Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian -stable distribution received much interest in the literature. Here, we introduce a type of expectation maximization algorithm that e…
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48 results for “Sub-Gaussian Mixture Model”
Proposes a new model for clustering with heavier tails.
problem Clustering with heavy-tailed data.
method Finite mixture of skewed sub-Gaussian stable distributions, maximum likelihood estimation, EM algorithm.
result The proposed model can robustly handle heavy-tailed data.
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.
One-bit clustering method for two-component sub-Gaussian mixture models
problem Clustering in sub-Gaussian mixture models
method One-bit clustering using dithered quantization
result Decaying misclassification rate with exponential signal-to-noise ratio
Hidden Integrality and Semi-random Robustness of SDP Relaxation for Sub-Gaussian Mixture Modelstat.ML
SDP relaxation for Sub-Gaussian Mixture Model achieves optimal error bound and robustness.
problem Estimating discrete clustering structures in Sub-Gaussian Mixture Model.
method Hidden integrality property of SDP relaxation and semi-random robustness analysis.
result SDP relaxation achieves optimal error bound and robustness in semi-random setting.
The paper proves a regret bound for a sub-Gaussian mixture on unbounded data.
problem Tackles the challenge of achieving regret bounds for sub-Gaussian mixtures on unbounded data.
method Uses path-wise (deterministic) regret bounds and a cumulative variance process to derive the bound.
result Shows that on a specific event, the regret is eventually bounded by ln(ln V_T).
Study shows how over-parameterized classifiers can still perform well on noisy data.
problem Understanding how maximum margin classifiers perform in over-parameterized settings with noisy data.
method Analyzes maximum margin classifiers on sub-Gaussian mixtures, providing risk bounds.
result Characterizes conditions for 'benign overfitting' in linear classification problems.
Paper presents robust clustering methods for general mixture models.
problem Clustering with sub-Gaussian error assumptions often invalid in practice.
method Hybrid clustering with robust centroid estimate and data-driven initialization.
result Provably near-optimal mislabeling guarantees for general error distributions.
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.
New method estimates hidden binary mixture model centers efficiently.
problem Estimating centers in high-dimensional binary mixture models with hidden Markov structure.
method Proposes a minimax optimal procedure and an adaptive variant.
result Achieves optimal rate of order .
Robust clustering algorithm for datasets with outliers.
problem Clustering with arbitrary outliers.
method Spectral clustering with a rounding scheme on a Gaussian kernel matrix.
result Misclassification error decays exponentially with signal-to-noise ratio.
Paper analyzes SGMs for learning sub-Gaussian distributions without dimensionality constraints.
problem Learning sub-Gaussian distributions in high dimensions with SGMs.
method Introduced complexity notion and proved approximation and generalization rates.
result SGMs can approximate target sub-Gaussian distributions in total variation with dimension-independent rate.
Paper establishes universal lower bounds and optimal rates for clustering sub-exponential mixture models.
problem Achieving optimal error rates in clustering sub-exponential mixture models.
method Establishes universal lower bounds and demonstrates iterative algorithms' optimality in sub-exponential mixture models.
result Iterative algorithms achieve the universal lower bound in sub-exponential mixture models.
Develops an ℓ_p theory for PCA and spectral clustering.
problem Lack of precise characterizations of PCA scores for low-dimensional embedding.
method An ℓ_p perturbation theory for PCA in Hilbert spaces, analyzing eigenvectors and Gram matrix.
result Optimal recovery results for Gaussian mixture and stochastic block models.
Robust Bregman Clusteringmath.ST
A robust clustering method for noisy data using Bregman divergences.
problem Clustering data corrupted with clutter noise.
method k-means type method based on Bregman divergences with a trimming approach.
result Empirically optimal codebook converges to an optimal codebook in the distortion sense.
Paper tackles learning mixture of RUMs from partial data.
problem Learning a mixture of Random Utility Models (RUMs) from pairwise comparisons.
method PCA-based spectral clustering to reduce mixture to single component.
result Algorithm correctly clusters data from a mixture of RUMs with high probability.
Cluster Quilting clusters fragmented data sets for neuroscience and genomics.
problem Clustering fragmented data sets in neuroscience and genomics.
method Cluster Quilting method using patch ordering, patchwise SVD, sequential linear mapping, and k-means.
result Cluster Quilting discovers more accurate clusters than other methods.
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.
