On-device research index

arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,786 papers · 148 categories

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48 results for “complex Gaussian mixture model”

Differentially Private Algorithms for Learning Mixtures of Separated Gaussianscs.DS

New algorithm learns Gaussian mixtures privately with optimal sample complexity.

problem Learning parameters of Gaussian mixtures under differential privacy constraints.

method Differentially private algorithm based on Achlioptas and McSherry's approach.

result Sample complexity matches non-private algorithm up to lower order terms.

differential privacy Gaussian mixture models sample complexity private learning

2019-09-09abs ↗pdf ↗

Pair Correlation Factor and the Sample Complexity of Gaussian Mixturescs.LG

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.

Gaussian Mixture Models Sample Complexity Pair Correlation Factor Minimum Gap Clustering

2025-08-05abs ↗pdf ↗

Spatial Covariance Constraints for Gaussian Mixture Modelsstat.ME

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.

spatial modeling Gaussian mixture models covariance constraints finite mixture models EM algorithm

2026-01-12abs ↗pdf ↗

Self-regularizing Property of Nonparametric Maximum Likelihood Estimator in Mixture Modelsmath.ST

NPMLE estimator automatically chooses the right model complexity for Gaussian mixtures.

problem Learning mixture models and empirical Bayes estimation with non-convex likelihoods.

method Nonparametric maximum likelihood estimator (NPMLE) using complex-analytic techniques.

result NPMLE solution has

O(\log n)

atoms with high probability, improving model complexity.

NPMLE Mixture models Complex analysis Self-regularization Hellinger risk bound

2020-08-19abs ↗pdf ↗

Model Selection and Parameter Estimation of One-Dimensional Gaussian Mixture Modelsstat.ML

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.

Gaussian mixture models model selection parameter estimation Fourier analysis sampling complexity

2024-04-19abs ↗pdf ↗

Deep Gaussian Mixture Modelsstat.ML

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…

2017-11-18abs ↗pdf ↗

Deep Gaussian Mixture Ensemblesstat.ML

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.

deep learning uncertainty quantification Gaussian mixture EM algorithm deep ensembles

2023-06-12abs ↗pdf ↗

Optimal Transport for Kernel Gaussian Mixture Modelscs.LG

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.

Optimal Transport Kernel Gaussian Mixtures Reproducing Kernel Hilbert Space Wasserstein Distance

2023-10-28abs ↗pdf ↗

Adaptive Mixtures of Factor Analyzersstat.ML

A mixture of factor analyzers is a semi-parametric density estimator that generalizes the well-known mixtures of Gaussians model by allowing each Gaussian in the mixture to be represented in a different lower-dimensional manifold. This paper presents a robust and parsimonious model selection algorithm for training a mi…

2015-07-10abs ↗pdf ↗

Mixtures of Gaussian process experts based on kernel stick-breaking processesstat.ML

Improved Gaussian process experts model for complex data.

problem Limitations of standard Gaussian processes: scalability and predictive performance.

method Proposes a new mixture model of Gaussian process experts based on kernel stick-breaking processes.

result Improved predictive performance compared to existing models.

Gaussian processes kernel stick-breaking Dirichlet processes slice sampling predictive performance

2023-04-26abs ↗pdf ↗

Mixtures of Gaussian Process Experts with SMC

^2

stat.ML

This work improves Gaussian process inference using mixtures of experts and nested SMC samplers.

problem High computational and memory costs of Gaussian processes.

method Mixtures of Gaussian process experts with nested SMC samplers.

result Significantly improved inference compared to importance sampling.

Gaussian processes Monte Carlo methods flexible models expert systems non-stationary

2022-08-26abs ↗pdf ↗

Sample-Efficient Private Learning of Mixtures of Gaussianscs.LG

Improved sample efficiency for private learning of Gaussian mixtures.

problem Learning mixtures of Gaussians with differential privacy.

method Inverse sensitivity mechanism, sample compression, sumset volume bounds.

result Proved optimal sample complexity for private learning of mixtures of Gaussians.

differential privacy mixtures of Gaussians sample complexity inverse sensitivity sample compression

2024-11-04abs ↗pdf ↗

Infinite Mixtures of Multivariate Gaussian Processescs.LG

This paper presents a new model called infinite mixtures of multivariate Gaussian processes, which can be used to learn vector-valued functions and applied to multitask learning. As an extension of the single multivariate Gaussian process, the mixture model has the advantages of modeling multimodal data and alleviating…

2013-07-26abs ↗pdf ↗

Demystifying Softmax Gating Function in Gaussian Mixture of Expertsstat.ML

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.

softmax gating Gaussian mixture parameter estimation MLE identifiability

2023-05-05abs ↗pdf ↗

Graph Neural Network Generalization with Gaussian Mixture Model Based Augmentationcs.LG

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.

