Tunable GMM kernels improve on original GMM in various classification tasks.
problem Improving the efficiency and performance of GMM kernels.
method Developed three tunable GMM kernels: eGMM, pGMM, and epGMM.
result Tunable GMM kernels typically improve over the original GMM kernel on 60 datasets.
Nystrom method approximates GMM kernel for large datasets.
problem Efficiently computing GMM kernel for large-scale datasets.
method Apply Nystrom method to approximate GMM kernel.
result GMM-NYS approximates GMM kernel with comparable accuracy using fewer samples.
Proposes tunable GMM kernels for classification tasks.
problem Lack of competitive performance of GMM kernels compared to tree methods on deep learning datasets.
method Introduces tunable GMM kernels with added parameters and combines basic kernels for improved performance.
result Tunable GMM kernels can produce good results for various classification tasks.
Improved kernel methods enhance data similarity estimation.
problem Efficiently estimating the RBF kernel's similarity.
method Normalized Random Fourier Features (NRFF) and Generalized Min-Max (GMM) kernel.
result GCWS typically requires fewer samples than NRFF for comparable accuracy.
Proposes new kernels for better classification performance.
problem Improving classification performance in computer vision.
method Developed GInt and NGMM kernels, and validated their effectiveness empirically.
result GInt kernel performs well in classification tasks, NGMM kernel outperforms GInt.
We investigate a Gaussian mixture model (GMM) with component means constrained in a pre-selected subspace. Applications to classification and clustering are explored. An EM-type estimation algorithm is derived. We prove that the subspace containing the component means of a GMM with a common covariance matrix also conta…
Proposes a robust time series cluster kernel for MTS with missing data.
problem Challenges of similarity-based approaches for multivariate time series with missing data.
method Leverages Gaussian mixture models (GMM) augmented with prior distributions and ensemble learning.
result Demonstrates robustness to parameter choices and outstanding results for missing data.
New algorithm selects GMM components robustly and efficiently.
problem Estimating the number of components in GMMs when not known in advance.
method Robust model selection for GMMs with poly(k/ε) samples.
result Constructs a GMM with O(k) components approximating the distribution within ε.
Meta-learning improves Gaussian process uncertainty estimation.
problem Poor uncertainty estimation in Gaussian processes with deep kernels.
method Meta-learning to calibrate deep kernel GPs using task-specific uncalibrated and calibrated distributions.
result Improves uncertainty estimation performance with high regression performance.
A new method of moments estimator goes beyond data reweighting.
problem Estimation of moment restrictions and conditional moment restrictions.
method Kernel Method of Moments (KMM) based on maximum mean discrepancy.
result KMM achieves competitive performance on conditional moment restriction tasks.
GMM-HMMs improve malware classification compared to discrete HMMs.
problem Improving malware classification accuracy using GMM-HMM models.
method Used GMM-HMM models for opcode and entropy-based features comparison with discrete HMMs.
result GMM-HMMs generally improve significantly on entropy-based features classification results.
Paper tackles MSDA with GMMs and OT, improving over prior art.
problem Adapting multiple heterogeneous source measures to a target measure.
method Optimal Transport between Gaussian Mixture Models, with novel barycenter calculation.
result Improves image classification and fault diagnosis benchmarks.
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.
The paper studies scaling limits of Wasserstein metrics on Gaussian mixture models.
problem Understanding the scaling limits of Wasserstein metrics on Gaussian mixture models.
method Scaling limit approach on Gaussian mixture models, including inhomogeneous and extended models.
result Existence of the limit of the Wasserstein metric after renormalization for GMMs with zero variance.
Efficiently trains large GMMs with millions to billions of parameters.
problem Training large Gaussian Mixture Models (GMMs) is computationally expensive.
method Derives a variational approximation integrated with mixtures of factor analyzers (MFAs) to reduce complexity.
result Sublinear scaling in training GMMs, achieving significant speed-ups.
