Gaussian Mixture Models

Also known as GMM

A Gaussian Mixture Model represents a distribution as a weighted set of Gaussian components, making it useful for finding clusters and describing uncertainty or multiple plausible outcomes. Researchers fit these models with expectation-maximization and gradient methods, and use spectral, Fourier, moment-based, and variational Bayesian methods to estimate parameters or choose the number of components. Neural mixture models extend them to conditional prediction and large datasets, with applications ranging from offline reinforcement learning on D4RL to trajectory forecasting on nuScenes and Argoverse. A central challenge is balancing expressive multimodal representations and scalable computation with reliable component recovery, especially when components overlap or data are high-dimensional.

Latest papers

63 papers12 papers in the last four weeks, against 1 the four weeks before. 0.1% of all new papers.

Low-degree polynomials lower bounds for clustering in small dimension
Oct 27, 2026Alexandra Carpentier, Nicolas VerzelenClustering Gaussian Mixture Models
MISTEA
Minimax Optimality of the NPMLE for Gaussian Mixtures in Hellinger Distance
Oct 21, 2026Shayan Hundrieser, Tudor ManoleGaussian Mixture Models Minimax Estimation
Department of Statistics and Data Science, Yale University · Department of Statistics, Stanford University
Solving the Ho--Nguyen Conjecture for Gaussian Mixtures: Applications to Mixtures of Experts
Oct 19, 2026Yuyang Zhang, Qihuang ZhangGaussian Mixture Models Parameter Identifiability
McGill University
Efficient Agnostic Learning of Univariate Densities Under Local Differential Privacy
Oct 15, 2026Mohammad Afzali, Hassan Ashtiani, Sivan SabatoDifferential Privacy Density Estimation
University of British Columbia · McMaster University · Vector Institute +1
Physical Layer Anomaly Detection via Adaptive Gaussian Mixture Model
Oct 13, 2026Mamady Delamou, Luan Chen, Arsenia ChortiUnsupervised Anomaly Detection Gaussian Mixture Models
ETIS UMR 8051, CY Cergy Paris Université, ENSEA, CNRS, Cergy, France · Barkhausen Institut, Dresden, Germany
Human Pose Estimation by Probabilistic Mixtures of Gaussian and Uniform Distributions
Oct 8, 2026Santiago Reina Alguacil, Ezequiel López RubioHuman Pose Estimation Gaussian Mixture Models
Department of Computer Languages and Computer Science, University of Málaga, 29071 Málaga, Spain · Instituto de Investigación Biomédica de Málaga y Plataforma en Nanomedicina – IBIMA Plataforma BIONAND, 29590 Málaga, Spain · ITIS Software, University of Málaga, 29071 Málaga, Spain
Context-aware Attention-based Gaussian Mixture Models for Vehicular Trajectory Prediction
Oct 6, 2026Arash Raftari, Babak Ebrahimi Soorchaei, Yaser P. FallahMultimodal Trajectory Prediction Vehicle Trajectory Prediction
Department of Electrical and Computer Engineering, University of Central Florida, Orlando, Florida, USA · Department of Computer Science, University of Central Florida, Orlando, Florida, USA
Is $\sqrt{d}$ Separation Necessary for Gradient EM to Learn Gaussian Mixtures in High Dimensions?
Oct 6, 2026Yiran Zhang, Mo Zhou, Weihang Xu +2Gaussian Mixture Models Expectation-Maximization
University of California, Berkeley · University of Washington · Amazon, Inc.
Robust Importance Sampling for Rare Events via Constrained Gaussian Mixtures
Oct 5, 2026Paweł Lorek, Rafał Nowak, Rafał Topolnicki +2Gaussian Mixture Models Importance Sampling
University of Wrocław · Tooploox · TRAILS University of Warsaw +3
Moment-Accurate Gaussian Mixtures for Constant-Step Stochastic Approximation
Oct 4, 2026Xiaoli Li, Wei Biao WuGaussian Mixture Models Stochastic Approximation
University of Chicago
Polylogarithmic Sparsity of Randomly Reweighted NPMLEs for Gaussian Mixtures
Oct 1, 2026Hansheng JiangGaussian Mixture Models Density Estimation
University of Toronto
Federated Clustering with Unknown Local and Global Cluster Cardinalities
Sep 29, 2026Mitushi Goyal, Tarun S., Riddhanya Senapathi +1Cluster Number Estimation Clustering
BITS Pilani K. K. Birla Goa Campus, Goa, India.
Unifying Distributional Training for One-Step Visual Generation
Sep 28, 2026Chi Zhang, Shi Haoyang, Yueyi Liu +9Gaussian Mixture Models T2I Generation
Tsinghua University · Fudan University · Xi’an Jiaotong University +4
Federated Soft Clustering via Generalized Total Variation Minimization
Sep 16, 2026Shamsiiat Abdurakhmanova, Alexander JungGaussian Mixture Models Non-IID Federated Learning
Department of Computer Science, Aalto University, Espoo, Finland
Hierarchical Exponential-Gaussian Mixtures for Watch-Time Distribution Prediction
Aug 24, 2026Sofia Gulevskaia, Mikhail Trapeznikov, Aleksandr Poslavsky +1Conditional Distribution Estimation Gaussian Mixture Models
AI VK & Lomonosov MSU, Moscow, Russia · AI VK, Moscow, Russia
DeMixPert: Decomposed Response Modeling with Gaussian Mixtures for OOD Single-Cell Perturbation Prediction