Graph Neural Networks Generalization Out-of-Distribution Data Augmentation Gaussian Mixture Models

2024-11-13abs ↗pdf ↗

Mixed Membership sub-Gaussian Modelsstat.ML

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.

Gaussian mixture mixed membership spectral algorithm vanishing error high probability

2026-04-24abs ↗pdf ↗

Support Recovery in Mixture Models with Sparse Parameterscs.LG

Efficient algorithms for sparse parameter recovery in mixture models.

problem Support recovery of high-dimensional sparse latent vectors in mixture models.

method Efficient algorithms with logarithmic sample complexity dependence on dimensionality.

result First guarantees on support recovery for various mixture models.

mixture models sparse parameters support recovery logarithmic sample complexity canonical distributions

2022-02-24abs ↗pdf ↗

The EM Algorithm gives Sample-Optimality for Learning Mixtures of Well-Separated Gaussianscs.LG

EM algorithm achieves optimal sample complexity for well-separated Gaussian mixtures.

problem Estimating parameters of well-separated Gaussian mixtures.

method New EM convergence proof for well-separated Gaussian mixtures.

result EM algorithm converges with

Ω(\sqrt{\log k})

separation, achieving

O(kd/ε^2)

samples.

EM algorithm Gaussian mixtures sample complexity well-separated spherical

2020-02-02abs ↗pdf ↗

Polynomial Time and Private Learning of Unbounded Gaussian Mixture Modelsstat.ML

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.

Gaussian Mixture Models Private Learning Differential Privacy Polynomial Time Unbounded Components

2023-03-07abs ↗pdf ↗

GAT-GMM: Generative Adversarial Training for Gaussian Mixture Modelscs.LG

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.

GANs Gaussian Mixture Models Optimal Transport Non-convex Optimization Stationary Point

2020-06-18abs ↗pdf ↗

SQ Lower Bounds for Learning Bounded Covariance GMMscs.LG

New SQ lower bounds show learning mixtures of bounded covariance Gaussians is hard.

problem Learning mixtures of Gaussians with bounded covariance matrices is hard.

method Statistical Query (SQ) lower bounds.

result Any SQ algorithm requires complexity at least

d^{Ω(1/ε)}

for learning mixtures of bounded covariance Gaussians.

Statistical Query Learning Mixtures Gaussian Mixture Models Bounded Covariance Fine-grained Lower Bounds

2023-06-22abs ↗pdf ↗

Summarizing Bayesian Nonparametric Mixture Posterior -- Sliced Optimal Transport Metrics for Gaussian Mixturesstat.ME

New method for summarizing Bayesian mixture models using sliced Wasserstein distances.

problem Estimating the mixing measure in nonparametric Bayesian mixture models.

method Decision-theoretic approach using sliced Wasserstein distances for Gaussian mixtures.

result Effective estimation of the mixing measure and mixture density.

Bayesian nonparametrics mixture models sliced Wasserstein Gaussian mixtures posterior inference

2024-11-22abs ↗pdf ↗

Gaussian mixture models as a proxy for interacting language modelscs.CL

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.

Gaussian mixture models large language models interactions computational efficiency polarization

2025-05-29abs ↗pdf ↗

A Discriminative Gaussian Mixture Model with Sparsitycs.LG

Proposes a sparse classifier for discriminative Gaussian Mixture Models.

problem Softmax-based discriminative models assume unimodality, leading to parameter redundancy.

method Sparse Bayesian learning for GMM-based discriminative model, reducing parameters and complexity.

result The SDGM outperforms existing softmax-based discriminative models.

Gaussian Mixture Model Discriminative Learning Sparse Bayesian Softmax Neural Networks

2019-11-14abs ↗pdf ↗

Variational Bayes Approximations for Clustering via Mixtures of Normal Inverse Gaussian Distributionsstat.ME

Parameter estimation for model-based clustering using a finite mixture of normal inverse Gaussian (NIG) distributions is achieved through variational Bayes approximations. Univariate NIG mixtures and multivariate NIG mixtures are considered. The use of variational Bayes approximations here is a substantial departure fr…

2013-09-07abs ↗pdf ↗

AutoGMM: Automatic Gaussian Mixture Modeling in Pythoncs.LG

AutoGMM automates Gaussian mixture modeling in Python.

problem Automatic clustering of complex data with uncertainty-aware grouping.

method Strategic initialization using an agglomerative Mahalanobis heuristic, parallelized model selection by information criteria.

result Strong out-of-the-box performance on classic benchmarks and real datasets.