Paper analyzes GMM for separable data with various parameter structures.
problem Classifying separable data with logistic models and their generalizations.
method Introduces and analyzes Generalized Margin Maximizer (GMM) for logistic models with specific parameter structures.
result GMM outperforms max-margin classifiers in various parameter settings and structures.
New method improves estimation of complex models from conditional moment restrictions.
problem Estimation of complex models from conditional moment restrictions.
method Functional Generalized Empirical Likelihood (GEL) with a practical method.
result The method achieves state-of-the-art performance on two problems.
NE-GMM uses ES and GMM to improve uncertainty quantification.
problem Challenges in estimating mean and variance of complex distributions.
method Integrates Gaussian Mixture Model with Energy Score.
result NE-GMM outperforms in predictive accuracy and uncertainty quantification.
We develop a new compressive sensing (CS) inversion algorithm by utilizing the Gaussian mixture model (GMM). While the compressive sensing is performed globally on the entire image as implemented in our lensless camera, a low-rank GMM is imposed on the local image patches. This low-rank GMM is derived via eigenvalue th…
Novel distances between distributions using conditional ground distances.
problem Quantifying distances between statistical multivariate distributions.
method Optimal transport with entropic regularization and ground distance on conditionals.
result Upper bounds for jointly convex distances and improved GMM learning.
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 improves GMM learning performance through multi-task and transfer learning.
problem Improving GMM learning performance through similar task structures.
method Proposes a multi-task GMM learning procedure based on EM algorithm, robust to outliers.
result Achieves minimax optimal rate of convergence for parameter estimation and mis-clustering.
A new algorithm using sliced Wasserstein distance improves GMM parameter estimation.
problem Inefficiency of EM algorithm in finding optimal GMM parameters.
method Proposes a new algorithm using sliced Wasserstein distance to minimize the distance between the mixture model and data distribution.
result The new algorithm yields more robust and accurate GMM parameter estimates.
Study uses GMM-UBM and i-vectors to assess Parkinson's patients via speech, handwriting, and gait.
problem Assessing neurological state of Parkinson's disease patients using speech, handwriting, and gait signals.
method GMM-UBM and i-vectors applied to speech, handwriting, and gait signals.
result Different feature sets from each signal are crucial for assessing Parkinson's patients.
Paper uses robust GMM to reconstruct missing data in Sentinel-2 images for crop monitoring.
problem Missing data in remote sensing images, especially from multispectral and SAR sensors.
method Robust Gaussian Mixture Models (GMM) with outlier detection using isolation forest.
result Robust GMM outperforms standard GMM in reconstructing imputed values, reducing errors.
New GMM models fit high-dimensional data with fewer parameters.
problem Overparameterization and lack of flexibility in GMMs for high-dimensional data.
method Piecewise-constant covariance eigenvalue profiles, EM and penalized EM algorithms.
result Superior likelihood-parsimony tradeoffs in density fitting, clustering, and denoising.
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.
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.
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.
Paper introduces new Gromov-type distances for comparing Gaussian mixture models.
problem Comparing distributions across different metric spaces using Gromov-Wasserstein distances.
method Incorporates invariance properties into MW2, introducing MGW2 and EW2.
result MGW2 and EW2 are efficient for estimating distances between GMMs in practical applications.
GMM uses mmWave radar to classify traffic modes in poor lighting.
problem Classifying traffic modes in poor lighting conditions.
method GMM on mmWave radar point clouds.
result Good segmentation performance in pedestrian and car classification.
Regularized EM algorithm improves GMM clustering in low sample settings.
problem Numerical instability and convergence issues in EM-GMM for low sample support.
method Regularized EM algorithm that maximizes penalized GMM likelihood, ensuring positive definiteness and structured covariance matrices.
result The regularized EM algorithm leads to better performing EM for structured covariance matrix models or low sample settings.
