We analyze training dynamics in Gaussian mixture models using a comparison theorem.
problem Analyzing training algorithms with Gaussian mixture data.
method Applying a Gaussian comparison theorem to a specific family of training algorithms.
result Validated dynamic mean-field expressions and provided iterative refinement schemes.
Proposes a deep generative model for robust forecasting on sparse multivariate time series.
problem Forecasting on sparse multivariate time series with suboptimal results when sparsity is high.
method Dynamic Gaussian Mixture distribution for modeling latent clusters, using neural networks and gating mechanism.
result Demonstrates robust modeling of sparse multivariate time series with improved accuracy.
Deep learning models converge to Gaussian dynamics with mixed structured inputs.
problem Understanding neural network dynamics with complex input distributions.
method Extended hidden manifold model to Gaussian mixtures, analyzed via SGD.
result Learning dynamics with mixed inputs converge to Gaussian behavior.
Analysis of SGD for Gaussian mixture classification using dynamical mean-field theory.
problem Learning dynamics of SGD for a neural network classifying Gaussian mixture.
method Applying dynamical mean-field theory to track SGD dynamics in high dimensions.
result Reveals how SGD navigates the non-convex loss landscape.
A new method for steering large agent populations efficiently.
problem Controlling the configuration of a swarm of identical, interacting cooperative agents.
method Mean-Field Schrodinger Bridges with Gaussian Mixture Models.
result A highly efficient parameterization to approximate optimal solutions of the MFSB problem in closed form.
New GM layers improve neural network performance.
problem Improving neural network performance.
method Employing Gaussian mixture models and Wasserstein gradient flows.
result GM layers achieve comparable performance to two-layer networks.
A novel Bayesian method for dynamic sparsity in Gaussian dynamic linear regression.
problem Variable selection and shrinkage in time-varying regression models.
method Time-varying sparsity via Markov switching priors for coefficients' variances, extending spike-and-slab priors.
result Induces smoothness or shrinkage towards zero at each time point, leading to improved model performance.
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.
This paper tackles online reinforcement learning for unseen tasks with unknown boundaries.
problem Real-world tasks violate assumptions of task distributions, independence, and clear task delineations.
method A mixture of Gaussian Processes models different dynamics, and a transition prior handles temporal dependencies.
result The approach reliably handles task distribution shifts and outperforms alternatives in non-stationary tasks.
Method for initializing Gaussian mixtures for variational inference with multi-modal distributions.
problem Challenges in variational inference with Gaussian mixtures due to multimodality and nonconvex loss functions.
method Optimization to find local maxima, local Gaussian approximations, and constrained least squares regression.
result Robust initialization improves variational inference performance and scalability.
Efficient inference for multimodal Gaussian mixture models of interacting dynamical systems.
problem Efficient inference for multimodal distributions in stochastic dynamical systems.
method Graph neural networks with moment matching for sample-free inference and structured covariance approximations.
result Sample-free inference with improved efficiency and stability compared to Monte Carlo alternatives.
Transformers converge linearly to optimal models for Gaussian mixtures classification.
problem Theoretical understanding of transformers' in-context classification.
method Gradient descent training of a single-layer transformer for Gaussian mixtures classification.
result Transformers converge linearly to globally optimal models for Gaussian mixtures classification.
The speed of convergence of the Expectation Maximization (EM) algorithm for Gaussian mixture model fitting is known to be dependent on the amount of overlap among the mixture components. In this paper, we study the impact of mixing coefficients on the convergence of EM. We show that when the mixture components exhibit …
A new filter estimates complex system states more accurately.
problem Non-Gaussian features in nonlinear systems violate Kalman-type filters.
method Adaptive split-combine Gaussian mixture filter (AMF) that splits and combines Gaussian particles.
result AMF consistently outperforms other filters across diverse benchmarks.
An adaptive filter improves state estimation for complex systems.
problem Estimating non-Gaussian, multimodal PDFs in nonlinear systems.
method Adaptive split-combine Gaussian mixture filter (AMF) that splits and combines Gaussian particles adaptively.
result AMF consistently outperforms other filters across diverse benchmarks.
Proposes GIC for graph convolution, improving graph classification.
problem Graphs lack local convolution kernels like images.
method GIC framework using edge-induced and vertex-induced Gaussian mixtures.
result GIC achieves state-of-the-art results on graph classification.
We create coresets for Gaussian Mixture Models of any shape.
problem Approximating the negative log-likelihood of Gaussian Mixture Models with arbitrary shapes.
method Reduction to projective clustering problems, maintaining coresets for streaming and dynamic data.
result The coreset size is (logn)O(1)/ε2, and can be computed in near-linear time. Paper analyzes Annealed Langevin Dynamics for multimodal sampling stability.
problem Ensuring stability of Annealed Langevin Dynamics across dimensions.
method Uniform-in-dimension analysis of ALD for Gaussian-mixture targets.
result ALD achieves prescribed accuracy in KL divergence with spectral conditions.
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.
Paper analyzes Langevin dynamics for multimodal Gaussian mixtures, controlling errors across dimensions.
problem Challenges in obtaining stable diffusion-based samplers in high- and infinite-dimensional settings.
method Study of preconditioned Annealed Langevin Dynamics (ALD) for Gaussian mixtures, focusing on Euler-Maruyama (EM) and exponential-integrator schemes.
result Proves dimension-uniform KL bounds for the exponential-integrator scheme, allowing arbitrarily small divergence with dimension.
