Related papers: Nearest Neighbor Dirichlet Mixtures
Multiple kernel learning algorithms are proposed to combine kernels in order to obtain a better similarity measure or to integrate feature representations coming from different data sources. Most of the previous research on such methods is…
We propose Bayesian extensions of two nonparametric regression methods which are kernel and mutual $k$-nearest neighbor regression methods. Derived based on Gaussian process models for regression, the extensions provide distributions for…
Bayesian hierarchical modeling is a natural framework to effectively integrate data and borrow information across groups. In this paper, we address problems related to density estimation and identifying clusters across related groups, by…
The Dirichlet process mixture model and more general mixtures based on discrete random probability measures have been shown to be flexible and accurate models for density estimation and clustering. The goal of this paper is to illustrate…
We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure…
Invoking the manifold assumption in machine learning requires knowledge of the manifold's geometry and dimension, and theory dictates how many samples are required. However, in applications data are limited, sampling may not be uniform, and…
Estimation of finite mixture models when the mixing distribution support is unknown is an important problem. This paper gives a new approach based on a marginal likelihood for the unknown support. Motivated by a Bayesian Dirichlet prior…
Robust tracking of a target in a clutter environment is an important and challenging task. In recent years, the nearest neighbor methods and probabilistic data association filters were proposed. However, the performance of these methods…
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.…
The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of…
We propose a kernel mixture of polynomials prior for Bayesian nonparametric regression. The regression function is modeled by local averages of polynomials with kernel mixture weights. We obtain the minimax-optimal rate of contraction of…
The parsimonious Gaussian mixture models, which exploit an eigenvalue decomposition of the group covariance matrices of the Gaussian mixture, have shown their success in particular in cluster analysis. Their estimation is in general…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
We consider the problem of boundary detection for areal data, focusing on situations where for each areal unit multiple observations are available. We propose a Bayesian nonparametric mixture model for the area-specific population…
Nonparametric density estimation for compositional data supported on the simplex is examined under a missing at random mechanism. Rather than imputing missing values and estimating the density from a completed data set, we adopt a strategy…
Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of…
We develop a Bayesian framework for tackling the supervised clustering problem, the generic problem encountered in tasks such as reference matching, coreference resolution, identity uncertainty and record linkage. Our clustering model is…
We introduce a density basis of the trigonometric polynomials that is suitable to mixture modelling. Statistical and geometric properties are derived, suggesting it as a circular analogue to the Bernstein polynomial densities. Nonparametric…
Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular,…
Current tools for multivariate density estimation struggle when the density is concentrated near a nonlinear subspace or manifold. Most approaches require choice of a kernel, with the multivariate Gaussian by far the most commonly used.…