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The conditional extremes framework allows for event-based stochastic modeling of dependent extremes, and has recently been extended to spatial and spatio-temporal settings. After standardizing the marginal distributions and applying an…
We introduce a nonparametric prior on the conditional distribution of a (univariate or multivariate) response given a set of predictors. The prior is constructed in the form of a two-stage generative procedure, which in the first stage…
Multivariate density estimation is a popular technique in statistics with wide applications including regression models allowing for heteroskedasticity in conditional variances. The estimation problems become more challenging when…
Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…
We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…
Tuning of measurement models is challenging in real-world applications of sequential Monte Carlo methods. Recent advances in differentiable particle filters have led to various efforts to learn measurement models through neural networks.…
We present a new Markov chain Monte Carlo method for estimating posterior probabilities of structural features in Bayesian networks. The method draws samples from the posterior distribution of partial orders on the nodes; for each sampled…
Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…
Partition-wise models offer a flexible approach for modeling complex and multidimensional data that are capable of producing interpretable results. They are based on partitioning the observed data into regions, each of which is modeled with…
This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
Many methods for modelling spatial processes assume global smoothness properties; such assumptions are often violated in practice. We introduce a method for modelling spatial processes that display heterogeneity or contain discontinuities.…
We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…
We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…
Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…
Density estimation, which estimates the distribution of data, is an important category of probabilistic machine learning. A family of density estimators is mixture models, such as Gaussian Mixture Model (GMM) by expectation maximization.…
We propose a data-driven method to learn the time-dependent probability density of a multivariate stochastic process from sample paths, assuming that the initial probability density is known and can be evaluated. Our method uses a novel…
Telling apart the cause and effect between two random variables with purely observational data is a challenging problem that finds applications in various scientific disciplines. A key principle utilized in this task is the algorithmic…
The slow processes of metastable stochastic dynamical systems are difficult to access by direct numerical simulation due the sampling problem. Here, we suggest an approach for modeling the slow parts of Markov processes by approximating the…
Multivariate Gaussian distributions enjoy Gaussian conditional distributions that makes conditioning easy: conditioning boils down to implementing analytical formulae for conditional means and covariances. For more general distributions,…