Related papers: Stochastic Variational Inference for GARCH Models
Heteroscedastic regression considering the varying noises among observations has many applications in the fields like machine learning and statistics. Here we focus on the heteroscedastic Gaussian process (HGP) regression which integrates…
Deep kernel learning combines the non-parametric flexibility of kernel methods with the inductive biases of deep learning architectures. We propose a novel deep kernel learning model and stochastic variational inference procedure which…
Monte Carlo estimation in plays a crucial role in stochastic reaction networks. However, reducing the statistical uncertainty of the corresponding estimators requires sampling a large number of trajectories. We propose control variates…
Gaussian processes (GPs) are commonly used for prediction and inference for spatial data analyses. However, since estimation and prediction tasks have cubic time and quadratic memory complexity in number of locations, GPs are difficult to…
Variational inference provides a powerful tool for approximate probabilistic in- ference on complex, structured models. Typical variational inference methods, however, require to use inference networks with computationally tractable proba-…
We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated…
Stochastic Gradient (SG) Markov Chain Monte Carlo algorithms (MCMC) are popular algorithms for Bayesian sampling in the presence of large datasets. However, they come with little theoretical guarantees and assessing their empirical…
Variational Optimization forms a differentiable upper bound on an objective. We show that approaches such as Natural Evolution Strategies and Gaussian Perturbation, are special cases of Variational Optimization in which the expectations are…
Inference in Gaussian process (GP) models is computationally challenging for large data, and often difficult to approximate with a small number of inducing points. We explore an alternative approximation that employs stochastic inference…
Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their scalability…
Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable,…
This study presents contemporaneous modeling of asset return and price range within the framework of stochastic volatility with leverage. A new representation of the probability density function for the price range is provided, and its…
Classical stochastic gradient methods for optimization rely on noisy gradient approximations that become progressively less accurate as iterates approach a solution. The large noise and small signal in the resulting gradients makes it…
Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…
Stochastic gradient Markov chain Monte Carlo (SGMCMC) is a popular class of algorithms for scalable Bayesian inference. However, these algorithms include hyperparameters such as step size or batch size that influence the accuracy of…
We investigate different mean-field-like approximations for stochastic dynamics on graphs, within the framework of a cluster-variational approach. In analogy with its equilibrium counterpart, this approach allows one to give a unified view…
We study online inference and asymptotic covariance estimation for the stochastic gradient descent (SGD) algorithm. While classical methods (such as plug-in and batch-means estimators) are available, they either require inaccessible…
Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed…
This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…
In this note we present a generative model of natural images consisting of a deep hierarchy of layers of latent random variables, each of which follows a new type of distribution that we call rectified Gaussian. These rectified Gaussian…