We study the problem of automatically discovering Granger causal relations from observational multivariate time-series data.
Estimating the structure of a Bayesian network, in the form of a directed acyclic graph (DAG), from observational data is a statistically and computationally hard problem with essential applications in areas such as causal discovery.
We propose the use of an alternative estimator based on the cross-entropy of the joint model distribution and a flexible proposal distribution.
However, inference in GPSSMs is computationally and statistically challenging due to the large number of latent variables in the model and the strong temporal dependencies between them.
We consider the Bayesian optimal filtering problem: i. e. estimating some conditional statistics of a latent time-series signal from an observation sequence.
Learning useful node and graph representations with graph neural networks (GNNs) is a challenging task.
Bayesian approaches developed to solve the optimal design of sequential experiments are mathematically elegant but computationally challenging.
Advances in differentiable numerical integrators have enabled the use of gradient descent techniques to learn ordinary differential equations (ODEs).
We develop a novel method for carrying out model selection for Bayesian autoencoders (BAEs) by means of prior hyper-parameter optimization.
Making predictions and quantifying their uncertainty when the input data is sequential is a fundamental learning challenge, recently attracting increasing attention.
Bayesian optimization (BO) is among the most effective and widely-used blackbox optimization methods.
In this paper, we develop a rigorous mathematical framework for distribution regression where inputs are complex data streams.
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models.
We show that QP matches quantile functions rather than moments as in EP and has the same mean update but a smaller variance update than EP, thereby alleviating EP's tendency to over-estimate posterior variances.
We propose a scalable framework for inference in an inhomogeneous Poisson process modeled by a continuous sigmoidal Cox process that assumes the corresponding intensity function is given by a Gaussian process (GP) prior transformed with a scaled logistic sigmoid function.
We propose a framework that lifts the capabilities of graph convolutional networks (GCNs) to scenarios where no input graph is given and increases their robustness to adversarial attacks.
We consider multi-task regression models where observations are assumed to be a linear combination of several latent node and weight functions, all drawn from Gaussian process (GP) priors that allow nonzero covariance between grouped latent functions.
We consider multi-task regression models where the observations are assumed to be a linear combination of several latent node functions and weight functions, which are both drawn from Gaussian process priors.
We formalize the problem of learning interdomain correspondences in the absence of paired data as Bayesian inference in a latent variable model (LVM), where one seeks the underlying hidden representations of entities from one domain as entities from the other domain.
The wide adoption of Convolutional Neural Networks (CNNs) in applications where decision-making under uncertainty is fundamental, has brought a great deal of attention to the ability of these models to accurately quantify the uncertainty in their predictions.
We propose a network structure discovery model for continuous observations that generalizes linear causal models by incorporating a Gaussian process (GP) prior on a network-independent component, and random sparsity and weight matrices as the network-dependent parameters.
We investigate the capabilities and limitations of Gaussian process models by jointly exploring three complementary directions: (i) scalable and statistically efficient inference; (ii) flexible kernels; and (iii) objective functions for hyperparameter learning alternative to the marginal likelihood.
The composition of multiple Gaussian Processes as a Deep Gaussian Process (DGP) enables a deep probabilistic nonparametric approach to flexibly tackle complex machine learning problems with sound quantification of uncertainty.
We develop an automated variational inference method for Bayesian structured prediction problems with Gaussian process (GP) priors and linear-chain likelihoods.
We evaluate our approach quantitatively and qualitatively with experiments on small datasets, medium-scale datasets and large datasets, showing its competitiveness under different likelihood models and sparsity levels.
We propose a sparse method for scalable automated variational inference (AVI) in a large class of models with Gaussian process (GP) priors, multiple latent functions, multiple outputs and non-linear likelihoods.
Using a mixture of Gaussians as the variational distribution, we show that (i) the variational objective and its gradients can be approximated efficiently via sampling from univariate Gaussian distributions and (ii) the gradients of the GP hyperparameters can be obtained analytically regardless of the model likelihood.