StepMix estimates mixture models with covariates for social science applications.
problem Estimating latent classes with covariates in social science models.
method Pseudo-likelihood estimation using one-, two-, and three-step approaches.
result Unified framework for expectation-maximization subroutines.
Proposes a method to ensure low losses across all subpopulations in large datasets.
problem Standard practice of minimizing average loss fails to guarantee low losses across all subpopulations in heterogeneous datasets.
method Convex procedure that controls worst-case performance over all subpopulations of a given size with finite-sample convergence guarantees.
result Empirically, the worst-case procedure learns models that do well against unseen subpopulations.
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.
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.
DM framework improves robustness and efficiency in latent-mixture models.
problem Efficient and robust inference in latent-mixture models.
method Divergence-minimization framework with monotonic convergence and robustness guarantees.
result DM yields consistent and asymptotically normal estimators under correct specification.
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…
Proposes a Varying-Coefficient MoE model for analyzing dynamic data.
problem Inadequate constant coefficients in MoE models for dynamic settings.
method Varying-Coefficient Mixture of Experts (VCMoE) model with varying coefficients in gating and expert models.
result Established identifiability and consistency of the VCMoE model.
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.
New method prevents posterior collapse in iVAE models.
problem Posterior collapse in iVAE models where observations and ICs are independent given covariates.
method Developed CI-iVAE by considering a mixture of encoder and posterior distributions in the objective function.
result Prevents posterior collapse, resulting in latent representations with more information of the observations.
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.
Develops a high-dimensional differentially-private EM algorithm with near-optimal statistical guarantees.
problem Designing differentially-private EM algorithms for high-dimensional latent variable models.
method Noisy iterative hard-thresholding, statistical guarantees, near-optimal convergence rates.
result Near-optimal statistical guarantees and minimax rate optimality in high-dimensional settings.
The paper explores strong identifiability and parameter learning in regression models with heterogeneous responses.
problem Understanding heterogeneity in data populations through conditional distributions of a response variable.
method Investigation of strong identifiability, convergence rates, and posterior contraction behavior in finite mixture of regression models.
result Theoretical findings on conditions for strong identifiability and rates of convergence in regression mixture models.
Early approaches to multiple-output Gaussian processes (MOGPs) relied on linear combinations of independent, latent, single-output Gaussian processes (GPs). This resulted in cross-covariance functions with limited parametric interpretation, thus conflicting with the ability of single-output GPs to understand lengthscal…
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.
Mixture models are a standard approach to dealing with heterogeneous data with non-i.i.d. structure. However, when the dimension p is large relative to sample size n and where either or both of means and covariances/graphical models may differ between the latent groups, mixture models face statistical and computati…
Bayesian framework for analyzing heterogeneous covariance data with a novel MoE-Wishart model.
problem Analyzing complex multivariate systems with varying covariance structures.
method Comprehensive Bayesian framework using mixture-of-experts Wishart model with predictor-dependent mixture weights.
result Accurate subpopulation recovery and estimation in heterogeneous covariance scenarios.
Optimizes clustering in Gaussian mixtures with varying covariance matrices.
problem Clustering with anisotropic Gaussian mixture models where covariance matrices vary.
method Proposes a computationally feasible hard EM type algorithm.
result Achieves optimal clustering rate with few iterations.
We introduce a mixture model for censored durations (C-mix), and develop maximum likelihood inference for the joint estimation of the time distributions and latent regression parameters of the model. We consider a high-dimensional setting, with datasets containing a large number of biomedical covariates. We therefore p…
Study reconstructs causal graph from latent variables using mixture oracles.
problem Reconstructing causal graphical model from data with latent variables.
method Reduction to mixture oracle to identify latent representations and causal structure.
result Conditions for identifying latent representations and causal model.
New method estimates sparse covariance matrices in logit mixtures.
problem Estimating correlations among random coefficients in logit models.
method Mixed-integer optimization (MIO) with Markov Chain Monte Carlo (MCMC) for posterior draws.
result Correctly recovers true covariance structure from synthetic data.
Discover causal structure from mixtures of DAGs using latent variable algorithms.
problem Discover causal structure from distributions arising from mixtures of DAGs.
method Causal structure discovery algorithms such as FCI for latent variables.
result Recover a 'union' of the component DAGs and identify varying conditional distributions.
ADHAM provides interpretable survival analysis for healthcare.
problem Limited interpretability in deep learning survival models.
method Additive Deep Hazard Analysis Mixtures (ADHAM) with latent subgroup structure.
result ADHAM offers interpretable insights into exposure-outcome associations.
Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides insight into the systems that generated the graphs. Moreover, in applications s…
Bayesian approach learns nonparametric mixture components from heterogeneous data.
problem Realistic modeling of heterogeneous data populations with nonparametric mixture components.
method Bayesian nonparametric modeling using Dirichlet process mixture priors.
result Posterior contraction rates for component densities are nearly polynomial, improving over deconvolution methods.
Meta-learning improves OoD detection with minimal in-distribution data.
problem Efficient OoD detection with limited in-distribution data.
method Meta-learning in latent space with Gaussian mixture models.
result Meta-learning enhances OoD detection performance.
