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.
Understanding proper distance measures between distributions is at the core of several learning tasks such as generative models, domain adaptation, clustering, etc. In this work, we focus on mixture distributions that arise naturally in several application domains where the data contains different sub-populations. For …
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…
Consistent estimator for mixtures of nonparametric elliptical distributions helps cluster analysis.
problem Consistency of maximum likelihood estimator for mixtures of nonparametric elliptical distributions.
method Maximum likelihood estimation for mixtures of elliptically-symmetric distributions under nonparametric P. result Components of the estimator correspond to well-separated components of the underlying distribution P. Paper proposes a new Wasserstein distance for mixtures of radially contoured distributions.
problem Generalization of Wasserstein distance to non-elliptically contoured distributions.
method Relaxed formulation for mixtures of radially contoured distributions without marginal consistency.
result The new distance yields more stable error and better color distribution in image transfer tasks.
NMDR estimates complex mixtures of distributions efficiently.
problem Estimating complex finite mixtures of distributions in high-dimensional settings.
method Flexible additive predictors, neural networks, and deep learning optimizers.
result Competitive performance in complex scenarios compared to existing approaches.
We study the problem of learning a mixture model of non-parametric product distributions. The problem of learning a mixture model is that of finding the component distributions along with the mixing weights using observed samples generated from the mixture. The problem is well-studied in the parametric setting, i.e., w…
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.
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.
The paper examines risk aggregation under mixtures of marginals, finding that more homogeneous distributions lead to larger uncertainty.
problem Investigating the impact of mixing on risk aggregation uncertainty.
method Analyzes ordering relations and inequalities for aggregation sets under distribution and quantile mixtures.
result More homogeneous marginals result in larger aggregation sets, indicating greater model uncertainty.
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.
A new method uses Mean Field Games to optimize mixture models of Bernoulli and categorical distributions.
problem Optimizing parameters of finite mixture models of Bernoulli and categorical distributions.
method Mean Field Games theory applied to multi-population systems.
result The Mean Field Games approach provides a method to compute mixture model parameters.
Mixture modelling involves explaining some observed evidence using a combination of probability distributions. The crux of the problem is the inference of an optimal number of mixture components and their corresponding parameters. This paper discusses unsupervised learning of mixture models using the Bayesian Minimum M…
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.
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.
We derive relations between theoretical properties of restricted Boltzmann machines (RBMs), popular machine learning models which form the building blocks of deep learning models, and several natural notions from discrete mathematics and convex geometry. We give implications and equivalences relating RBM-representable …
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.
We present two different approaches for parameter learning in several mixture models in one dimension. Our first approach uses complex-analytic methods and applies to Gaussian mixtures with shared variance, binomial mixtures with shared success probability, and Poisson mixtures, among others. An example result is that …
This paper is a step-by-step tutorial for fitting a mixture distribution to data. It merely assumes the reader has the background of calculus and linear algebra. Other required background is briefly reviewed before explaining the main algorithm. In explaining the main algorithm, first, fitting a mixture of two distribu…
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…
New insights into identifying mixtures of product distributions using Hadamard extensions.
problem Identifying mixtures of product distributions on binary variables.
method Analysis of Hadamard extensions of matrix products.
result Conditions for full column rank of Hadamard extensions.
New EM algorithm for mixtures of elliptical distributions handles missing data and outliers.
problem Missing data imputation for noisy and non-Gaussian data.
method Investigation of a new EM algorithm for mixtures of elliptical distributions.
result The proposed algorithm is robust to outliers and competitive with other methods.
In this paper, we generalize the parametric Delta-VaR methods from portfolios with elliptic distributed risk factors to portfolios with mixture of elliptically distributed ones. We treat both the Expected Shortfall and the Value-at-Risk of such portfolios. Special attention is given to the particular case of the mixtur…
SMT trains generative models by estimating mixture scores, outperforming existing methods.
problem Training one-step generative models efficiently and effectively.
method Score-of-Mixture Training (SMT) estimates the score of mixture distributions between real and fake samples.
result SMT/SMD outperform existing methods on CIFAR-10 and ImageNet 64x64 datasets.
SFSVI uses Gaussian mixtures to approximate neural network outputs for continual learning.
problem Learning new tasks without forgetting old ones in neural networks.
method Sequential function-space variational inference with Gaussian mixture approximation.
result Gaussian mixture SFSVI outperforms other methods in continual learning.
Refined analysis of Mitra's algorithm for discrete mixtures.
problem Classifying general discrete mixture distribution models.
method Spectral clustering tailored to bipartite stochastic block models.
result Improved separation conditions for probability distributions.
