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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Proposes a new model for mixed membership in Gaussian mixture.
problem Limited to single component membership in Gaussian mixture models.
method Mixed membership sub-Gaussian model, spectral algorithm.
result Estimation error can be made arbitrarily small with high probability.
Study exact community detection in k-community Gaussian mixtures with different intensities.
problem Community detection in k-community Gaussian mixtures with varying intensities.
method Explicitly find the threshold for exact recovery of maximum likelihood estimation.
result Threshold for exact recovery of maximum likelihood estimation is identified.
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.
Study uniform rates for estimating Gaussian mixtures without separation assumption.
problem Estimating parameters in two-component Gaussian mixtures without separation.
method Uniform convergence rates derived using minimax lower bounds and careful analysis of polynomial equalities.
result Phase transition in optimal estimation rate based on mixture balance.
Conditional diffusion models can approximate target distributions well with Gaussian-mixture reverse kernels.
problem Approximating target distributions in conditional diffusion models.
method Using finite Gaussian mixtures with ReLU-network logits as reverse kernels, reducing the problem to static conditional density approximation.
result The resulting neural reverse-kernel class is dense in conditional KL divergence under exact terminal matching.
New algorithm for tensor decomposition and Gaussian mixture models.
problem Efficiently decompose overcomplete order-3 tensors and estimate parameters of Gaussian mixtures.
method Proposes Jennrich's algorithm adapted for tensor decomposition and Gaussian mixture models.
result Efficient algorithm for decomposing symmetric overcomplete order-3 tensors and estimating parameters of Gaussian mixtures.
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.
This paper optimizes Gaussian mixture model learning with optimal sampling complexity.
problem Learning the number of components and mixing distribution in 1D Gaussian mixtures.
method Fourier-based approach to estimate model order and mixing distribution.
result The proposed method matches the optimal sampling complexity and outperforms conventional techniques.
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.
This paper studies clustering and embedding in high-dimensional Gaussian mixture block models.
problem Clustering and embedding in high-dimensional Gaussian mixture block models.
method Spectral clustering and embedding algorithms for graphs sampled from Gaussian mixture block models.
result Performance analysis of spectral clustering and embedding algorithms for 2-component spherical Gaussian mixtures.
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).
Improved sample complexity for Gaussian Mixture Models using Pair Correlation Factor.
problem Understanding the sample complexity of Gaussian Mixture Models.
method Introducing Pair Correlation Factor (PCF) to measure clustering of component means and improving sample complexity bounds.
result The Pair Correlation Factor (PCF) more accurately determines the difficulty of parameter recovery in Gaussian Mixture Models.
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 study calculates the risk of semi-supervised multitask learning on Gaussian mixtures.
problem Understanding the risk in semi-supervised multitask learning on Gaussian mixtures.
method Statistical physics methods applied to Gaussian mixture models.
result The study evaluates the performance gain of learning tasks together versus separately.
Optimizes clustering in Gaussian mixtures with varying covariance matrices.
problem Clustering with anisotropic Gaussian mixture models where covariance matrices vary.
method Proposes a computationally feasible hard EM type algorithm.
result Achieves optimal clustering rate with few iterations.
Paper introduces a new distance measure for Gaussian Mixture Models.
problem Developing a new distance measure for Gaussian Mixture Models.
method Embedding K-component Gaussian Mixture Models into the manifold of symmetric positive definite matrices and calculating a lower bound for the Fisher-Rao metric.
result Demonstrated effectiveness through experiments on standard datasets.
Bayesian approach approximates probability functions of Gaussian mixtures.
problem Approximating probability functions of non-spherical Gaussian mixtures.
method Bayesian decomposition, spherical radial decomposition, random sampling.
result Established differentiability and integral representation of gradient for probability functions.
Solves challenges in estimating parameters of softmax gating Gaussian mixture models.
problem Identifiability issues and complex interactions in Gaussian mixture of experts.
method Proposes novel Voronoi loss functions and establishes convergence rates of MLE.
result Connects convergence rate of MLE to a solvability problem of polynomial equations.
uGMM-NN integrates probabilistic reasoning into neural networks.
problem Capturing multimodality and uncertainty in neural network activations.
method Parameterizes activations as univariate Gaussian mixtures with learnable parameters.
result Competitive discriminative performance with probabilistic activations.
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.
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.
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.
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.
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.
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…
GAT-GMM improves GANs' performance in learning Gaussian mixture models.
problem GANs struggle with multi-modal distributions like Gaussian mixtures.
method Proposes a minimax GAN framework using random linear generator and softmax-based quadratic discriminator.
result Gradient Descent Ascent method converges to an approximate minimax point.
A new credit scoring method using Gaussian Mixture Models.
problem Differentiating good from bad borrowers in credit scoring.
method Gaussian Mixture Models for consumer classification.
result The model performs comparably to others and avoids overfitting.
A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture terms and this is handled here by utilising a Gaussian mixture reduction step after …
Learning word representations has garnered greater attention in the recent past due to its diverse text applications. Word embeddings encapsulate the syntactic and semantic regularities of sentences. Modelling word embedding as multi-sense gaussian mixture distributions, will additionally capture uncertainty and polyse…
We will establish that the VC dimension of the class of d-dimensional ellipsoids is (d^2+3d)/2, and that maximum likelihood estimate with N-component d-dimensional Gaussian mixture models induces a geometric class having VC dimension at least N(d^2+3d)/2. Keywords: VC dimension; finite dimensional ellipsoid; Gaussian m…
Paper presents a reparameterized DP-DLGMM for clustering.
problem Non-parametric DP priors in DLGMM are hard to couple with variational inference.
method Closed-form updates for DP-DLGMM's variational posterior.
result Model generates realistic samples and performs competitively in semi-supervised settings.
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.
Survey on Bayesian inference for Gaussian mixture models.
problem Estimating parameters of Gaussian mixture models using Bayesian methods.
method Uses Bayesian inference to estimate parameters and uncertainty of Gaussian mixture models.
result Bayesian approach provides point estimates and associated uncertainty for mixture model parameters.
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.
Private learning of Gaussian Mixture Models without boundedness assumptions.
problem Private estimation of parameters of Gaussian Mixture Models with unbounded components.
method Reduction to non-private problem, blackbox privatization, Moitra and Valiant's algorithm.
result First sample complexity upper bound and polynomial time algorithm for privately learning GMMs.
A new method for learning Gaussian Mixture Models using gradient descent.
problem Learning Gaussian Mixture Models efficiently and with gradient descent.
method Sliced Cramér 2-distance for multivariate GMMs, compatible with gradient descent.
result Closed-form solution for univariate case, easy to implement.
The paper stabilizes invertible neural networks by using Gaussian mixture models.
problem Invertible neural networks can have exploding Lipschitz constants, leading to numerical errors.
method The authors use Gaussian mixture models to stabilize the latent distribution of invertible neural networks.
result Numerical simulations confirm that this modification improves sampling quality in multimodal applications.