Gaussian mixture models automatic clustering Python Bayesian Information Criterion Mahalanobis heuristic

2019-09-06abs ↗pdf ↗

Deep Bayesian Unsupervised Source Separation Based on a Complex Gaussian Mixture Modelcs.SD

A new unsupervised method separates speech sources without requiring labeled data.

problem Lack of supervised data for effective neural source separation.

method Uses a complex Gaussian mixture model (cGMM) for joint training of separation and localization networks.

result The method outperforms conventional initialization methods in monaural and multichannel separation.

source separation unsupervised learning neural networks complex Gaussian mixture model speech processing

2019-08-29abs ↗pdf ↗

Diagonally-Weighted Generalized Method of Moments Estimation for Gaussian Mixture Modelingcs.LG

DGMM improves Gaussian mixture modeling efficiency and stability.

problem Efficiently estimating Gaussian mixtures in high dimensions.

method Diagonally-weighted generalized method of moments (DGMM).

result DGMM achieves smaller estimation errors with shorter runtime.

Gaussian mixture modeling Generalized method of moments Diagonally-weighted High-dimensional data Efficiency

2025-07-28abs ↗pdf ↗

Training Gaussian Mixture Models at Scale via Coresetsstat.ML

How can we train a statistical mixture model on a massive data set? In this work we show how to construct coresets for mixtures of Gaussians. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset also provide a good fit for the original data set. We show that, perhaps surprisingly…

2017-03-23abs ↗pdf ↗

Clustering of non-Gaussian data by variational Bayes for normal inverse Gaussian mixture modelsstat.ML

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.

VB algorithm NIG mixtures Dirichlet process clustering non-Gaussian data

2020-09-13abs ↗pdf ↗

GGMPs: Generalized Gaussian Mixture Processescs.LG

GGMPs improve non-Gaussian conditional density estimation.

problem Multimodality, heteroscedasticity, and strong non-Gaussianity in conditional density estimation.

method GGMP combines local Gaussian mixture fitting, cross-input component alignment, and per-component heteroscedastic GP training.

result GGMPs improve distributional approximation on synthetic and real-world datasets.

Gaussian mixture processes conditional density estimation multimodality heteroscedasticity non-Gaussianity

2026-03-11abs ↗pdf ↗

Asymptotic Analysis of Two-Layer Neural Networks after One Gradient Step under Gaussian Mixtures Data with Structurestat.ML

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.

two-layer neural networks Gaussian mixtures asymptotic analysis generalization polynomial models

2025-03-02abs ↗pdf ↗

Gaussian Process-Gated Hierarchical Mixtures of Expertscs.LG

Proposes GPHMEs using Gaussian processes for hierarchical expert models.

problem Hierarchical mixtures of experts with complex gating functions.

method Gaussian process-gated hierarchical mixtures of experts (GPHMEs) with non-linear gating and expert functions.

result Outperforms tree-based HMEs and achieves good performance with reduced complexity.

Gaussian processes hierarchical mixtures of experts non-linear gating deep Bayesian neural networks variational inference

2023-02-09abs ↗pdf ↗

Dimension-Free Convergence of Diffusion Models for Approximate Gaussian Mixturescs.LG

Diffusion models achieve high-quality samples from complex high-dimensional Gaussian mixtures without scaling with dimension.

problem Achieving accurate sampling from high-dimensional distributions using diffusion models.

method Investigates the effectiveness of diffusion models in sampling from Gaussian Mixture Models (GMMs) without scaling with dimension.

result DDPM requires at most

O(1/\varepsilon)

iterations to attain an

\varepsilon

-accurate distribution in total variation distance, independent of dimension and number of components.

Diffusion models Gaussian mixtures Approximation High-dimensional Total variation

2025-04-07abs ↗pdf ↗

Learning Mixtures of Gaussians Using Diffusion Modelscs.LG

Algorithm learns mixtures of Gaussians efficiently using diffusion models.

problem Learning mixtures of Gaussians with identity covariance.

method Analytic approach using diffusion models to learn score functions.

result Quasi-polynomial time and sample complexity for learning mixtures.

Gaussian mixtures Diffusion models Score functions Polynomial regression Generative modeling

2024-04-29abs ↗pdf ↗

A Method of Moments for Mixture Models and Hidden Markov Modelscs.LG

Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics (e.g., the EM algorithm) which are prone to failure, and existing consistent methods …

2012-03-03abs ↗pdf ↗

A survey on Bayesian inference for Gaussian mixture modelcs.LG

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.

