Spatially constrained Gaussian mixture models reduce covariance complexity.
problem High dimensionality in finite mixture models for spatial data.
method Spatial covariance constraint with only four free parameters.
result Improves clustering of multi-way spatial data and inference of spatial patterns.
Tensor decomposition recovers Gaussian mixtures from moments.
problem Recovering Gaussian mixture models from datasets.
method Symmetric tensor decomposition of moment tensors built from empirical moments.
result Identifiable tensors with interpolation degree less than half their order.
A Gaussian mixture model improves generalization for long-tailed data.
problem Optimizing generalization for rare data in long-tailed distributions.
method Suggested Gaussian mixture model and comparison of linear vs. nonlinear classifiers.
result Nonlinear classifiers outperform linear ones for long-tailed data.
Flexible model captures varying scales in data clusters.
problem Real-world data often exhibits varying scales or intensities, violating the homogeneity assumption of classical Gaussian mixture models.
method Individual-heterogeneous sub-Gaussian mixture model with an efficient spectral method for exact recovery.
result The method provably achieves exact recovery of true cluster labels under mild separation conditions.
Paper uses Gaussian mixture models and Wasserstein distance for schema matching.
problem Schema matching between different datasets.
method Gaussian mixture models and Wasserstein distance for comparison.
result Derives an approximation for Wasserstein distance between Gaussian mixture models.
New method improves Gaussian Mixture Model fitting speed.
problem Slow convergence of EM algorithm for complex data.
method Riemannian Newton Trust-Region method for Gaussian Mixture Models.
result Outperforms existing methods in runtime and iterations.
Study of two-layer NNs under Gaussian mixtures data, proving polynomial models equivalent to neural networks.
problem Training and generalization performance of two-layer NNs under structured Gaussian mixture data.
method Asymptotic analysis of two-layer NNs after one gradient descent step under Gaussian mixture data assumption.
result High-order polynomial models equivalent to nonlinear neural networks under certain conditions.
The paper uses Gaussian mixture models for Bayesian networks and proposes an optimization algorithm.
problem Modeling nodes in Bayesian networks with complex distributions.
method Gaussian mixture models combined with double iteration algorithm.
result The double iteration algorithm optimizes Gaussian mixture models effectively.
DGMEs use Gaussian mixtures to quantify uncertainty in deep learning.
problem Quantifying uncertainty in complex predictive densities.
method DGMEs use a Gaussian mixture model with an EM algorithm for parameter learning.
result DGMEs outperform state-of-the-art models in uncertainty quantification.
The paper proposes a Gaussian mixture model for Hilbert-space-valued data.
problem Challenges in characterizing probability measures for infinite-dimensional random objects.
method Gaussian mixture framework based on kernel mean embeddings.
result The proposed algorithm yields a dense class of approximations in infinite-dimensional spaces.
Study proposes a new metric for comparing Gaussian mixtures in RKHS.
problem Comparing complex multimodal densities in RKHS.
method Wasserstein-type metric for kernel Gaussian mixtures.
result Enhanced capability to model multimodal densities.
Graph Neural Networks struggle with generalization, especially OOD data; GRATIN solves this with Gaussian Mixture Model-based augmentation.
problem Graph Neural Networks struggle with generalization, particularly to unseen or out-of-distribution data.
method Theoretical framework using Rademacher complexity to compute a regret bound on generalization error. GRATIN algorithm leveraging Gaussian Mixture Models for efficient data augmentation.
result GRATIN outperforms existing augmentation techniques in terms of generalization and offers improved time complexity.
Paper tackles online multi-source domain adaptation using Gaussian mixtures and dictionary learning.
problem Adapting multiple, heterogeneous source domains to a target domain in a streaming fashion.
method Introduces a novel approach for online fitting of Gaussian Mixture Models based on Wasserstein geometry, combined with dataset dictionary learning.
result Demonstrates ability to adapt 'on the fly' to target domain data streams.
Deep learning representations of GAN data are like Gaussian mixtures, according to this study.
problem Understanding the statistical nature of deep learning representations of GAN-generated data.
method Using Random Matrix Theory, the study shows that DL representations of GAN data are concentrated random vectors that behave like Gaussian mixtures.
result Deep learning representations of GAN data can be fully described by their first two statistical moments.
New algorithms improve Gaussian mixture model estimation in DFL with heterogeneous data.
problem Bias in EM algorithm for Gaussian mixtures in DFL with heterogeneous data.
method MNEM and semi-MNEM algorithms integrating historical and partially labeled data.
result MNEM and semi-MNEM achieve asymptotic efficiency and improved convergence.
Study learns Gaussian mixtures from censored data.
problem Learning Gaussian mixtures with incomplete data.
method Proposes an algorithm to estimate weights and means with minimal samples.
result Achieves accurate estimation with very few samples.