New algorithm optimizes complex model selection for non-homogeneous hidden Markov models.
problem Complex combinatorial optimization problem for model selection in NHHMMs.
method Adaptive simulated annealing EM algorithm (ASA-EM).
result Joint optimization of models and parameters for a criterion of interest.
This paper studies convergence behavior of latent mixing measures that arise in finite and infinite mixture models, using transportation distances (i.e., Wasserstein metrics). The relationship between Wasserstein distances on the space of mixing measures and f-divergence functionals such as Hellinger and Kullback-Leibl…
Mixture components improve VAE performance by increasing latent flexibility.
problem Improving variational autoencoder (VAE) performance through more flexible latent representations.
method Modeling mixture components with separate encoder networks and analyzing their impact on ELBO.
result Increasing the number of mixture components improves VAE performance on various datasets.
New algorithm clusters Gaussian mixtures with unknown covariance efficiently.
problem Clustering data from a mixture of Gaussians with unknown covariance.
method Developed an efficient spectral algorithm based on a Max-Cut integer program.
result Achieves optimal misclassification rate with quadratic sample size.
ROME improves algorithmic fairness by learning latent group structure robustly.
problem Latent subgroup disparities and distribution shifts in machine learning models.
method ROME uses an Expectation-Maximization algorithm for linear models and a neural Mixture-of-Experts for nonlinear settings.
result ROME significantly improves fairness compared to standard methods while maintaining average performance.
Generalized autoregressive conditional heteroscedasticity (GARCH) models have long been considered as one of the most successful families of approaches for volatility modeling in financial return series. In this paper, we propose an alternative approach based on methodologies widely used in the field of statistical mac…
Paper estimates GMMs with unknown covariances using sparse regularization.
problem Estimating GMMs with unknown diagonal covariances from samples.
method Employed Beurling-LASSO (BLASSO) for sparse estimation of component means, covariances, and weights.
result Established non-asymptotic recovery guarantees with nearly parametric convergence rates.
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.
Multi-task/Multi-output learning seeks to exploit correlation among tasks to enhance performance over learning or solving each task independently. In this paper, we investigate this problem in the context of Gaussian Processes (GPs) and propose a new model which learns a mixture of latent processes by decomposing the c…
Unified approach for interpretable regression with flexible modeling.
problem Combining predictive adaptivity with interpretability in heterogeneous data.
method Combining random Fourier features, spectral feature map, principal component analysis, Gaussian mixture model, and cluster-specific generalized additive models.
result Consistently improves upon classical and black-box models across benchmark datasets.
We aim to create a framework for transfer learning using latent factor models to learn the dependence structure between a larger source dataset and a target dataset. The methodology is motivated by our goal of building a risk-assessment model for surgery patients, using both institutional and national surgical outcomes…
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.
Study improves choice model accuracy and heterogeneity representation using mixture models.
problem Improving prediction accuracy and heterogeneity representation in choice models.
method Semi-nonparametric Latent Class Choice Model with mixture models and EM algorithm.
result Mixture models enhance prediction accuracy and heterogeneity representation without sacrificing interpretability.
A new model DKMPP integrates covariates and uses an integration-free method for spatio-temporal point processes.
problem Training intractable deep spatio-temporal point processes with multimodal covariates.
method DKMPP uses a deep kernel to model complex relationships and an integration-free score matching method.
result DKMPP and score-based estimators outperform baseline models in spatio-temporal point processes.
Hybrid model combines continuous and tractable probabilistic models.
problem Intractable probabilistic inference in continuous latent-space models.
method Continuous mixtures of tractable probabilistic models with finite integration points.
result Hybrid models achieve state-of-the-art performance in density estimation.
New kernel models multi-output Gaussian processes accurately.
problem Challenges in modelling cross-covariances for multiple-output Gaussian processes.
method Replaced Gaussian components with block components of finite bandwidth in spectral mixture kernel.
result First multi-output generalization of spectral mixture kernel that can approximate any stationary multi-output kernel to arbitrary precision.
New SQ lower bounds show learning mixtures of bounded covariance Gaussians is hard.
problem Learning mixtures of Gaussians with bounded covariance matrices is hard.
method Statistical Query (SQ) lower bounds.
result Any SQ algorithm requires complexity at least dΩ(1/ε) for learning mixtures of bounded covariance Gaussians. 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…
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.
Bayesian model clusters brain activity time series.
problem Heterogeneous multivariate time series in brain imaging.
method Group-based Bayesian mixture of smoothing splines with covariate effects.
result Distinct brain activity patterns identified.
New method clusters high-dimensional data with anisotropic noise.
problem Clustering high-dimensional anisotropic mixtures with varying noise structures.
method Covariance Projected Spectral Clustering (COPO) method that projects data onto a low-dimensional space and reassigns clusters based on estimated covariances.
result COPO achieves minimax-optimal misclustering rates in Gaussian settings.
New spectral clustering method handles discrete covariates for better community detection.
problem Community detection in networks with discrete covariates.
method Spectral algorithm that separates latent network structure from observed covariates.
result Achieves perfect clustering with high probability in large, sparse networks.
The Expectation-Maximization (EM) algorithm is a widely used method for maximum likelihood estimation in models with latent variables. For estimating mixtures of Gaussians, its iteration can be viewed as a soft version of the k-means clustering algorithm. Despite its wide use and applications, there are essentially no …