Nonparametric Bayesian Density Modeling with Gaussian Processes
نویسندگان
چکیده
The Gaussian process is a useful prior on functions for Bayesian kernel regression and classification. Density estimation with a Gaussian process prior is difficult, however, as densities must be nonnegative and integrate to unity. The statistics community has explored the use of a logistic Gaussian process for density estimation, relying on approximations of the normalization constant (e.g. [1, 2, 3]).
منابع مشابه
Bayesian nonparametric estimation of the spectral density of a long or intermediate memory Gaussian process
A stationary Gaussian process is said to be long-range dependent (resp. anti-persistent) if its spectral density f(λ) can be written as f(λ) = |λ|g(|λ|), where 0 < d < 1/2 (resp. −1/2 < d < 0), and g is continuous. We propose a novel Bayesian nonparametric approach for the estimation of the spectral density of such processes. Within this approach, we prove posterior consistency for both d and g...
متن کاملNonparametric Mixtures of Multi-Output Heteroscedastic Gaussian Processes for Volatility Modeling
In this work, we present a nonparametric Bayesian method for multivariate volatility modeling. Our approach is based on postulation of a novel mixture of multioutput heteroscedastic Gaussian processes to model the covariance matrices of multiple assets. Specifically, we use the Pitman-Yor process prior as the nonparametric prior imposed over the components of our model, which are taken as multi...
متن کاملLocation Dependent Dirichlet Processes
Dirichlet processes (DP) are widely applied in Bayesian nonparametric modeling. However, in their basic form they do not directly integrate dependency information among data arising from space and time. In this paper, we propose location dependent Dirichlet processes (LDDP) which incorporate nonparametric Gaussian processes in the DP modeling framework to model such dependencies. We develop the...
متن کاملEstimating Continuous Distributions in Bayesian Classi ers
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated by a single Gaussian. In this paper we abandon the normality assumption and instead use statistical methods for nonparametric density estimation. For a naive...
متن کاملCopula based factorization in Bayesian multivariate infinite mixture models
Bayesian nonparametric models based on infinite mixtures of density kernels have been recently gaining in popularity due to their flexibility and feasibility of implementation even in complicated modeling scenarios. However, these models have been rarely applied in more than one dimension. Indeed, implementation in the multivariate case is inherently difficult due to the rapidly increasing numb...
متن کامل