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.
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.
Proposes a new method for estimating sparse precision matrices in GMRF-MM models.
problem Difficulty in learning GMMs with large parameters and limited data.
method Restricts GMM to GMRF-MM, proposes efficient optimization for sparse precision matrices, and debiases the estimates.
result Debiasing approach outperforms GLASSO in single-GMRF and GMRF-MM cases.
Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns and enable extrapolation. These kernels are derived by modelling a spectral dens…
PbP strategy improves logistic model prediction with missing values.
problem Predicting with missing inputs in logistic models.
method Pattern-by-Pattern (PbP) strategy for logistic models with missing values.
result PbP accurately approximates Bayes probabilities under GPMM across various missing data scenarios.
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.
Variation Autoencoder (VAE) has become a powerful tool in modeling the non-linear generative process of data from a low-dimensional latent space. Recently, several studies have proposed to use VAE for unsupervised clustering by using mixture models to capture the multi-modal structure of latent representations. This st…
EMODM detects abnormal patterns in complex systems.
problem Detecting abnormal patterns in complex systems.
method Probabilistic models and statistical algorithms.
result EMODM detects abnormal patterns in real-time raw data.
In data-mining applications, we are frequently faced with a large fraction of missing entries in the data matrix, which is problematic for most discriminant machine learning algorithms. A solution that we explore in this paper is the use of a generative model (a mixture of Gaussians) to compute the conditional expectat…
Discovering human mobility patterns with geo-location data collected from smartphone users has been a hot research topic in recent years. In this paper, we attempt to discover daily mobile patterns based on GPS data. We view this problem from a probabilistic perspective in order to explore more information from the ori…
Standard kernels such as Matérn or RBF kernels only encode simple monotonic dependencies within the input space. Spectral mixture kernels have been proposed as general-purpose, flexible kernels for learning and discovering more complicated patterns in the data. Spectral mixture kernels have recently been generalized in…
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.
Learning representation on graph plays a crucial role in numerous tasks of pattern recognition. Different from grid-shaped images/videos, on which local convolution kernels can be lattices, however, graphs are fully coordinate-free on vertices and edges. In this work, we propose a Gaussian-induced convolution (GIC) fra…
The expressive power of Gaussian processes depends heavily on the choice of kernel. In this work we propose the novel harmonizable mixture kernel (HMK), a family of expressive, interpretable, non-stationary kernels derived from mixture models on the generalized spectral representation. As a theoretically sound treatmen…
GMVAEs cluster and generate game levels without labels.
problem Manual exploration of latent space for VAE-generated game levels.
method Apply Gaussian Mixture VAEs (GMVAEs) to learn latent clusters and generate levels.
result GMVAEs can cluster and generate game levels without requiring labels.
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.
BN^2MF identifies unknown exposure patterns in environmental mixtures.
problem Identifying unknown exposure patterns in environmental mixtures.
method Bayesian non-parametric non-negative matrix factorization (BN^2MF) with non-negative continuous priors and a non-parametric sparse prior.
result Estimates patterns of chemical exposures without specifying the number of patterns.
Although Recurrent Neural Network (RNN) has been a powerful tool for modeling sequential data, its performance is inadequate when processing sequences with multiple patterns. In this paper, we address this challenge by introducing a novel mixture layer and constructing an adaptive RNN. The mixture layer augmented RNN (…
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.
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.
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.
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…
FABLE incorporates instance features into PWS label models for improved performance.
problem Lack of instance features in existing label models limits their performance.
method FABLE uses a mixture of Bayesian label models and a Gaussian Process classifier to incorporate instance features.
result FABLE achieves the highest averaged performance across nine baselines on benchmark datasets.
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 α-stable distribution received much interest in the literature. Here, we introduce a type of expectation maximization algorithm that e…
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.
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.
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.
A method models continuous-time glucose distributions in children with diabetes.
problem Capturing subtle temporal changes in glucose distributions.
method Probabilistic framework using Gaussian mixtures and neural ODEs.
result Detects treatment-related improvements in glucose dynamics.
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.
