Related papers: Bayesian prediction via nonparametric transformati…
Parameter estimation is a foundational step in statistical modeling, enabling us to extract knowledge from data and apply it effectively. Bayesian estimation of parameters incorporates prior beliefs with observed data to infer distribution…
Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick…
Convolutional neural networks (CNNs) work well on large datasets. But labelled data is hard to collect, and in some applications larger amounts of data are not available. The problem then is how to use CNNs with small data -- as CNNs…
A Bayesian approach termed BAyesian Least Squares Optimization with Nonnegative L1-norm constraint (BALSON) is proposed. The error distribution of data fitting is described by Gaussian likelihood. The parameter distribution is assumed to be…
In many real problems, dependence structures more general than exchangeability are required. For instance, in some settings partial exchangeability is a more reasonable assumption. For this reason, vectors of dependent Bayesian…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables in which it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone…
Using nonparametric methods has been increasingly explored in Bayesian hierarchical modeling as a way to increase model flexibility. Although the field shows a lot of promise, inference in many models, including Hierachical Dirichlet…
Time series prediction is challenging due to our limited understanding of the underlying dynamics. Conventional models such as ARIMA and Holt's linear trend model experience difficulty in identifying nonlinear patterns in time series. In…
Uncertainty quantification and robustness to distribution shifts are important goals in machine learning and artificial intelligence. Although Bayesian Neural Networks (BNNs) allow for uncertainty in the predictions to be assessed,…
We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…
Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are…
Tracer-kinetic analysis of dynamic contrast-enhanced magnetic resonance imaging data is commonly performed with the well-known Tofts model and nonlinear least squares (NLLS) regression. This approach yields point estimates of model…
Diffusion-based models decompose sampling into many small Gaussian denoising steps -- an assumption that breaks down when generation is compressed to a few coarse transitions. Existing few-step methods address this through distillation,…
We provide a comprehensive semi-parametric study of Bayesian partially identified econometric models. While the existing literature on Bayesian partial identification has mostly focused on the structural parameter, our primary focus is on…
The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for…
Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…
Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…
We consider Bayesian inverse problems wherein the unknown state is assumed to be a function with discontinuous structure a priori. A class of prior distributions based on the output of neural networks with heavy-tailed weights is…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…