Develops a robust GMM estimator for outlier-tolerant inference.
problem Sensitive GMM estimation to outliers in inference problems.
method Robustified GMM estimator with computational efficiency and recovery guarantees.
result First computationally efficient GMM estimator for ε ε ε fraction of adversarial outliers with O ( ε ) O(\sqrtε) O ( ε ) recovery guarantee. This paper analyzes MFVBI for GMM using statistical mechanics.
problem Approximate fast computation of Gaussian Mixture Model.
method Statistical mechanics and MFVBI applied to GMM.
result Rigorous analysis and mathematical foundation for MFVBI applied to GMM.
A new metric for comparing HMMs, especially GMM-HMMs, without Monte Carlo samples.
problem Comparing Hidden Markov Models (HMMs) with Gaussian conditional distributions.
method Aggregated Wasserstein metric based on optimal transport between Gaussian mixtures.
result The Aggregated Wasserstein metric is a semi-metric that can be computed efficiently and is invariant to state relabeling.
Study shows k k k -means and GMM can scale sublinearly with clusters using variational EM.
problem Improving clustering efficiency with sublinear complexity.
method Applying variational EM to reduce complexity of k k k -means and GMM iterations. result Reduces computational complexity from linear to sublinear with respect to the number of clusters.
Paper proposes PCA-GMM for efficient superresolution of material images.
problem Efficiently handling large and high-dimensional data sets.
method PCA-GMM combining Gaussian Mixture Model and PCA for dimensionality reduction.
result PCA-GMM improves superresolution of material images with moderate dimensionality reduction.
Unified perspective on natural gradient methods for GMMs, improving variational inference.
problem Efficiently learning multi-modal approximations of complex distributions.
method Comparison and optimization of VIPS and iBayes-GMM methods for Gaussian mixture models.
result Hybrid approach significantly outperforms both VIPS and iBayes-GMM.
Automatically differentiable estimation for BLP model reduces bias in demand estimation.
problem Estimating the BLP model with reduced bias and improved performance.
method Phrasing BLP as an automatically differentiable moment function, using CUE for estimation, and incorporating MCMC credible intervals.
result CUE estimation shows lower bias but higher MAE compared to 2S-GMM, with MCMC providing closest empirical coverage.
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.
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.
A comparative study of the application of Gaussian Mixture Model (GMM) and Radial Basis Function (RBF) in biometric recognition of voice has been carried out and presented. The application of machine learning techniques to biometric authentication and recognition problems has gained a widespread acceptance. In this res…
SLIM efficiently solves overidentified models in a scalable manner.
problem Overidentified models with many moment conditions.
method Stochastic approximation framework using mini-batches and unbiased updates.
result SLIM solves overidentified models in under 1.4 hours, compared to 18 hours for full-sample GMM.
This paper finds the noise threshold for learning Gaussian mixture models equals channel capacity.
problem Learning Gaussian mixture models with noisy data.
method Bayesian formulation with uniformly distributed centers on a sphere, analyzing the large system limit.
result The maximal noise level σ 2 σ^2 σ 2 for which GMM learning is as easy as labeled observations is the channel capacity. Estimates RL data for dynamic treatment effects using GMM.
problem Estimating dynamic treatment effects from RL data with nonstationary behavior policies.
method Weighted GMM approach to stabilize variance in adaptive RL settings.
result Valid hypothesis testing and confidence regions for dynamic treatment effects.
Modeling the Drosophila connectome using semiparametric spectral methods.
problem Understanding the structure and function of the Drosophila mushroom body network.
method Semiparametric spectral modeling, latent structure model (LSM), Gaussian mixture modeling (GMM), adjacency spectral embedding (ASE).
result Captures latent connectome structure and elucidates neuronal properties.
Develops a GMM method to estimate roughness in stochastic volatility models.
problem Estimating roughness in stochastic volatility models with fractional Brownian motion.
method GMM approach for log-normal models with integrated variance and noisy realized variance.
result Consistent and asymptotically normal parameter estimator with bias correction.
New slicing methods speed up Gaussian mixture Wasserstein distance computations.
problem High computational cost of the mixture Wasserstein distance.
method Slicing-based approximations to reduce computational complexity.
result Significant reduction in computational complexity while preserving key properties.