihuang Zhang

A useful strategy to deal with complex classification scenarios is the "divide and conquer" approach. The mixture of experts (MOE) technique makes use of this strategy by joinly training a set of classifiers, or experts, that are…

Machine Learning · Computer Science 2014-05-30 Billy Peralta

The classical mixture of linear experts (MoE) model is one of the widespread statistical frameworks for modeling, classification, and clustering of data. Built on the normality assumption of the error terms for mathematical and…

Methodology · Statistics 2020-07-15 Elham Mirfarah , Mehrdad Naderi , Ding-Geng Chen

Mixture of Experts (MoE), an ensemble of specialized models equipped with a router that dynamically distributes each input to appropriate experts, has achieved successful results in the field of machine learning. However, theoretical…

Machine Learning · Computer Science 2025-08-19 Ryotaro Kawata , Kohsei Matsutani , Yuri Kinoshita , Naoki Nishikawa , Taiji Suzuki

The Mixture-of-Experts (MoE) model uses a set of expert networks that specialize on subsets of a dataset under the supervision of a gating network. A common issue in MoE architectures is ``expert collapse'' where overlapping class…

Neural and Evolutionary Computing · Computer Science 2026-03-31 Abien Fred Agarap , Arnulfo P. Azcarraga

The mixture of experts (MoE) model is a versatile framework for predictive modeling that has gained renewed interest in the age of large language models. A collection of predictive ``experts'' is learned along with a ``gating function''…

Methodology · Statistics 2024-10-14 Oh-Ran Kwon , Gourab Mukherjee , Jacob Bien

We propose Preferential MoE, a novel human-ML mixture-of-experts model that augments human expertise in decision making with a data-based classifier only when necessary for predictive performance. Our model exhibits an interpretable gating…

Machine Learning · Computer Science 2021-01-15 Melanie F. Pradier , Javier Zazo , Sonali Parbhoo , Roy H. Perlis , Maurizio Zazzi , Finale Doshi-Velez

Mixture-of-Experts (MoE) architectures combine specialized predictors through a learned gate and are effective across regression and classification, but for classification with softmax multinomial-logistic gating, rigorous guarantees for…

Machine Learning · Statistics 2026-02-10 TrungKhang Tran , TrungTin Nguyen , Md Abul Bashar , Nhat Ho , Richi Nayak , Christopher Drovandi

Mixture of Experts (MoE) is a popular framework in the fields of statistics and machine learning for modeling heterogeneity in data for regression, classification and clustering. MoE for continuous data are usually based on the normal…

Methodology · Statistics 2016-12-22 Faicel Chamroukhi
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