Langevin Dynamics fails to sample from mixture distributions efficiently.
problem Analyzing Langevin Dynamics for sampling from mixture distributions.
method Theoretical analysis of Langevin Dynamics and proposing Chained-Langevin Dynamics.
result Langevin Dynamics fails to sample from mixture distributions efficiently.
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.
DGMM uses deep layers of Gaussian mixtures for flexible data modeling.
problem Efficiently modeling complex data relationships.
method Deep Gaussian Mixture Models (DGMM) with nested mixtures of linear models and factor models.
result DGMM provides a flexible nonlinear model for data description.
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.
Neural networks outperform kernel methods in classifying high-dimensional Gaussian mixtures.
problem Classifying high-dimensional Gaussian mixtures using kernel methods and neural networks.
method Theoretical analysis and derivation of learning dynamics for 2LNN and comparison with kernel methods.
result 2LNN can achieve near-optimal performance on high-dimensional Gaussian mixture classification tasks, surpassing kernel methods.
The paper explores methods for inference in multiplicative latent force models.
problem Inference in hybrid models combining mechanistic and flexible components.
method Two methods of approximate inference: gradient matching and mixtures of local approximations.
result Comparison of methods on simulated and motion capture data.
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.
EM algorithm converges to true mean for truncated mixtures of Gaussians.
problem Analyzing EM algorithm for truncated mixtures of two Gaussians.
method Using dynamical systems, probability, and statistics techniques.
result EM converges almost surely to true mean for various measurable sets S.
New algorithm models data robustly with sub-Gaussian stable distributions.
problem Robust mixture modelling of heavy-tailed data.
method Expectation maximization algorithm for sub-Gaussian stable distributions.
result Sub-Gaussian stable distributions improve robustness in mixture modelling.
Autoencoders can learn generative models like mixtures of gaussians and sparse coding.
problem Learning generative models with autoencoders.
method Gradient descent on two-layer autoencoder architectures with shared weights.
result Autoencoders can recover parameters of generative models under certain conditions.
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.
A new MFG framework for evolving clusters from Gaussian mixtures.
problem Evolutionary clustering of time-dependent Gaussian mixtures.
method Control-theoretic framework based on Mean Field Games (MFG) with coupled HJB and Fokker-Planck systems.
result MFG dynamics recover classical EM algorithm trajectories with mass conservation.
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 for analyzing learning dynamics in singular models.
problem Challenges in analyzing learning of singular models with no one-to-one parameter space.
method Relative reparameterization technique to extract regular sub-models.
result Demonstrated differences in convergence behavior due to algorithmic and intrinsic aspects.
Bayesian algorithm filters Gaussian mixtures efficiently.
problem State-space systems with Gaussian mixtures.
method Gaussian mixture reduction and square-root implementation.
result Efficient state estimation for non-linear systems.
Gradient EM converges globally for over-parameterized Gaussian mixtures.
problem Recovering ground truth Gaussian mixtures with over-parameterized models.
method Gradient EM with over-parameterization, using Hermite polynomials and tensor decomposition.
result Gradient EM globally converges to ground truth with n=Ω(mlogm) over-parameterization. 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.
Tractable model explains market dynamics using Langevin and SUSY QM.
problem Understanding non-linear market dynamics and option pricing.
method Langevin dynamics mapped to QM, using SUSY to find solutions.
result NES model provides accurate option pricing with a single volatility parameter.
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.
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.
A scalable Gaussian process model using a mixture-of-experts approach.
problem Training Gaussian process models is computationally expensive and not scalable.
method A mixture-of-experts model with low-dimensional matrix inversions and importance sampling.
result The model offers comparable performance to Gaussian process regression at a lower computational cost.
Proposes a method to decompose multivariate signals into Gaussian components.
problem Decomposing multivariate signals into Gaussian components.
method Greedy variational method for non-negative multivariate signals as a weighted sum of Gaussians.
result Upper bound for the distance from any mode of a Gaussian mixture model to the set of corresponding means.
New algorithm separates audio sources better using alpha-stable distributions.
problem Improving audio source separation using complex distributions.
method Estimating mixtures of alpha-stable distributions using characteristic function matching.
result Better separation performance than Gaussian-based methods.
This paper formed part of a preliminary research report for a risk consultancy and academic research. Stochastic Programming models provide a powerful paradigm for decision making under uncertainty. In these models the uncertainties are represented by a discrete scenario tree and the quality of the solutions obtained i…
This tutorial explains fitting mixture distributions to data.
problem Fitting mixture distributions to data.
method Step-by-step tutorial covering two and multiple distributions, including numerical simulations.
result Detailed explanation of fitting mixture distributions, including examples and applications.
Quantum interference improves clustering accuracy.
problem Improving clustering accuracy in Gaussian mixture models.
method Modeling classes as wave functions, then mixing them.
result Quantum method outperforms Gaussian mixture in all aspects.
Study finds the cutoff for exact recovery in Gaussian mixture models.
problem Determining the separation of cluster centers for exact recovery in Gaussian mixture models.
method Used information theory and SDP relaxation of K-means clustering. result Sharp threshold for exact recovery of cluster labels without assuming cluster center symmetry.