The mixture of Gaussian distributions, a soft version of k-means , is considered a state-of-the-art clustering algorithm. It is widely used in computer vision for selecting classes, e.g., color, texture, and shapes. In this algorithm, each class is described by a Gaussian distribution, defined by its mean and covarianc…
Study exact community detection in k-community Gaussian mixtures with different intensities.
problem Community detection in k-community Gaussian mixtures with varying intensities.
method Explicitly find the threshold for exact recovery of maximum likelihood estimation.
result Threshold for exact recovery of maximum likelihood estimation is identified.
Proposes a new model for handling missing data.
problem Nonignorable missingness in data.
method Variational autoencoder architecture with pattern-set mixtures.
result Achieves state-of-the-art imputation performance.
New method improves Gaussian Mixture Model fitting speed.
problem Slow convergence of EM algorithm for complex data.
method Riemannian Newton Trust-Region method for Gaussian Mixture Models.
result Outperforms existing methods in runtime and iterations.
This paper studies clustering and embedding in high-dimensional Gaussian mixture block models.
problem Clustering and embedding in high-dimensional Gaussian mixture block models.
method Spectral clustering and embedding algorithms for graphs sampled from Gaussian mixture block models.
result Performance analysis of spectral clustering and embedding algorithms for 2-component spherical Gaussian mixtures.
Spectral mixture (SM) kernels comprise a powerful class of generalized kernels for Gaussian processes (GPs) to describe complex patterns. This paper introduces model compression and time- and phase (TP) modulated dependency structures to the original (SM) kernel for improved generalization of GPs. Specifically, by adop…
Tensor decomposition recovers Gaussian mixtures from moments.
problem Recovering Gaussian mixture models from datasets.
method Symmetric tensor decomposition of moment tensors built from empirical moments.
result Identifiable tensors with interpolation degree less than half their order.
We propose a greedy variational method for decomposing a non-negative multivariate signal as a weighted sum of Gaussians, which, borrowing the terminology from statistics, we refer to as a Gaussian mixture model. Notably, our method has the following features: (1) It accepts multivariate signals, i.e. sampled multivari…
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.
Study learns Gaussian mixtures from censored data.
problem Learning Gaussian mixtures with incomplete data.
method Proposes an algorithm to estimate weights and means with minimal samples.
result Achieves accurate estimation with very few samples.
Gradient descent on DDPM objective learns Gaussian mixtures efficiently.
problem Learning Gaussian mixtures using gradient-based methods.
method Gradient descent on DDPM objective, connecting to EM and spectral methods.
result Gradient descent can efficiently recover Gaussian mixture parameters under certain conditions.
The paper proposes a method to identify high-quality financial patterns using entropy.
problem Extracting reliable short-term patterns from noisy financial data.
method Entropy-assisted framework for clustering and pruning patterns.
result High-quality patterns with low local entropy and historical profitability.
Generative model improves EMG pattern recognition accuracy.
problem Stochastic characteristics of EMG signals not fully considered in existing classification methods.
method Scale mixture-based stochastic generative model with variational Bayesian learning.
result Proposed method outperforms conventional classifiers in EMG pattern recognition.
New algorithm for tensor decomposition and Gaussian mixture models.
problem Efficiently decompose overcomplete order-3 tensors and estimate parameters of Gaussian mixtures.
method Proposes Jennrich's algorithm adapted for tensor decomposition and Gaussian mixture models.
result Efficient algorithm for decomposing symmetric overcomplete order-3 tensors and estimating parameters of Gaussian mixtures.
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.
GCMM improves clustering and fits un-synchronized data.
problem Improving clustering performance with copulas.
method Mathematical definition, copula concepts, Expectation Maximum algorithms, nonparametric estimation.
result GCMM outperforms GMM in goodness-of-fit and data analysis.
The parsimonious Gaussian mixture models, which exploit an eigenvalue decomposition of the group covariance matrices of the Gaussian mixture, have shown their success in particular in cluster analysis. Their estimation is in general performed by maximum likelihood estimation and has also been considered from a parametr…
A new vine copula mixture model improves clustering accuracy for non-Gaussian data.
problem Finite mixture models struggle with asymmetric tail dependencies and non-elliptical clusters.
method Proposes a vine copula mixture model for clustering non-Gaussian data, addressing model selection and parameter estimation.
result Significant improvement in clustering accuracy for data with asymmetric tail dependencies or non-Gaussian margins.
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.