MixTS uses a mixture prior to analyze Thompson Sampling in multi-task learning.
problem Analyzing Thompson Sampling in environments with uncertain and multi-class problems.
method Developed MixTS by incorporating a mixture prior into Thompson Sampling and using a novel proof technique for mixture distributions.
result Proved Bayes regret bounds for MixTS in linear bandits and finite-horizon reinforcement learning.
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 proposes a method for interpretable mixture density estimation using a tree structure.
problem Complex probability distributions in machine learning models.
method Interpretable tree structure for mixture density estimation with fast inference.
result The method achieves both high speed and interpretability for mixture density estimation.
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…
Model-based clustering imposes a finite mixture modelling structure on data for clustering. Finite mixture models assume that the population is a convex combination of a finite number of densities, the distribution within each population is a basic assumption of each particular model. Among all distributions that have …
Improved VAE estimation from incomplete data using variational mixtures.
problem Estimating VAEs from incomplete data increases posterior complexity.
method Introducing variational mixtures based on finite and imputation distributions.
result Variational mixtures improve VAE estimation accuracy from incomplete data.
Algorithm estimates nonparametric mixtures from grouped data.
problem Estimating identifiable nonparametric mixture models from grouped observations.
method Oracle inequality for weighted kernel density estimators and general consistency result.
result Consistent estimation of mixture components from grouped observations.
Algorithm identifies sources in product distributions with improved complexity.
problem Identifying sources in mixtures of product distributions.
method Approximate multilinear moments input, 2^{O(k^2)} n^{O(k)} operations.
result First explicit bound on computational complexity of source identification.
We consider a covariate shift problem where one has access to several different training datasets for the same learning problem and a small validation set which possibly differs from all the individual training distributions. This covariate shift is caused, in part, due to unobserved features in the datasets. The objec…
The study applies spatial density models to mobile node movements using Möbius distributions.
problem Modeling the steady-state density of mobile nodes on a 2D terrain.
method Used mixture density networks with Möbius distributions to describe node density over a disk.
result Möbius distributions are more suitable for capturing radial changes in node density compared to Gaussian distributions.
The modelling of empirically observed data is commonly done using mixtures of probability distributions. In order to model angular data, directional probability distributions such as the bivariate von Mises (BVM) is typically used. The critical task involved in mixture modelling is to determine the optimal number of co…
A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse Gaussian distribution. This approach is mathematically elegant and relatively comput…
New sampling and identity-testing methods for mixtures of distributions that don't satisfy approximate tensorization of entropy.
problem Sampling and identity-testing for mixtures of distributions that don't satisfy approximate tensorization of entropy.
method Fast mixing of Glauber dynamics and efficient identity-testers in the coordinate-conditional sampling access model.
result Efficient identity-testers for mixtures of ATE distributions in the coordinate-conditional sampling access model.
New theorem improves spectral gap for sampling from mixture distributions.
problem Sampling from multimodal distributions with simulated tempering.
method Introduced a decomposition theorem for the restricted spectral gap of simulated tempering.
result Lower bound on the restricted spectral gap for mixture distributions.
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.
Adaptive importance sampling for stochastic optimization is a promising approach that offers improved convergence through variance reduction. In this work, we propose a new framework for variance reduction that enables the use of mixtures over predefined sampling distributions, which can naturally encode prior knowledg…
The thesis models financial returns using mixtures of generalized normal distributions.
problem Estimation issues in financial return analysis.
method Mixtures of generalized normal distributions (MGND), ECM/GEM algorithms, constrained mixture models (CMGND), GND-HMMs.
result Enhanced accuracy and interpretability in financial return modeling.
New framework optimizes label shift adaptation using aligned distribution mixture.
problem Label shift where source and target label distributions differ.
method Aligned Distribution Mixture (ADM) framework, incorporating insights from generalization theory.
result The ADM framework improves four typical label shift methods and introduces a one-step approach.
We study the problem of separating a mixture of distributions, all of which come from interventions on a known causal bayesian network. Given oracle access to marginals of all distributions resulting from interventions on the network, and estimates of marginals from the mixture distribution, we want to recover the mixi…
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.
Diffusion models accurately recover mixture weights from generated samples despite score function insensitivity.
problem Score-based generative models often fail to learn correct relative mode amplitudes (mixture weights) from generated samples.
method Relate diffusion score matching (DSM) loss to mixture weight estimation error, define diffusion score sensitivity index (DSSI), and prove its governing role in mixture weight recovery.
result Generated samples can accurately recover mixture weights from the DSM loss, even when the target score is insensitive to mixture weights.
New Gamma-Poisson model improves topic selection for short text.
problem Topic modelling for short text using Poisson distribution.
method Gamma-Poisson mixture model with collapsed Gibbs sampler.
result Gamma-Poisson model selects more accurate number of topics.