Bayesian inference Gaussian mixture model Mixture model Clustering Machine learning

2021-08-20abs ↗pdf ↗

Gaussian mixture modeling of nodes in Bayesian network according to maximal parental cliquesstat.ML

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.

Bayesian networks Gaussian mixture models Optimization algorithms Expectation maximization Gradient descent

2022-04-20abs ↗pdf ↗

Model Selection and Parameter Estimation of Multi-dimensional Gaussian Mixture Modelstat.ML

The paper optimizes model selection and parameter estimation for multi-dimensional Gaussian Mixture Models.

problem Learning and distinguishing multi-dimensional Gaussian Mixture Models with reliable model order selection and efficient estimation.

method The paper establishes an information-theoretic lower bound and proposes a thresholding-based estimation algorithm with a time complexity of O(k^2 n). It also introduces a gradient-based minimization method with PCA for high-dimensional cases.

result The proposed method matches the established lower bound in sample complexity and achieves optimal parametric convergence rate.

Gaussian Mixture Models Model Selection Parameter Estimation Thresholding Spectral Gap

2026-03-20abs ↗pdf ↗

The Parametric Stability of Well-separated Spherical Gaussian Mixturesstat.ML

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.

Gaussian mixtures spherical Gaussian Mixture Model parameter stability total variation distance sharp thresholds

2023-02-01abs ↗pdf ↗

On the Geometry of Separation in Finite Gaussian Mixturesmath.ST

Understanding separation effects on parameter estimation in finite Gaussian mixtures

problem Minimum component separation impact on convergence rates in finite Gaussian mixtures

method Developing a unified geometric framework using Hellinger lower bounds and specialized moment-extraction test functions

result Separation complexity driven by spatial configuration of mixture components

Hellinger Wasserstein convergence rates parameter estimation finite Gaussian mixtures

2026-06-15abs ↗pdf ↗

Generalized Fast Multichannel Nonnegative Matrix Factorization Based on Gaussian Scale Mixtures for Blind Source Separationcs.SD

Enhanced FastMNMF for better speech separation.

problem Improving blind source separation for speech.

method Gaussian scale mixture (GSM) for heavy-tailed distributions.

result GSM-FastMNMF outperforms existing methods in speech enhancement.

blind source separation speech enhancement fast MNMF Gaussian scale mixture heavy-tailed distributions

2022-05-11abs ↗pdf ↗

Algebraic and Analytic Approaches for Parameter Learning in Mixture Modelscs.LG

Two approaches improve parameter learning in various mixture models.

problem Parameter learning in mixture models.

method Complex-analytic and algebraic-combinatorial methods.

result Improved sample sufficiency for parameter estimation in specific mixture models.

mixture models parameter learning complex analysis algebraic methods binomial mixtures

2020-01-19abs ↗pdf ↗

Optimal transport for vector Gaussian mixture modelsstat.ML

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 transport Gaussian mixtures vector-valued distributions mass transport computational efficiency

2020-12-16abs ↗pdf ↗

Gaussian Universality in Neural Network Dynamics with Generalized Structured Input Distributionsstat.ML

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.

neural networks deep learning Gaussian mixtures stochastic gradient descent hidden manifold model

2024-05-01abs ↗pdf ↗

Schema matching using Gaussian mixture models with Wasserstein distancecs.LG

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.

schema matching Gaussian mixture models Wasserstein distance machine learning

2021-11-28abs ↗pdf ↗

MIMO Detection via Gaussian Mixture Expectation Propagation: A Bayesian Machine Learning Approach for High-Order High-Dimensional MIMO Systemscs.IT

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.

MIMO detection Gaussian Mixture Model Expectation Propagation High-order systems Robust communication

2024-12-12abs ↗pdf ↗

Mixtures of Gaussians are Privately Learnable with a Polynomial Number of Samplesstat.ML

Study shows private learning of mixtures of Gaussians is possible with polynomial samples.

problem Estimating mixtures of Gaussians under differential privacy constraints.

method Developed a new framework for privately learning mixtures of Gaussians without structural assumptions.

result Polynomial number of samples (poly(k,d,1/α,1/ε,log(1/δ))) sufficient for estimation up to total variation distance α with (ε, δ)-DP.

Differential Privacy Mixtures of Gaussians Private Learning Polynomial Samples Total Variation Distance

2023-09-07abs ↗pdf ↗