Latent variable model

About: Latent variable model is a research topic. Over the lifetime, 3589 publications have been published within this topic receiving 235061 citations.

Metrics for Probabilistic Geometries

Abstract: We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the necessary algorithms to compute expected metric tensors where the distribution over mappings is given by a Gaussian process. We treat the corresponding latent variable model as a Riemannian manifold and we use the expectation of the metric under the Gaussian process prior to define interpolating paths and measure distance between latent points. We show how distances that respect the expected metric lead to more appropriate generation of new data.

Latent Coincidence Analysis: A Hidden Variable Model for Distance Metric Learning

Abstract: We describe a latent variable model for supervised dimensionality reduction and distance metric learning. The model discovers linear projections of high dimensional data that shrink the distance between similarly labeled inputs and expand the distance between differently labeled ones. The model's continuous latent variables locate pairs of examples in a latent space of lower dimensionality. The model differs significantly from classical factor analysis in that the posterior distribution over these latent variables is not always multivariate Gaussian. Nevertheless we show that inference is completely tractable and derive an Expectation-Maximization (EM) algorithm for parameter estimation. We also compare the model to other approaches in distance metric learning. The model's main advantage is its simplicity: at each iteration of the EM algorithm, the distance metric is re-estimated by solving an unconstrained least-squares problem. Experiments show that these simple updates are highly effective.

Regression analysis of additive hazards model with latent variables

Abstract: We propose an additive hazards model with latent variables to investigate the observed and latent risk factors of the failure time of interest. Each latent risk factor is characterized by correlated observed variables through a confirmatory factor analysis model. We develop a hybrid procedure that combines the expectation–maximization (EM) algorithm and the borrow-strength estimation approach to estimate the model parameters. We establish the consistency and asymptotic normality of the parameter estimators. Various nice features, including finite sample performance of the proposed methodology, are demonstrated by simulation studies. Our model is applied to a study concerning the risk factors of chronic kidney disease for Type 2 diabetic patients. Supplementary materials for this article are available online.

A Note on Cluster Effects in Latent Class Analysis

Abstract: This article examines the effects of clustering in latent class analysis. A comprehensive simulation study is conducted, which begins by specifying a true multilevel latent class model with varying...

Bayesian Premium Rating with Latent Structure

Abstract: We propose a fully Bayesian approach to non-life risk premium rating, based on hierarchical models with latent variables for both claim frequency and claim size. Inference is based on the joint posterior distribution and is performed by Markov Chain Monte Carlo. Rather than plug-in point estimates of all unknown parameters, we take into account all sources of uncertainty simultaneously when the model is used to predict claims and estimate risk premiums. Several models are fitted to both a simulated dataset and a small portfolio regarding theft from cars. We show that interaction among latent variables can improve predictions significantly. We also investigate when interaction is not necessary. We compare our results with those obtained under a standard generalized linear model and show through numerical simulation that geographically located and spatially interacting latent variables can successfully compensate for missing covariates. However, when applied to the real portfolio data, the proposed models a...