Related papers: Fuzzy sets in nonparametric Bayes regression
Mixed membership models, or partial membership models, are a flexible unsupervised learning method that allows each observation to belong to multiple clusters. In this paper, we propose a Bayesian mixed membership model for functional data.…
Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…
In this paper we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for…
We present a novel Bayesian nonparametric regression model for covariates X and continuous, real response variable Y. The model is parametrized in terms of marginal distributions for Y and X and a regression function which tunes the…
While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function…
It is well known that the output of a Neural Network trained to disentangle between two classes has a probabilistic interpretation in terms of the a-posteriori Bayesian probability, provided that a unary representation is taken for the…
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…
The purpose of the paper is to provide a new way of seeing the p-value in terms of a fuzzy membership function. According to the ASAs statement, we aim at removing the arbitrary choice of the significance level and at demonstrating that the…
Univariate or multivariate ordinal responses are often assumed to arise from a latent continuous parametric distribution, with covariate effects which enter linearly. We introduce a Bayesian nonparametric modeling approach for univariate…
We introduce a new method for learning Bayesian neural networks, treating them as a stack of multivariate Bayesian linear regression models. The main idea is to infer the layerwise posterior exactly if we know the target outputs of each…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
High-throughput data analyses are becoming common in biology, communications, economics and sociology. The vast amounts of data are usually represented in the form of matrices and can be considered as knowledge networks. Spectra-based…
We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…
A fuzzy Boolean function is a map $f:\cube^n\to [0,1]$, where $n\in\mathbb N$. We introduce and compare three ways of saying that such a function has bounded complexity. The first is a sampling property: the value $f(x)$ can be recovered,…
We establish a general semiparametric Bernstein-von Mises theorem for Bayesian nonparametric priors based on continuous observations in a periodic reversible multidimensional diffusion model. We consider a wide range of functionals…
In this paper, distributed Bayesian detection problems with unknown prior probabilities of hypotheses are considered. The sensors obtain observations which are conditionally dependent across sensors and their probability density functions…
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…
Bayesian predictive synthesis (BPS) provides a method for combining multiple predictive distributions based on agent/expert opinion analysis theory and encompasses a range of existing density forecast pooling methods. The key ingredient in…
The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…
Here we develop a method for performing nonparametric Bayesian inference on quantiles. Relying on geometric measure theory and employing a Hausdorff base measure, we are able to specify meaningful priors for the quantile while treating the…