Improving inference of Gaussian mixtures using auxiliary variables
نویسندگان
چکیده
Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference for mixture models by using auxiliary variables. Despite the large literature in mixture models and several empirical examples, there is no previous work that gives general theoretical justification for including auxiliary variables in mixture models, even for special cases. We provide a theoretical basis for comparing inference for mixture multivariate models with the corresponding inference for marginal univariate mixture models. Analytical results for several special cases are established. We show that the probability of correctly allocating mixture memberships and the information number for the means of the primary outcome in a bivariate model with two Gaussian mixtures are generally larger than those in each univariate model. Simulations under a range of scenarios, including misspecified models, are conducted to examine the improvement. The method is illustrated by two real applications in ecology and causal inference.
منابع مشابه
Computational aspects of DNA mixture analysis - Exact inference using auxiliary variables in a Bayesian network
Statistical analysis of DNA mixtures is known to pose computational challenges due to the enormous state space of possible DNA profiles. We propose a Bayesian network representation for genotypes, allowing computations to be performed locally involving only a few alleles at each step. In addition, we describe a general method for computing the expectation of a product of discrete random variabl...
متن کاملModeling Nonlinear Deterministic Relationships in Bayesian Networks
In a Bayesian network with continuous variables containing a variable(s) that is a conditionally deterministic function of its continuous parents, the joint density function for the variables in the network does not exist. Conditional linear Gaussian distributions can handle such cases when the deterministic function is linear and the continuous variables have a multi-variate normal distributio...
متن کاملNonlinear Deterministic Relationships in Bayesian Networks
In a Bayesian network with continuous variables containing a variable(s) that is a conditionally deterministic function of its continuous parents, the joint density function does not exist. Conditional linear Gaussian distributions can handle such cases when the deterministic function is linear and the continuous variables have a multi-variate normal distribution. In this paper, operations requ...
متن کاملApproximate Inference for Deep Latent Gaussian Mixtures
Deep latent Gaussian models (DLGMs) composed of density and inference networks [14]—the pipeline that defines a Variational Autoencoder [8]—have achieved notable success on tasks ranging from image modeling [3] to semi-supervised classification [6, 11]. However, the approximate posterior in these models is usually chosen to be a factorized Gaussian, thereby imposing strong constraints on the po...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Statistical Analysis and Data Mining
دوره 8 شماره
صفحات -
تاریخ انتشار 2015