Paper presents a reparameterized DP-DLGMM for clustering.
problem Non-parametric DP priors in DLGMM are hard to couple with variational inference.
method Closed-form updates for DP-DLGMM's variational posterior.
result Model generates realistic samples and performs competitively in semi-supervised settings.
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.
The paper optimizes hyperplanes for binary classification in high-dimensional data with latent Gaussian mixtures.
problem Binary classification in high-dimensional data with latent Gaussian mixtures.
method Generalized least squares estimator for estimating the direction of the optimal separating hyperplane. Simple correction for intercept estimation.
result The procedure is minimax optimal in many scenarios and can retain the interpolation property.
GMVAE improves open-set classification by clustering latent representations.
problem Improving open-set classification accuracy and robustness.
method Cooperative learning of reconstruction and clustering in the latent space of a GMVAE.
result Achieved an average F1 improvement of 29.5% in open-set classification.
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.
Latent Dirichlet Allocation models discrete data as a mixture of discrete distributions, using Dirichlet beliefs over the mixture weights. We study a variation of this concept, in which the documents' mixture weight beliefs are replaced with squashed Gaussian distributions. This allows documents to be associated with e…
A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce nonparametric cluster shapes. The possibly low-dimensional latent mixture model allow…
A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce nonparametric cluster shapes. The possibly low-dimensional latent mixture model allow…
Finite mixture models have become a popular tool for clustering. Amongst other uses, they have been applied for clustering longitudinal data and clustering high-dimensional data. In the latter case, a latent Gaussian mixture model is sometimes used. Although there has been much work on clustering using latent variables…
Unified framework for clustering with auxiliary data.
problem Clustering with datasets reflecting similar but different latent structures.
method Adaptive Transfer Clustering (ATC) algorithm that optimizes bias-variance decomposition.
result ATC proves optimal under Gaussian mixture model and shows transfer benefits.
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…
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.
In this paper, we learn disentangled representations of timbre and pitch for musical instrument sounds. We adapt a framework based on variational autoencoders with Gaussian mixture latent distributions. Specifically, we use two separate encoders to learn distinct latent spaces for timbre and pitch, which form Gaussian …
In sensing applications, sensors cannot always measure the latent quantity of interest at the required resolution, sometimes they can only acquire a blurred version of it due the sensor's transfer function. To recover latent signals when only noisy mixed measurements of the signal are available, we propose the Gaussian…
Proposes a VAE with Student-t mixture model for authorship attribution.
problem Traditional authorship attribution in closed-set scenarios.
method Extends variational autoencoder with embedded Student-t mixture model. result Superior performance over existing methods on Amazon review dataset.
PDGMM-VAE uses adaptive priors for better ICA recovery.
problem Nonlinear ICA recovery of latent source signals.
method Adaptive per-dimension Gaussian mixture model priors in a variational autoencoder.
result PDGMM-VAE effectively recovers source-specific non-Gaussian marginals.
UT module refines VAE latent space, improving disentanglement and interpretability.
problem Irregular latent distributions cause posterior collapse and misalignment in VAEs.
method UT module uses G-KDE clustering, GM modeling, and PIT to transform latent space into uniform distribution.
result UT module enhances disentanglement and interpretability of latent representations.
GGMPs improve non-Gaussian conditional density estimation.
problem Multimodality, heteroscedasticity, and strong non-Gaussianity in conditional density estimation.
method GGMP combines local Gaussian mixture fitting, cross-input component alignment, and per-component heteroscedastic GP training.
result GGMPs improve distributional approximation on synthetic and real-world datasets.
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…
This paper presents a new model called infinite mixtures of multivariate Gaussian processes, which can be used to learn vector-valued functions and applied to multitask learning. As an extension of the single multivariate Gaussian process, the mixture model has the advantages of modeling multimodal data and alleviating…
Corrected whitening restores orthogonality in high-dimensional spherical Gaussian mixtures.
problem In high-dimensional data, standard whitening fails to preserve orthogonality of mixture means.
method Derived exact limits for whitened means dot products using random matrix theory, constructed a corrected whitening matrix.
result Corrected whitening allows for improved estimation of spherical Gaussian mixtures in the large-dimensional regime.
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.
Efficient algorithms for sparse parameter recovery in mixture models.
problem Support recovery of high-dimensional sparse latent vectors in mixture models.
method Efficient algorithms with logarithmic sample complexity dependence on dimensionality.
result First guarantees on support recovery for various mixture models.
Training Gaussian process-based models typically involves an O(N3) computational bottleneck due to inverting the covariance matrix. Popular methods for overcoming this matrix inversion problem cannot adequately model all types of latent functions, and are often not parallelizable. However, judicious choice of model…
X-VAE uses data-adaptive Gaussian priors to improve latent space modeling.
problem Limitations of standard Gaussian priors in complex datasets.
method Data-adaptive Gaussian prior derived from pretrained autoencoder latent codes.
result Improved latent space modeling and generation quality.
The paper stabilizes invertible neural networks by using Gaussian mixture models.
problem Invertible neural networks can have exploding Lipschitz constants, leading to numerical errors.
method The authors use Gaussian mixture models to stabilize the latent distribution of invertible neural networks.
result Numerical simulations confirm that this modification improves sampling quality in multimodal applications.