Improved VB algorithm for NIG mixtures outperforms Gaussian mixtures for non-Gaussian data.
problem Clustering non-Gaussian data, especially heavy-tailed and asymmetric.
method Proposed an improved VB algorithm for NIG mixture models and extended Dirichlet process mixture models.
result Outperforms Gaussian mixtures and existing NIG mixture models, especially for highly non-normative data.
The study characterizes learning Gaussian mixtures using GLMs in high dimensions.
problem Learning Gaussian mixtures with generalised linear models in high-dimensional settings.
method Empirical risk minimization with convex loss and regularisation.
result Exact asymptotics of the ERM estimator for Gaussian mixtures in high dimensions.
Corrected whitening restores orthogonality in high-dimensional spherical Gaussian mixtures.
problem In high-dimensional data, standard whitening fails to preserve orthogonality of mixture means.
method Derived exact limits for whitened means dot products using random matrix theory, constructed a corrected whitening matrix.
result Corrected whitening allows for improved estimation of spherical Gaussian mixtures in the large-dimensional regime.
Gradient EM converges globally for over-parameterized Gaussian mixtures.
problem Global convergence of gradient EM for Gaussian mixtures with more than 2 components.
method Likelihood-based convergence analysis framework.
result Gradient EM converges globally with a sublinear rate of O(1/√t).
The study improves representation learning bounds using data-dependent Gaussian mixtures.
problem Improving generalization in representation learning.
method Established bounds using relative entropy and MDL of latent variables.
result The approach significantly improves generalization over existing methods.
This paper uses Gaussian mixtures to mimic interactions in large language models.
problem Simulating interactions in large language models (LLMs) is computationally expensive.
method Developed an interacting Gaussian mixture model (GMM) system to mimic LLM interactions.
result The interacting Gaussian mixture model system can generate, exchange, and update data and parameters efficiently.
A new clustering model for mixed datasets combines continuous and non-continuous data.
problem Challenges in clustering mixed data due to heterogeneous variables.
method Mixed Deep Gaussian Mixture Model (MDGMM) with multilayer architecture.
result Automatic selection of model specifications and optimal number of clusters.
DEQs and explicit networks are nearly equivalent for Gaussian mixtures.
problem Understanding the equivalence between DEQs and explicit neural networks.
method Random matrix theory and analysis of kernel matrices.
result A shallow explicit network can mimic the kernel of a DEQ.
Optimal transport between Gaussian Mixture Models improves domain adaptation efficiency.
problem Adapting machine learning models to new data distributions with minimal access.
method Optimal transport between Gaussian Mixture Models (GMMs) for domain adaptation.
result Our methods are more efficient and scalable with sample size and dimensions.
Paper proposes a new MIMO detection algorithm using Gaussian Mixture Expectation Propagation.
problem Challenges in MIMO detection due to interference and noise in high-order high-dimensional systems.
method The approach uses a Gaussian Mixture Model (GMM) approximation for Belief Propagation (BP) and Expectation Propagation (EP) messages to improve detection accuracy.
result The proposed algorithm outperforms state-of-the-art detection algorithms while maintaining low computational complexity.
Estimates parameters in a deviated Gaussian mixture model.
problem Testing goodness-of-fit between a known function and a mixture of experts.
method Constructs novel Voronoi-based loss functions to estimate parameters.
result Characterizes local convergence rates of parameter estimation more accurately.
Deep neural networks converge to Gaussian mixtures as layer width increases.
problem Understanding the distribution of outputs from deep neural networks.
method Proof and experiments with a simple model showing the convergence of neural network outputs to Gaussian mixtures.
result Neural networks converge to Gaussian mixtures as the width of the last hidden layer increases.
Optimal transport for vector Gaussian mixtures improves efficiency and structure preservation.
problem Optimal mass transport for vector-valued Gaussian mixtures.
method Vectorizing Gaussian mixture models and studying optimal mass transport problems.
result Computational efficiency and structure preservation in optimal mass transport.
Optimal classifiers derived from GMMs are approximated by deep neural networks.
problem Binary classification of high-dimensional overlapping Gaussian mixtures.
method Closed-form expressions for Bayes optimal decision boundaries derived from GMMs' eigenstructure. Empirical validation through synthetic and real-world data.
result Deep neural networks approximate optimal classifiers for GMMs, with decision thresholds related to covariance eigenvectors.
Deep neural networks classify unbounded Gaussian mixture data without dimensionality issues.
problem Binary classification of unbounded Gaussian mixture data.
method Deep ReLU neural networks with non-asymptotic upper bounds and convergence rates.
result Deep ReLU networks can classify unbounded Gaussian mixture data without dimensionality constraints.