Efficient algorithm learns mixture models of heavy-tailed distributions.
problem Learning mixture models of heavy-tailed distributions.
method Efficient high-dimensional sparse Fourier transforms.
result Algorithm succeeds for heavy-tailed distributions, including Laplace but excluding Gaussians.
Adversarial training can lead to overfitting without compromising robustness.
problem Explaining benign overfitting in adversarially robust linear classification.
method Theoretical analysis and numerical experiments on adversarial training.
result Adversarially trained linear classifiers can achieve near-optimal risks despite overfitting noisy data.
We develop time-uniform confidence spheres for estimating means of random vectors.
problem Sequential mean estimation in high-dimensional spaces.
method Derive time-uniform confidence sphere sequences (CSSs) for various types of random vectors.
result Optimal CSSs for log-concave, sub-Gaussian, and sub- random vectors.
New method tightens sub-Gaussian concentration inequalities.
problem Estimating variance-type parameters of sub-Gaussian distributions.
method Using sub-Gaussian intrinsic moment norm to maximize normalized moments.
result Provides tighter sub-Gaussian concentration inequalities.
Picard-O improves ICA for faster, robust separation of signals.
problem Efficiently separating signals in multi-channel data.
method Preconditioned L-BFGS over orthogonal matrices.
result Picard-O outperforms FastICA in speed and robustness.
New private algorithms estimate location parameters with sub-Gaussian deviations.
problem Estimating location parameters with differential privacy and sub-Gaussian deviations for heavy-tailed data.
method Design two private algorithms for estimating the median and mean under differential privacy, showing sub-Gaussian deviations for unbounded random variables.
result Private median and mean estimators achieve sub-Gaussian deviations, unlike non-private counterparts which can have strictly worse deviations.
Optimizes sub-Gaussian matrices for preserving data distances.
problem Improving the performance of sub-Gaussian matrices in preserving data distances.
method Analyzes sub-Gaussian matrices and their dependence on the sub-Gaussian norm, presenting optimal bounds.
result Optimal dependence on the sub-Gaussian norm for sub-Gaussian matrices as near isometries on sets.
Algorithmic Gaussianization through Sketching: Converting Data into Sub-gaussian Random Designscs.LG
New algorithm converts data into sub-gaussian designs efficiently.
problem Efficiently converting large datasets into sub-gaussian random designs for robust performance.
method Algorithmic Gaussianization through sketching and averaging, using LESS embeddings.
result Efficient data sketches nearly indistinguishable from sub-gaussian designs.
Sharp sub-Gaussian upper bounds for subsolutions of Trudinger's equation on Riemannian manifoldsmath.AP
Sharp sub-Gaussian bounds for subsolutions of Trudinger's equation on Riemannian manifolds.
problem Bounding weak subsolutions of Trudinger's equation on Riemannian manifolds.
method Proving sub-Gaussian upper bounds for weak subsolutions.
result The upper bounds are sharp for specific classes of manifolds, including \(\mathbb{R}^{n}\).
UCB algorithm adapted for large-scale, non-sub-Gaussian problems.
problem Selecting the best alternative from a large set of options with non-sub-Gaussian performance distributions.
method Adapted UCB algorithm for non-sub-Gaussian settings, focusing on sample size and meta-UCB selection.
result UCB algorithms can achieve sample optimality in large-scale, non-sub-Gaussian problems.
Proves new concentration inequalities for sub-gaussian and sub-exponential variables.
problem Understanding functions of independent random variables better.
method Sub-gaussian and sub-exponential conditions, Rademacher complexities, Lipschitz function classes.
result Extension of Rademacher complexities to unbounded sub-exponential distributions.
Study improves self-normalized bounds for vector-valued processes beyond sub-Gaussianity.
problem Limited understanding of self-normalized concentration for vector-valued processes outside sub-Gaussian frameworks.
method Developed concentration inequalities for self-normalized processes with light tails (e.g., Bennett, Bernstein bounds) for vector-valued data.
result Provided new insights and bounds for self-normalized processes with non-sub-Gaussian distributions.
Faster mean estimation with sub-Gaussian error bounds.
problem Estimating the mean of a random vector with optimal statistical efficiency.
method An estimator for the mean of a random vector in R^d with optimal statistical efficiency and sub-Gaussian error bounds.
result Achieves optimal statistical efficiency with sub-Gaussian error bounds and a significantly faster runtime.
Kernel matrix concentration leads to KSC consistency.
problem High-dimensional clustering with noisy data.
method Nonasymptotic concentration inequalities for Lipschitz kernels.
result KSC algorithm consistency for noisy nested manifolds.