Improved vector quantization using Gaussian mixtures for better codebook utilization.
problem Training instability and information loss in discrete vector quantization.
method Generalized vector quantization with Gaussian mixture model and aggregated categorical posterior evidence lower bound.
result GM-VQ improves codebook utilization and reduces information loss without heuristics.
Improves VAEs for generating data from mixed distributions.
problem Inability of VAEs to generate from individual data modalities.
method Conditional Prior VAE (CP-VAE) with two-level generative process.
result Generations from individual mixture components of multimodal data.
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.
Deep generative models are commonly used for generating images and text. Interpretability of these models is one important pursuit, other than the generation quality. Variational auto-encoder (VAE) with Gaussian distribution as prior has been successfully applied in text generation, but it is hard to interpret the mean…
In this paper, we develop an unsupervised generative clustering framework that combines the Variational Information Bottleneck and the Gaussian Mixture Model. Specifically, in our approach, we use the Variational Information Bottleneck method and model the latent space as a mixture of Gaussians. We derive a bound on th…
The paper tackles model collapse in GPLVMs by improving kernel flexibility and projection variance.
problem Model collapse in GPLVMs leading to vague latent representations.
method Theoretical analysis of projection variance, integration of SM and RFF kernels, and variational inference.
result The advisedRFLVM outperforms competing models in informative latent representations and missing data imputation.
VBphenoR uses variational Bayes for EHR-based patient phenotyping.
problem Phenotyping patients from EHR data for targeted treatments.
method Variational Bayes Gaussian Mixture Model (GMM) and logistic regression.
result Closed-form inference for efficient patient phenotype determination.
VampPrior Mixture Model improves clustering in DLVMs.
problem Simplicity of standard priors in DLVMs leads to poor clustering performance.
method Leverages VampPrior concepts to fit a Bayesian GMM prior in a VAE.
result VMM achieves highly competitive clustering performance on benchmark datasets.
MMGAN stabilizes GANs for multi-modal data clustering.
problem Stability and data distribution loss in GANs for multi-modal data.
method Model latent space as Gaussian mixture model, clusters data manifolds, and trains with clustering network.
result MMGAN outperforms state-of-the-art models in clustering multi-modal data.
Improved clustering and anomaly detection using latent space conditioning.
problem Anomaly detection on unlabeled data.
method Conditional latent space variational autoencoder (cLSVAE) that separates latent space by conditioning on data labels.
result The method outperforms typical variational autoencoders in clustering and anomaly detection.
A new clustering model for mixed datasets combines continuous and non-continuous data.
problem Challenges in clustering mixed data due to heterogeneous variables.
method Mixed Deep Gaussian Mixture Model (MDGMM) with multilayer architecture.
result Automatic selection of model specifications and optimal number of clusters.
We assume that a high-dimensional datum, like an image, is a compositional expression of a set of properties, with a complicated non-linear relationship between the datum and its properties. This paper proposes a factorial mixture prior for capturing latent properties, thereby adding structured compositionality to deep…
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.
In clustering we normally output one cluster variable for each datapoint. However it is not necessarily the case that there is only one way to partition a given dataset into cluster components. For example, one could cluster objects by their colour, or by their type. Different attributes form a hierarchy, and we could …
Mixture of multi-task GPs for clustering and prediction of functional data.
problem Handling multi-task learning, clustering, and prediction for functional data.
method A mixture of multi-task Gaussian processes with a variational EM algorithm for hyper-parameter optimization.
result Enhanced predictive performance for group-structured data.
Unified model for reducing dimensions and clustering high-dimensional data.
problem High-dimensional data clustering and dimensionality reduction.
method Hierarchical mixtures of Gaussians (HMoGs) with closed-form likelihood and inference.
result Efficiently models hundreds of latent dimensions, improving clustering performance.
Enhances GPLVM for multi-view data with scalable latent representation learning.
problem Limited kernel expressiveness and computational inefficiency in multi-view GPLVM.
method Introduces a new duality between spectral density and kernel function, uses NG-SM kernel, and applies random Fourier feature approximation for scalability.
result Consistently outperforms state-of-the-art models in learning meaningful latent representations across diverse datasets.
We present a multi-task learning formulation for Deep Gaussian processes (DGPs), through non-linear mixtures of latent processes. The latent space is composed of private processes that capture within-task information and shared processes that capture across-task dependencies. We propose two different methods for segmen…
Paper uses GMM and MAF for probabilistic classification, outperforming simpler models.
problem Classifying data with complex distributions.
method Density estimation using Gaussian Mixture Model and Masked Autoregressive Flow.
result Proposed classifiers outperform simpler models like linear discriminant analysis.
Differentiable EM for Gaussian Mixture Models improves model integration.
problem Non-differentiability of EM algorithm limits its use in modern learning pipelines.
method Presented and compared several differentiation strategies for EM.
result Differentiable EM enables the use of Mixture Wasserstein distance in machine learning tasks.
Generative Adversarial Networks (GANs) have been shown to produce realistically looking synthetic images with remarkable success, yet their performance seems less impressive when the training set is highly diverse. In order to provide a better fit to the target data distribution when the dataset includes many different…
PIMA autoencoders discover shared features in multimodal scientific data.
problem Discovering shared information in high-throughput scientific datasets.
method Physics-informed multimodal autoencoders (PIMA) with Gaussian mixture prior and product of experts formulation.
result Accurate cross-modal inference between images and mechanical stress-strain response in lattice metamaterials.