A new 1-iteration GMM learning algorithm improves robustness and accuracy.
problem Improving robustness and accuracy in Gaussian Mixture Model learning.
method GMM expansion idea, 1-iteration learning algorithm, theoretical proof of convergence.
result Guaranteed convergence of the new algorithm regardless initial parameters.
Study shows how over-parameterized classifiers can still perform well on noisy data.
problem Understanding how maximum margin classifiers perform in over-parameterized settings with noisy data.
method Analyzes maximum margin classifiers on sub-Gaussian mixtures, providing risk bounds.
result Characterizes conditions for 'benign overfitting' in linear classification problems.
A novel PP algorithm using GMMs and GAs for detecting informative structures.
problem Detecting informative structures in multivariate datasets.
method Gaussian mixture models (GMMs) and Genetic Algorithms (GAs) for optimal projection.
result The approach effectively detects informative structures in multivariate datasets.
New approach for distributed learning of Gaussian mixtures.
problem Large datasets distributed across different centers.
method Split-and-conquer approach with MM algorithm.
result New estimator is consistent and retains root-n consistency.
Unified framework for clustering with auxiliary data.
problem Clustering with datasets reflecting similar but different latent structures.
method Adaptive Transfer Clustering (ATC) algorithm that optimizes bias-variance decomposition.
result ATC proves optimal under Gaussian mixture model and shows transfer benefits.
Confirmation bias leads to biased estimates in noisy data analysis.
problem Confirmation bias affects scientific conclusions in noisy data environments.
method Investigation of confirmation bias in Gaussian mixture models using K-means and EM algorithms.
result Estimates from algorithms are biased and resemble initial hypotheses, not the noise.
UAPCA projects uncertain data to low dimensions using GMMs.
problem Uncertain multidimensional data not well described by normal distributions.
method Model data with Gaussian mixture models, derive UAPCA projection from general formulation.
result Low-dimensional projections better represent multidimensional distributions.
Two new methods improve clustering with missing data.
problem Handling missing data in Gaussian Mixture Models.
method Proposes two methods using Monte Carlo Expectation-Maximization (MCEM) for data augmentation.
result Proposed methods outperform multiple imputation in clustering and density estimation.
The paper optimizes hyperplanes for binary classification in high-dimensional data with latent Gaussian mixtures.
problem Binary classification in high-dimensional data with latent Gaussian mixtures.
method Generalized least squares estimator for estimating the direction of the optimal separating hyperplane. Simple correction for intercept estimation.
result The procedure is minimax optimal in many scenarios and can retain the interpolation property.
A fast method estimates Gaussian mixture components without iterative fitting.
problem Estimating the number of components in high-dimensional Gaussian mixtures.
method Center data, compute singular values, and count above a threshold.
result The estimator consistently recovers the true number of components under mild separation condition.
The paper proves a regret bound for a sub-Gaussian mixture on unbounded data.
problem Tackles the challenge of achieving regret bounds for sub-Gaussian mixtures on unbounded data.
method Uses path-wise (deterministic) regret bounds and a cumulative variance process to derive the bound.
result Shows that on a specific event, the regret is eventually bounded by ln(ln V_T).
Deep learning is a hierarchical inference method formed by subsequent multiple layers of learning able to more efficiently describe complex relationships. In this work, Deep Gaussian Mixture Models are introduced and discussed. A Deep Gaussian Mixture model (DGMM) is a network of multiple layers of latent variables, wh…
New algorithm for fitting Gaussian mixtures using Wasserstein-Fisher-Rao geometry.
problem Hard problem of fitting Gaussian mixture models to data computationally.
method Gradient descent over Wasserstein-Fisher-Rao geometry for probability measures.
result Established convergence guarantees for the proposed algorithm.
Transformers can cluster data from Gaussian mixtures without supervision.
problem Clustering data from Gaussian mixtures without labeled data.
method Theoretical analysis of attention-based layers, focusing on a simplified two-head attention layer and an identity matrix attention layer.
result Attention-based layers can align with true mixture centroids and adapt to input-specific distributions.
Estimates Gaussian mixtures from weighted samples efficiently.
problem Estimating Gaussian mixtures from weighted samples with correct weight treatment.
method Density interpretation and expectation-maximization method considering weights.
result Correctly estimates Gaussian mixtures with weighted samples.
Theoretical analysis of entropy approximation for Gaussian mixtures.
problem Lack of theoretical guarantees for entropy approximation of Gaussian mixtures.
method Theoretical analysis of the error between true and approximate entropy.
result The error converges to zero as the ratios of means to variances tend to infinity, providing a guarantee for high-dimensional problems.
The study bounds the stability of Gaussian mixtures under small perturbations.
problem Stability of Gaussian mixtures under small changes in distribution.
method Deriving an explicit bound on parameter stability of spherical Gaussian Mixture Models (sGMM) in a pre-defined model class.
result Upper bound on parameter distance of close sGMMs to the original sGMM, dependent only on the original model.