RESUMO

We consider unsupervised classification by means of a latent multinomial variable which categorizes a scalar response into one of the L components of a mixture model which incorporates scalar and functional covariates. This process can be thought as a hierarchical model with the first level modelling a scalar response according to a mixture of parametric distributions and the second level modelling the mixture probabilities by means of a generalized linear model with functional and scalar covariates. The traditional approach of treating functional covariates as vectors not only suffers from the curse of dimensionality, since functional covariates can be measured at very small intervals leading to a highly parametrized model, but also does not take into account the nature of the data. We use basis expansions to reduce the dimensionality and a Bayesian approach for estimating the parameters while providing predictions of the latent classification vector. The method is motivated by two data examples that are not easily handled by existing methods. The first example concerns identifying placebo responders on a clinical trial (normal mixture model) and the other predicting illness for milking cows (zero-inflated mixture of the Poisson model).

RESUMO

The development of Brain-Computer Interfaces based on Motor Imagery (MI) tasks is a relevant research topic worldwide. The design of accurate and reliable BCI systems remains a challenge, mainly in terms of increasing performance and usability. Classifiers based on Bayesian Neural Networks are proposed in this work by using the variational inference, aiming to analyze the uncertainty during the MI prediction. An adaptive threshold scheme is proposed here for MI classification with a reject option, and its performance on both datasets 2a and 2b from BCI Competition IV is compared with other approaches based on thresholds. The results using subject-specific and non-subject-specific training strategies are encouraging. From the uncertainty analysis, considerations for reducing computational cost are proposed for future work.

Assuntos

Interfaces Cérebro-Computador , Eletroencefalografia , Eletroencefalografia/métodos , Teorema de Bayes , Imaginação , Redes Neurais de Computação , Imagens, Psicoterapia , Algoritmos

RESUMO

In this paper, we estimate the dynamic parameters of a time-varying coefficient model through radial kernel functions in the context of a longitudinal study. Our proposal is based on a linear combination of weighted kernel functions involving a bandwidth, centered around a given set of time points. In addition, we study different alternatives of estimation and inference including a Frequentist approach using weighted least squares along with bootstrap methods, and a Bayesian approach through both Markov chain Monte Carlo and variational methods. We compare the estimation strategies mention above with each other, and our radial kernel functions proposal with an expansion based on regression spline, by means of an extensive simulation study considering multiples scenarios in terms of sample size, number of repeated measurements, and subject-specific correlation. Our experiments show that the capabilities of our proposal based on radial kernel functions are indeed comparable with or even better than those obtained from regression splines. We illustrate our methodology by analyzing data from two AIDS clinical studies.

RESUMO

There is not much literature on objective Bayesian analysis for binary classification problems, especially for intrinsic prior related methods. On the other hand, variational inference methods have been employed to solve classification problems using probit regression and logistic regression with normal priors. In this article, we propose to apply the variational approximation on probit regression models with intrinsic prior. We review the mean-field variational method and the procedure of developing intrinsic prior for the probit regression model. We then present our work on implementing the variational Bayesian probit regression model using intrinsic prior. Publicly available data from the world's largest peer-to-peer lending platform, LendingClub, will be used to illustrate how model output uncertainties are addressed through the framework we proposed. With LendingClub data, the target variable is the final status of a loan, either charged-off or fully paid. Investors may very well be interested in how predictive features like FICO, amount financed, income, etc. may affect the final loan status.