Bivariate Beta-LSTM

Long Short-Term Memory (LSTM) infers the long term dependency through a cell state maintained by the input and the forget gate structures, which models a gate output as a value in [0,1] through a sigmoid function. However, due to the graduality of the sigmoid function, the sigmoid gate is not flexible in representing multi-modality or skewness. Besides, the previous models lack modeling on the correlation between the gates, which would be a new method to adopt inductive bias for a relationship between previous and current input. This paper proposes a new gate structure with the bivariate Beta distribution. The proposed gate structure enables probabilistic modeling on the gates within the LSTM cell so that the modelers can customize the cell state flow with priors and distributions. Moreover, we theoretically show the higher upper bound of the gradient compared to the sigmoid function, and we empirically observed that the bivariate Beta distribution gate structure provides higher gradient values in training. We demonstrate the effectiveness of bivariate Beta gate structure on the sentence classification, image classification, polyphonic music modeling, and image caption generation.Comment: AAAI 202

CopulaDTA: An R Package for Copula Based Bivariate Beta-Binomial Models for Diagnostic Test Accuracy Studies in a Bayesian Framework

The current statistical procedures implemented in statistical software packages for pooling of diagnostic test accuracy data include hSROC regression and the bivariate random-effects meta-analysis model (BRMA). However, these models do not report the overall mean but rather the mean for a central study with random-effect equal to zero and have difficulties estimating the correlation between sensitivity and specificity when the number of studies in the meta-analysis is small and/or when the between-study variance is relatively large. This tutorial on advanced statistical methods for meta-analysis of diagnostic accuracy studies discusses and demonstrates Bayesian modeling using CopulaDTA package in R to fit different models to obtain the meta-analytic parameter estimates. The focus is on the joint modelling of sensitivity and specificity using copula based bivariate beta distribution. Essentially, we extend the work of Nikoloulopoulos by: i) presenting the Bayesian approach which offers flexibility and ability to perform complex statistical modelling even with small data sets and ii) including covariate information, and iii) providing an easy to use code. The statistical methods are illustrated by re-analysing data of two published meta-analyses. Modelling sensitivity and specificity using the bivariate beta distribution provides marginal as well as study-specific parameter estimates as opposed to using bivariate normal distribution (e.g., in BRMA) which only yields study-specific parameter estimates. Moreover, copula based models offer greater flexibility in modelling different correlation structures in contrast to the normal distribution which allows for only one correlation structure.Comment: 26 pages, 5 figure

A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence

A bivariate copula mixed model has been recently proposed to synthesize diagnostic test accuracy studies and it has been shown that it is superior to the standard generalized linear mixed model in this context. Here, we call trivariate vine copulas to extend the bivariate meta-analysis of diagnostic test accuracy studies by accounting for disease prevalence. Our vine copula mixed model includes the trivariate generalized linear mixed model as a special case and can also operate on the original scale of sensitivity, specificity, and disease prevalence. Our general methodology is illustrated by re-analyzing the data of two published meta-analyses. Our study suggests that there can be an improvement on trivariate generalized linear mixed model in fit to data and makes the argument for moving to vine copula random effects models especially because of their richness, including reflection asymmetric tail dependence, and computational feasibility despite their three dimensionality

A mixed effect model for bivariate meta-analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution

Diagnostic test accuracy studies typically report the number of true positives, false positives, true negatives and false negatives. There usually exists a negative association between the number of true positives and true negatives, because studies that adopt less stringent criterion for declaring a test positive invoke higher sensitivities and lower specificities. A generalized linear mixed model (GLMM) is currently recommended to synthesize diagnostic test accuracy studies. We propose a copula mixed model for bivariate meta-analysis of diagnostic test accuracy studies. Our general model includes the GLMM as a special case and can also operate on the original scale of sensitivity and specificity. Summary receiver operating characteristic curves are deduced for the proposed model through quantile regression techniques and different characterizations of the bivariate random effects distribution. Our general methodology is demonstrated with an extensive simulation study and illustrated by re-analysing the data of two published meta-analyses. Our study suggests that there can be an improvement on GLMM in fit to data and makes the argument for moving to copula random effects models. Our modelling framework is implemented in the package CopulaREMADA within the open source statistical environment R

copulaedas: An R Package for Estimation of Distribution Algorithms Based on Copulas

The use of copula-based models in EDAs (estimation of distribution algorithms) is currently an active area of research. In this context, the copulaedas package for R provides a platform where EDAs based on copulas can be implemented and studied. The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known optimization problems, and utility functions to study the performance of the algorithms. Newly developed EDAs can be easily integrated into the package by extending an S4 class with generic functions for their main components. This paper presents copulaedas by providing an overview of EDAs based on copulas, a description of the implementation of the package, and an illustration of its use through examples. The examples include running the EDAs defined in the package, implementing new algorithms, and performing an empirical study to compare the behavior of different algorithms on benchmark functions and a real-world problem