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.
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.
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.
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.
Introduces tunable basis functions for Gaussian processes.
problem Reduces computational complexity in Gaussian process approximations.
method Introduces tunable, local, and bounded basis functions for kernel approximation.
result Demonstrates superior performance compared to state-of-the-art methods, especially with poorly chosen kernel functions.
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.
Kernel ridgeless regression with random features shows good generalization without explicit regularization.
problem Generalization of kernel ridgeless regression without explicit regularization.
method Investigation of ridgeless regression with random features and stochastic gradient descent, exploring the effect of random features error and spectral density optimization.
result Random features error exhibits the double-descent curve, leading to improved generalization.
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.
A new GAN model α α α -GAN with tunable loss function addresses gradient vanishing and mode collapse issues.
problem Addressing vanishing gradients and mode collapse in GANs.
method Introduced a tunable GAN α α α -GAN using a supervised α α α -loss function. result Holistic understanding of α α α -GAN related to Arimoto divergence and convergence properties. 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.
ARS visualization improves t-SNE dynamics with tunable attraction and repulsion.
problem Improve data visualization techniques for complex data sets.
method ARS framework based on t-SNE dynamics with normalized interactions and tunable kernels.
result ARS visualization provides better control over cluster tightness and spacing.
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.
Tunable sensitivity helps neural networks learn from hard examples.
problem Improving neural network learning from hard examples.
method A new generalized cross-entropy gradient step with tunable sensitivity.
result Test prediction error is lower with tunable sensitivity.
This paper presents a practical, and theoretically well-founded, approach to improve the speed of kernel manifold learning algorithms relying on spectral decomposition. Utilizing recent insights in kernel smoothing and learning with integral operators, we propose Reduced Set KPCA (RSKPCA), which also suggests an easy-t…
This paper enhances the Random Survival Forest model for better predictive maintenance.
problem Improving time-to-failure estimation in predictive maintenance with Random Survival Forest.
method A three-level framework for quantifying hyperparameter tunability, including model-level and hyperparameter-level metrics.
result Hyperparameter tuning significantly improves Random Survival Forest model performance in predictive maintenance.
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 proposes a new landmark selection method for kernel ridge regression.
problem Efficient landmark selection for scalable kernel methods.
method Two-step approach: first computes importance scores, then clusters them into landmarks.
result Proposed method provides better accuracy and efficiency trade-offs.
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.
Graph convolutional deep kernel machine learns representations for graph tasks.
problem Limited representation learning in infinite-width neural networks.
method Developed a graph convolutional deep kernel machine as an infinite-width limit.
result Representation learning improves performance for heterophilous node classification tasks.
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.
Quantum memristors created in photonic platforms with real-time control.
problem Creating quantum memristors for integrated quantum photonics.
method Designing a tunable beam splitter with real-time control, using weak measurements and classical feedback.
result Demonstrated that the tunable beam splitter behaves as a quantum memristor.
Paper introduces MRCs that minimize worst-case 0-1 loss, providing tight performance guarantees.
problem Minimizing worst-case 0-1 loss in classification.
method MRCs that minimize worst-case 0-1 loss with uncertainty sets of distributions.
result MRCs provide tight performance guarantees and are strongly universally consistent.
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.
Wiener-Granger causality is a widely used framework of causal analysis for temporally resolved events. We introduce a new measure of Wiener-Granger causality based on kernelization of partial canonical correlation analysis with specific advantages in the context of large high-dimensional data. The introduced measure is…
MLtuner automates tuning machine learning parameters for better performance.
problem Manual tuning of machine learning parameters is error-prone and requires domain knowledge.
method Snapshotting, branching, and optimization-guided online trial-and-error.
result MLtuner finds and re-tunes parameters robustly and efficiently for various ML 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.
The paper formalizes hyperparameter tuning and benchmarks six algorithms.
problem Optimizing machine learning hyperparameters.
method Formalized problem, defined defaults, conducted benchmarking study.
result Default values and tunability measures for hyperparameters.