Related papers: Data Augementation with Polya Inverse Gamma
We explain how to use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Diffusion models are a class of machine learning models which have been used to generate samples from complex…
Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we…
Data augmentation is a key element in training high-dimensional models. In this approach, one synthesizes new observations by applying pre-specified transformations to the original training data; e.g.~new images are formed by rotating old…
Bayesian hierarchical models are used to share information between related samples and obtain more accurate estimates of sample-level parameters, common structure, and variation between samples. When the parameter of interest is the…
Mixtures of multivariate normal inverse Gaussian (MNIG) distributions can be used to cluster data that exhibit features such as skewness and heavy tails. However, for cluster analysis, using a traditional finite mixture model framework,…
In this paper, we present an effective data augmentation framework leveraging the Large Language Model (LLM) and Diffusion Model (DM) to tackle the challenges inherent in data-scarce scenarios. Recently, DMs have opened up the possibility…
This paper studies fundamental aspects of modelling data using multivariate Watson distributions. Although these distributions are natural for modelling axially symmetric data (i.e., unit vectors where $\pm \x$ are equivalent), for…
We introduce a new dynamical system for sequentially observed multivariate count data. This model is based on the gamma--Poisson construction---a natural choice for count data---and relies on a novel Bayesian nonparametric prior that ties…
A reparametrized Dirichlet-multinomial distribution is introduced, and the covariance matrix, as well as, the algorithm for calculating the PDF for n species are provided. The distribution is suited for modelling the joint distribution of…
We study modeling and inference with the Elliptical Gamma Distribution (EGD). We consider maximum likelihood (ML) estimation for EGD scatter matrices, a task for which we develop new fixed-point algorithms. Our algorithms are efficient and…
In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…
In this article, we discuss two specific classes of models - Gaussian Mixture Copula models and Mixture of Factor Analyzers - and the advantages of doing inference with gradient descent using automatic differentiation. Gaussian mixture…
Data augmentation is a widely used training trick in deep learning to improve the network generalization ability. Despite many encouraging results, several recent studies did point out limitations of the conventional data augmentation…
Mixup is a widely adopted data augmentation technique known for enhancing the generalization of machine learning models by interpolating between data points. Despite its success and popularity, limited attention has been given to…
Bayesian graphical modeling provides an appealing way to obtain uncertainty estimates when inferring network structures, and much recent progress has been made for Gaussian models. These models have been used extensively in applications to…
Pan-sharpening algorithms utilize a panchromatic image and a multispectral image to generate a high spatial and high spectral image. However, the optimizations of the algorithms are designed with different standards. We employ a simple…
In this paper we introduce two Bayesian estimators for learning the parameters of the Gamma distribution. The first algorithm uses a well known unnormalized conjugate prior for the Gamma shape and the second one uses a non-linear…
This paper provides a framework for estimating the mean and variance of a high-dimensional normal density. The main setting considered is a fixed number of vector following a high-dimensional normal distribution with unknown mean and…
Data augmentation is a popular pre-processing trick to improve generalization accuracy. It is believed that by processing augmented inputs in tandem with the original ones, the model learns a more robust set of features which are shared…
Imbalanced regression arises when the target distribution is skewed, causing models to focus on dense regions and struggle with underrepresented (minority) samples. Despite its relevance across many applications, few methods have been…