Dimensional Gaussian Mixture

Dimensional Gaussian Mixture Models (GMMs) are probabilistic models representing data as a combination of multiple Gaussian distributions, aiming to effectively capture complex, high-dimensional data structures. Current research focuses on efficient fitting and evaluation of these models, particularly in high dimensions, exploring techniques like locality-sensitive hashing and loss-adaptive density control for improved scalability and accuracy. These advancements are impacting various fields, including generative modeling, classification, and clustering, by enabling more robust and efficient analysis of high-dimensional datasets with complex underlying structures. The development of both explicit and implicit model architectures, along with theoretical analyses of their properties, is driving progress in this area.

Papers

October 25, 2024

Statistical Inference in Classification of High-dimensional Gaussian Mixture
Hanwen Huang, Peng Zeng
Classification Code High Dimensional Mixture Component Generalization Error Covariance Matrix Gaussian Distribution Statistical Inference Nonsmooth Regularization Dimensional Gaussian Mixture

October 8, 2024

The Breakdown of Gaussian Universality in Classification of High-dimensional Mixtures
Xiaoyi Mai, Zhenyu Liao
Classification Code Gaussian Mixture Gaussian Model Gaussian Data Dimensional Gaussian Mixture Gaussian Universality

May 30, 2024

N-Dimensional Gaussians for Fitting of High Dimensional Functions
Stavros Diolatzis, Tobias Zirr, Alexandr Kuznetsov, Georgios Kopanas, Anton Kaplanyan
High Dimensional 3D Scene Gaussian Mixture Model Gaussian Distribution Dimensional Gaussian Mixture

February 5, 2024

Deep Equilibrium Models are Almost Equivalent to Not-so-deep Explicit Models for High-dimensional Gaussian Mixtures
Zenan Ling, Longbo Li, Zhanbo Feng, Yixuan Zhang, Feng Zhou, Robert C. Qiu, Zhenyu Liao
Random Matrix Shallow Network Implicit Neural Network Deep Equilibrium Model Explicit Modelling Dimensional Gaussian Mixture

October 5, 2023

Analysis of learning a flow-based generative model from limited sample complexity
Hugo Cui, Florent Krzakala, Eric Vanden-Eijnden, Lenka Zdeborová
General Analysis Auto Encoder Flow Based Generative Generative Flow Dimensional Gaussian Mixture

March 7, 2023

Polynomial Time and Private Learning of Unbounded Gaussian Mixture Models
Jamil Arbas, Hassan Ashtiani, Christopher Liaw
Polynomial Time Gaussian Mixture Private Algorithm Private Learning Gaussian Distribution Dimensional Gaussian Mixture

October 25, 2022

Interpolating Discriminant Functions in High-Dimensional Gaussian Latent Mixtures
Xin Bing, Marten Wegkamp
Binary Classification Gaussian Mixture High Dimensional Feature Low Dimensional Latent Dimensional Gaussian Mixture Discriminant Function

June 6, 2022

Mean Estimation in High-Dimensional Binary Markov Gaussian Mixture Models
Yihan Zhang, Nir Weinberger
High Dimensional Gaussian Mixture Model Mean Estimation Gaussian Model Markov Model Homogeneous Markov Dimensional Gaussian Mixture

May 16, 2022

The Role of Pseudo-labels in Self-training Linear Classifiers on High-dimensional Gaussian Mixture Data
Takashi Takahashi
Strong Generalization Pseudo Label Integral Role Generalization Performance Linear Classifier Convex Regularization Dimensional Gaussian Mixture

February 18, 2022

Gaussian Mixture Convolution Networks
Adam Celarek, Pedro Hermosilla, Bernhard Kerbl, Timo Ropinski, Michael Wimmer
Gaussian Mixture Convolution Kernel Dimensional Gaussian Mixture

December 7, 2021

Lattice-Based Methods Surpass Sum-of-Squares in Clustering
Ilias Zadik, Min Jae Song, Alexander S. Wein, Joan Bruna
Computational Gap Dimensional Gaussian Mixture Lattice Free MMI