Aug 24, 2026Jiawen Liu, Xuechenxiao Cao, Yutong Li +5Single-Cell Perturbation Modeling Single-Cell Transcriptomics
School of Computer Science and Engineering, South China University of Technology, Guangzhou, China · School of Future Technology, South China University of Technology, Guangzhou, China
Class-Conditioned Gaussian Mixture Modeling for Imbalanced Time Series Quantification
Aug 21, 2026Md Shahriar Kabir, Mayesha Maliha R. Mithila, Anne H. H. Ngu +2Gaussian Mixture Models Class-Imbalanced Learning
Texas State University, United States
Gauss--Hermite Quadrature for Gaussian-Mixture Entropy with an Action-Space Hermite Surrogate
Aug 21, 2026Jae Wan ShimNumerical Integration Surrogate-Assisted Optimization
Extreme Materials Research Center, Korea Institute of Science and Technology, 5 Hwarang-ro 14-gil, Seongbuk, Seoul, 02792, Republic of Korea · Climate and Environmental Research Institute, Korea Institute of Science and Technology, 5 Hwarang-ro 14-gil, Seongbuk, Seoul, 02792, Republic of Korea · Division of AI-Robotics, KIST Campus, University of Science and Technology, 5 Hwarang-ro 14-gil, Seongbuk, Seoul, 02792, Republic of Korea
RagGAD: Rationale-Aware Conditional Gaussian Mixture Normalizing Flow for Unsupervised Graph Anomaly Detection
Aug 17, 2026Junxin Lu, Jing Zhao, Shiliang SunGraph-Based Anomaly Detection Unsupervised Anomaly Detection
School of Computer Science and Technology, East China Normal University, Shanghai 200062, China · State Key Laboratory of Submarine Geoscience, School of Automation and Intelligent Sensing, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
Identifying parameter couplings and uncertainties of mixed-noise stochastic systems via full-covariance Gaussian mixture network
Aug 15, 2026Xiaolong Wang, Xiangwen Hao, Jing Feng +2Parameter Estimation System Identification
School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, 710119, China · School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, 710129, China · MOE Key Laboratory for Complexity Science in Aerospace, Northwestern Polytechnical University, Xi’an, 710072, China +1
Minimax Optimal Early-Stopped Gradient Descent for Gaussian Mixture Classification
Aug 6, 2026Alex Buna, Shirley Xiaoqi Liu, Patrick RebeschiniEarly Stopping Gradient Descent
Department of Statistics, University of Oxford
Robot Learning from Human Demonstrations: Handwritten Alphabet Trajectories and Human-Likeness Evaluation
Aug 6, 2026Alperen Kenan, Paul Bremner, Manuel GiulianiRobot Skill Learning Gaussian Mixture Models
Bristol Robotics Laboratory, University of the West of England, Bristol, United Kingdom · Faculty of Electrical Engineering, Kempten University of Applied Sciences, Kempten, Germany
PYPM-GGD: Pitman-Yor Process Mixture with Generalized Gaussian Density using ADAM
Jul 27, 2026Kart-Leong LimBayesian Mixture Models Clustering
Institute of Microelectronics, A*Star Singapore
Sparse Gaussian-Mixture-Model Q-Functions via Hadamard Overparametrization for Online Reinforcement Learning
Jul 26, 2026Minh Vu, Konstantinos SlavakisGaussian Mixture Models Interpretability in RL
Institute of Science Tokyo, Department of Information and Communications Engineering, Yokohama, Japan.
Robust Chance-Constrained Optimization using a Continuous Parameter Space Wasserstein-2 Ambiguity Set of Gaussian Mixtures
Jul 19, 2026Shibshankar Dey, Sanjay MehrotraChance-Constrained Optimization Gaussian Mixture Models
Department of Industrial Engineering and Management Sciences, Northwestern University
Dimension-Calibrated Unexplained Mass: An Interpretable Drift Statistic for Contamination Monitoring in Data Streams
Jul 18, 2026Behnam AsadiConcept Drift Gaussian Mixture Models
DP-BOA: Dirichlet-Process Birth-or-Assign for On-the-Fly Category Discovery
Jul 15, 2026Peiyan Gu, Zixin Teng, Xuming HeDirichlet Process Mixture Models Bayesian Mixture Models
ShanghaiTech University, Shanghai, China · Shanghai Engineering Research Center of Intelligent Vision and Imaging
DP-Splat: Bayesian Nonparametric Complexity Control for Gaussian Splatting
Jul 12, 2026Aqi DongBayesian Mixture Models Dirichlet Process Mixture Models
Embry-Riddle Aeronautical University
Rethinking Training & Inference for Forecasting: Linking Winner-Take-All back to GMMs
Jun 24, 2026Qiyuan Wu, Katie Z Luo, Bharath Hariharan +2Gaussian Mixture Models Probabilistic Forecasting
Cornell University · Stanford University · Boston University
From Point Estimates to Distributions: GMM Pooling for MIL in Preterm Birth Prediction
Jun 22, 2026Hussain Alasmawi, Numan Saeed, Soha Said +1Medical Image Analysis Gaussian Mixture Models
Division of Computing and Mathematical Sciences, Mohamed bin Zayed University of Artificial Intelligence (MBZUAI), Abu Dhabi, United Arab Emirates · Corniche Hospital, Abu Dhabi Health Services Company (SEHA), Abu Dhabi, UAE

