相关论文: Identifiability and optimal rates of convergence f…

Phylogenetic mixture models are statistical models of character evolution allowing for heterogeneity. Each of the classes in some unknown partition of the characters may evolve by different processes, or even along different trees. The…

Recent work has shown that finite mixture models with $m$ components are identifiable, while making no assumptions on the mixture components, so long as one has access to groups of samples of size $2m-1$ which are known to come from the…

One of the distinguishing characteristics of modern deep learning systems is that they typically employ neural network architectures that utilize enormous numbers of parameters, often in the millions and sometimes even in the billions.…

Survival analysis is a widely-used technique for analyzing time-to-event data in the presence of censoring. In recent years, numerous survival analysis methods have emerged which scale to large datasets and relax traditional assumptions…

Finite mixture models are a useful statistical model class for clustering and density approximation. In the Bayesian framework finite mixture models require the specification of suitable priors in addition to the data model. These priors…

Machine learning (ML) and deep learning models are extensively used for parameter optimization and regression problems. However, not all inverse problems in ML are ``identifiable,'' indicating that model parameters may not be uniquely…

Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…

Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is…

The problem of identifiability of finite mixtures of finite product measures is studied. A mixture model with $K$ mixture components and $L$ observed variables is considered, where each variable takes its value in a finite set with…

Mixture models have been widely used in modeling of continuous observations. For the possibility to estimate the parameters of a mixture model consistently on the basis of observations from the mixture, identifiability is a necessary…

Finite mixtures of regression models offer a flexible framework for investigating heterogeneity in data with functional dependencies. These models can be conveniently used for unsupervised learning on data with clear regression…

The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by…

A line of recent work has analyzed the behavior of the Expectation-Maximization (EM) algorithm in the well-specified setting, in which the population likelihood is locally strongly concave around its maximizing argument. Examples include…

We prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent (unobservable) groups. The connectivities between nodes are…

Finite mixture models are statistical models which appear in many problems in statistics and machine learning. In such models it is assumed that data are drawn from random probability measures, called mixture components, which are…

In this paper, we develop a finite mixture of convolutional distributions, a statistical model to analyze continuous data distributed approximately on a mixture of low-dimensional affine subspaces. The observations are assumed independent…

We study a class of weakly identifiable location-scale mixture models for which the maximum likelihood estimates based on $n$ i.i.d. samples are known to have lower accuracy than the classical $n^{- \frac{1}{2}}$ error. We investigate…

Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…

We consider a semiparametric mixture of two univariate density functions where one of them is known while the weight and the other function are unknown. Such mixtures have a history of application to the problem of detecting differentially…

An important and yet difficult problem in fitting multivariate mixture models is determining the mixture complexity. We develop theory and a unified framework for finding the nonparametric maximum likelihood estimator of a multivariate…