Related papers: Nonparametric Bayesian label prediction on a graph
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…
We present some nonparametric methods for graphical modeling. In the discrete case, where the data are binary or drawn from a finite alphabet, Markov random fields are already essentially nonparametric, since the cliques can take only a…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
We propose a general algorithmic framework for Bayesian model selection. A spike-and-slab Laplacian prior is introduced to model the underlying structural assumption. Using the notion of effective resistance, we derive an EM-type algorithm…
In the literature surrounding Bayesian penalized regression, the two primary choices of prior distribution on the regression coefficients are zero-mean Gaussian and Laplace. While both have been compared numerically and theoretically, there…
Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…
Gaussian graphical models, where it is assumed that the variables of interest jointly follow a multivariate normal distribution with a sparse precision matrix, have been used to study intrinsic dependence among variables, but the normality…
We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed…
Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on…
This paper develops a class of Bayesian non- and semiparametric methods for estimating regression curves and surfaces. The main idea is to model the regression as locally linear, and then place suitable local priors on the local parameters.…
Binary classification is one of the most common problem in machine learning. It consists in predicting whether a given element belongs to a particular class. In this paper, a new algorithm for binary classification is proposed using a…
We propose a novel Bayesian nonparametric classification model that combines a Gaussian process prior for the latent function with a Dirichlet process prior for the link function, extending the interpretative framework of de Finetti…
Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…
The increasing availability of graph-structured data motivates the task of optimising over functions defined on the node set of graphs. Traditional graph search algorithms can be applied in this case, but they may be sample-inefficient and…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
We propose a mixed integer programming (MIP) model and iterative algorithms based on topological orders to solve optimization problems with acyclic constraints on a directed graph. The proposed MIP model has a significantly lower number of…
In this paper, we propose a nonparametric Bayesian approach for Lindsey and penalized Gaussian mixtures methods. We compare these methods with the Dirichlet process mixture model. Our approach is a Bayesian nonparametric method not based…
We tackle the problem of system identification, where we select inputs, observe the corresponding outputs from the true system, and optimize the parameters of our model to best fit the data. We propose a practical and computationally…
Three different inferential problems related to a two dimensional categorical data from a Bayesian perspective have been discussed in this article. Conjugate prior distribution with symmetric and asymmetric hyper parameters are considered.…
Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…