Quantum algorithm estimates mean with sub-Gaussian error.
problem Estimating mean of quantum-computed random variables.
method Quantum mean estimation algorithm with sub-Gaussian error rate.
result Achieves nearly-optimal quadratic speedup over classical methods.
Sharp comparison for sub-Gaussian random variables in convex order.
problem Comparing sub-Gaussian random variables in convex order.
method Proving dominance using moment generating functions and convex functions.
result Sharp comparison established between specific sub-Gaussian random variables.
Thompson Sampling bounds for contextual bandits with sub-Gaussian rewards.
problem Improving the performance of Thompson Sampling in contextual bandits with sub-Gaussian rewards.
method Proved comprehensive bounds on Thompson Sampling expected cumulative regret based on mutual information and lifted information ratio for sub-Gaussian rewards.
result Explicit regret bounds for various contextual bandit scenarios.
Low-Rank Thinningstat.ML
New method reduces summary points for datasets while maintaining quality.
problem Thinning datasets to reduce summary points while maintaining quality.
method Low-rank analysis of sub-Gaussian thinning.
result Guarantees high-quality compression for any distribution and kernel.
Estimates sub-Gaussian parameter with consistent and optimal rates.
problem Estimating sub-Gaussian parameter from random variables.
method Constrained maximization of empirical weighted cumulant generating function.
result Root-n rate estimator is consistent and optimal under certain conditions.
New study shows mean estimation algorithms can't beat sub-Gaussian rate in general.
problem Improving mean estimation beyond worst-case scenarios.
method Constructing counterexamples and introducing neighborhood optimality.
result No reasonable estimator can achieve better than sub-Gaussian error rate for any distribution.
Paper analyzes neural network models for sub-Gaussian distributions, proving approximation and generalization abilities.
problem Estimating unknown distributions from i.i.d. observations using neural network models.
method Score-based neural network generative models (SGMs) with specific network architectures and stopping strategies.
result SGMs can approximate scores with high accuracy and achieve nearly optimal convergence rates under mild assumptions.
New winsorized mean improves robustness to up to 50% contamination.
problem Improving robustness of mean estimation in the presence of outliers.
method Outlyingness-induced winsorized mean approach.
result Achieves up to 50% contamination robustness with sub-Gaussian performance.
Nonparametric Thompson Sampling achieves optimal regret for risk-averse bandits with sub-Gaussian rewards.
problem Optimizing risk-averse bandit problems with sub-Gaussian rewards.
method Anchor-free nonparametric Thompson Sampling algorithm .
result Achieves regret matching the instance-dependent lower bound to leading order in .
We study the problem of estimating the mean of a random vector given a sample of independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of exists. The estimator is based on a novel concept of a…
Two new algorithms improve robust PCA and Schatten packing.
problem Robustly estimating the top eigenvector of corrupted sub-Gaussian data.
method Two iterative filtering and nearly-linear time algorithms.
result First polynomial-time algorithms for non-trivial covariance estimation.
SVGD algorithm converges at rate 1/sqrt(log log n) for sub-Gaussian distributions.
problem Approximating a probability distribution with particles.
method Stein variational gradient descent (SVGD) with finite particles and sub-Gaussian target distribution.
result SVGD achieves a convergence rate of 1/sqrt(log log n) for sub-Gaussian distributions.
Study improves least squares estimation for heavy-tailed errors.
problem Improving least squares estimation under heteroscedastic and heavy-tailed errors.
method Analyzes the rate of convergence of least squares estimator under bounded conditional variance and finitely many moments of errors.
result Upper bounds on rates of convergence of LSE for heavy-tailed errors are found.
Paper improves SLCB regret bound for bounded noise.
problem Stochastic linear contextual bandits with bounded noise.
method Set-membership estimation (SME) and optimism in the face of uncertainty (OFU).
result Improved regret bound of .
Improved median of means estimator with tighter bounds.
problem Improving the efficiency and reliability of median of means estimator.
method Modification of the median of means estimator with sub-Gaussian deviation bounds.
result Achieves nearly optimal constants under minimal assumptions.
Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptionsmath.ST
Score-based diffusion models achieve optimal error bounds under non-parametric assumptions.
problem Improving the minimax optimality of score-based diffusion models.
method Kernel-based score estimation and early stopping strategy.
result Achieves minimax optimal error bounds under sub-Gaussian and Sobolev space assumptions.