Proposes scale mixture of NNGPs for more flexible stochastic processes.
problem Limited focus on broadening the class of stochastic processes from NNGPs.
method Scale mixture of NNGPs with scale priors on last-layer parameters.
result Turns neural networks into a richer class of stochastic processes.
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.
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.
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.
In this paper we propose a novel framework for the construction of sparsity-inducing priors. In particular, we define such priors as a mixture of exponential power distributions with a generalized inverse Gaussian density (EP-GIG). EP-GIG is a variant of generalized hyperbolic distributions, and the special cases inclu…
ELU algorithm improves on EM for over-specified Gaussian mixtures.
problem Slow convergence of EM in over-specified Gaussian mixtures.
method Developed ELU algorithm for two-component mixtures, combining exponential location update and gradient descent.
result ELU converges to final statistical radius after logarithmic iterations, resolving open question.
We propose a practical and scalable Gaussian process model for large-scale nonlinear probabilistic regression. Our mixture-of-experts model is conceptually simple and hierarchically recombines computations for an overall approximation of a full Gaussian process. Closed-form and distributed computations allow for effici…
Paper introduces scalable clustering for large datasets with outliers.
problem Lack of scalable algorithms for large datasets with outliers.
method Provable robust clustering algorithm based on loss minimization for Gaussian mixture models.
result Algorithm provides high accuracy with theoretical guarantees and outperforms existing methods.
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.
Novel methods for splitting Gaussian mixtures improve uncertainty propagation in nonlinear systems.
problem Improving accuracy and efficiency in nonlinear uncertainty propagation.
method Preserving mean and covariance, novel heuristics for selecting splitting direction informed by initial uncertainty and nonlinear function properties.
result Improved accuracy and efficiency in uncertainty propagation compared to existing techniques.
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.
The Perona-Malik model has been very successful at restoring images from noisy input. In this paper, we reinterpret the Perona-Malik model in the language of Gaussian scale mixtures and derive some extensions of the model. Specifically, we show that the expectation-maximization (EM) algorithm applied to Gaussian scale …
Study how depth affects inference in deep Bayesian neural networks.
problem Understanding how depth impacts inference in overparameterized linear Bayesian neural networks.
method Interpreting finite deep linear Bayesian neural networks as scale mixtures of Gaussian process predictors.
result Advances analytical understanding of how depth affects inference in a simple class of Bayesian neural networks.
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…
Optimal transport between Gaussian Mixture Models improves domain adaptation efficiency.
problem Adapting machine learning models to new data distributions with minimal access.
method Optimal transport between Gaussian Mixture Models (GMMs) for domain adaptation.
result Our methods are more efficient and scalable with sample size and dimensions.
Bayesian model averaging improves causal effect estimation by averaging over multiple models.
problem Estimating causal effects under linear Structural Causal Models (SCMs).
method Bayesian model averaging using Gaussian scale mixture distributions for computational efficiency.
result Bayesian model averaging is optimal for causal effect estimation.
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/ε) iterations to attain an ε-accurate distribution in total variation distance, independent of dimension and number of components. 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.
We present a probabilistic model for natural images which is based on Gaussian scale mixtures and a simple multiscale representation. In contrast to the dominant approach to modeling whole images focusing on Markov random fields, we formulate our model in terms of a directed graphical model. We show that it is able to …
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.
Model detects epileptic seizures in EEG with high sensitivity.
problem Detecting epileptic seizures in EEG signals.
method Time-series scale mixture model with hidden Markov structure.
result Model outperformed baselines in seizure detection.
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 …
This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components. First, we present a general theory for strong identifiability, which extends from the previous work of Nguyen [2013] and Chen [1995] to address…
In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex forms and better properties than traditional Cauchy and double exponential priors. W…
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.
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.
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.
We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical Gaussian components, where the clusters are distinguished by only a few relevant dimens…
Multi-output Gaussian processes (MOGPs) are an extension of Gaussian Processes (GPs) for predicting multiple output variables (also called channels, tasks) simultaneously. In this paper we use the convolution theorem to design a new kernel for MOGPs, by modeling cross channel dependencies through cross convolution of t…
Elliptical processes extend Gaussian models with heavier tails.
problem Regression and classification with non-Gaussian likelihoods or heavy tails.
method Spline normalizing flow for variational inference of elliptical distributions.
result Elliptical processes outperform Gaussian processes in non-Gaussian settings.
New spectral mixture representation for isotropic kernels simplifies random Fourier features.
problem Applying Random Fourier Features to complex kernels.
method Decompose isotropic kernels into scale mixtures of α-stable random vectors.
result Constructive spectral sampling formula for various kernels.
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.
Method identifies latent variables from high-dimensional data with piecewise affine mixing.
problem Identifying latent variables from high-dimensional observations with dependencies and piecewise affine transformations.
method Proposes a two-stage method with sparsity and Gaussianity regularization.
result Effectively recovers ground-truth latent variables from synthetic and image data.
A family of parsimonious shifted asymmetric Laplace mixture models is introduced. We extend the mixture of factor analyzers model to the shifted asymmetric Laplace distribution. Imposing constraints on the constitute parts of the resulting decomposed component scale matrices leads to a family of parsimonious models. An…
Study calculates tail risk for various mixture distributions.
problem Estimating tail risk for complex distribution mixtures.
method Analyzes tail conditional expectation for location-scale mixtures of elliptical distributions.
result Developed methods for calculating tail risk in various distributions.
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 method identifies causal DAG structure from non-Gaussian errors.
problem Learning causal structure from non-Gaussian errors in Bayesian networks.
method Bayesian hierarchical model with DAG prior for non-Gaussian errors.
result Posterior DAG selection consistency achieved under mild assumptions.
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.
Method estimates mixture components without discretizing parameters.
problem Learning from mixtures of continuous features with noise.
method Off-the-grid optimization method for continuous parameter space.
result Prediction error bound similar to Lasso predictor.
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.
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.
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.
The exponential growth of complex data demands fully automatic clustering. Gaussian mixture models (GMMs) provide uncertainty-aware grouping but often require expertise to specify hyperparameters, e.g., component count and covariance structure. While mclust (R) automates this via Bayesian Information Criterion (BIC), P…
Theoretical analysis of entropy approximation for Gaussian mixtures.
problem Lack of theoretical guarantees for entropy approximation of Gaussian mixtures.
method Theoretical analysis of the error between true and approximate entropy.
result The error converges to zero as the ratios of means to variances tend to infinity, providing a guarantee for high-dimensional problems.
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.
HTFM improves mode coverage and tail-statistic recovery for heavy-tailed data.
problem Tackles heavy-tailed data in various domains with rare events.
method Proposes a framework using clock-conditioned Gaussian sources and truncated logsignature features.
result Improves mode coverage, sample quality, and tail-statistic recovery over Gaussian flow matching and baselines.
Algorithm estimates mixtures of arbitrary Gaussians robustly in presence of corruptions.
problem Estimating mixtures of arbitrary Gaussians in the presence of a constant fraction of arbitrary corruptions.
method Polynomial-time algorithm using partial clustering and tensor decomposition.
result Resolves the main open problem in several previous works on algorithmic robust statistics.
Estimates Gaussian mixtures from weighted samples efficiently.
problem Estimating Gaussian mixtures from weighted samples with correct weight treatment.
method Density interpretation and expectation-maximization method considering weights.
result Correctly estimates Gaussian mixtures with weighted samples.