Oct 27, 2026J/K move · Enter open · S save

Low-degree polynomials lower bounds for clustering in small dimension

Alexandra Carpentier, Nicolas Verzelen

MISTEA

Clustering Gaussian Mixture Models Low-Degree Polynomial Method

Open paper AskPDF arXiv

We study the computational limits of clustering

n

observations drawn from a mixture of

K

isotropic distributions in

\mathbb R^d

, in the regime where the number

K

of groups is much larger than the dimension

d

. In this regime, tensor-based procedures recover the partition with a polylogarithmic separation between the centers, but they require a sample size that is a large and non-explicit polynomial of

dK

, whereas the existing low-degree lower bounds only show that

n

must be larger than

dK^2

. We introduce a mixture of

2K

product Bernoulli distributions on

\{0,1\}^d

, with

K=(d+1)^m

, whose centers are built from a dual BCH code. This construction ensures that the moment tensors of the observations coincide with those of the uniform distribution on

\{-1,1\}^d

up to the order

2m+1

. For any fixed

m

, we establish a low-degree polynomial lower bound showing that clustering is hard as long as the separation

Δ

satisfies

Δ^2\ll(K^2d^{3/2}/n)^{1/(2m+2)}\wedge\sqrt d

, up to polylogarithmic factors. In particular, with a polylogarithmic separation, low-degree polynomials require

n\gtrsim K^2d^{3/2}

observations, up to polylogarithmic factors. Through a Gaussianization argument, this hardness carries over, in the sense of reductions, to isotropic Gaussian mixtures. Our proof relies on a family of polynomials of the observations, indexed by bipartite graphs, which is almost orthonormal. The moments of these polynomials are governed by the number of solutions of polynomial systems over the finite field

\mathbb F\_{d+1}

that are induced by the BCH code, and the crux of our analysis is to connect the combinatorial structure of the bipartite graphs with the structure of the solution sets of these systems.