Related papers: Data Augementation with Polya Inverse Gamma

We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We…

This paper generalises the exponential family GLM to allow arbitrary distributions for the response variable. This is achieved by combining the model-assisted regression approach from survey sampling with the GLM scoring algorithm, weighted…

Exploiting symmetry in dynamical systems is a powerful way to improve the generalization of deep learning. The model learns to be invariant to transformation and hence is more robust to distribution shift. Data augmentation and equivariant…

For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labelled as…

The theory of normal variance mixture distributions is used to provide elementary derivations of closed-form expressions for the definite integrals $\int_0^\infty x^{-2\nu}\cos(bx)\gamma(\nu,\alpha x^2)\,\mathrm{d}x$ (for $\nu>1/2$, $b>0$…

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability…

We propose a scalable stochastic variational approach to GP classification building on Polya-Gamma data augmentation and inducing points. Unlike former approaches, we obtain closed-form updates based on natural gradients that lead to…

Data augmentation is one of the most widely used techniques to improve generalization in modern machine learning, often justified by its ability to promote invariance to label-irrelevant transformations. However, its theoretical role…

Data augmentation has been widely applied as an effective methodology to improve generalization in particular when training deep neural networks. Recently, researchers proposed a few intensive data augmentation techniques, which indeed…

In this work, we consider the problem of imbalanced data in a regression framework when the imbalanced phenomenon concerns continuous or discrete covariates. Such a situation can lead to biases in the estimates. In this case, we propose a…

Data augmentation (DA) methods tailored to specific domains generate synthetic samples by applying transformations that are appropriate for the characteristics of the underlying data domain, such as rotations on images and time warping on…

Data augmentation is one of the most prevalent tools in deep learning, underpinning many recent advances, including those from classification, generative models, and representation learning. The standard approach to data augmentation…

Data augmentation is an effective technique to improve the generalization of deep neural networks. However, previous data augmentation methods usually treat the augmented samples equally without considering their individual impacts on the…

This paper presents likelihood-based inference methods for the family of univariate gamma-normal distributions GN({\alpha}, r, {\mu}, {\sigma}^2 ) that result from summing independent gamma({\alpha}, r) and N({\mu}, {\sigma}^2 ) random…

Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…

In order to better fit real-world datasets, studying asymmetric distribution is of great interest. In this work, we derive several mathematical properties of a general class of asymmetric distributions with positive support which shows up…

Efficiently sampling from the P\'olya-Gamma distribution, ${PG}(b,z)$, is an essential element of P\'olya-Gamma data augmentation. Polson et. al (2013) show how to efficiently sample from the ${PG}(1,z)$ distribution. We build two new…

In this paper, we discuss the construction of a multivariate generalisation of the Dirichlet-multinomial distribution. An example from forensic genetics in the statistical analysis of DNA mixtures motivates the study of this multivariate…

Supervised topic models with a logistic likelihood have two issues that potentially limit their practical use: 1) response variables are usually over-weighted by document word counts; and 2) existing variational inference methods make…

Mixture models with Gamma and or inverse-Gamma distributed mixture components are useful for medical image tissue segmentation or as post-hoc models for regression coefficients obtained from linear regression within a Generalised Linear…