Related papers: Exchangeable random permutations with an applicati…

We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…

We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…

Gaussian Process Networks (GPNs) are a class of directed graphical models which employ Gaussian processes as priors for the conditional expectation of each variable given its parents in the network. The model allows the description of…

Finite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, since the number of model parameters scales quadratically with the number of variables, these models can be easily…

In a recent paper, Caron and Fox suggest a probabilistic model for sparse graphs which are exchangeable when associating each vertex with a time parameter in $\mathbb{R}_+$. Here we show that by generalizing the classical definition of…

Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify…

Many biological networks include cyclic structures. In such cases, Bayesian networks (BNs), which must be acyclic, are not sound models for structure learning. Dynamic BNs can be used but require relatively large time series data. We…

The importance of interpretability of machine learning models has been increasing due to emerging enterprise predictive analytics, threat of data privacy, accountability of artificial intelligence in society, and so on. Piecewise linear…

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…

Species sampling processes have long served as the fundamental framework for modeling random discrete distributions and exchangeable sequences. However, data arising from distinct but related sources require a broader notion of…

Many popular network models rely on the assumption of (vertex) exchangeability, in which the distribution of the graph is invariant to relabelings of the vertices. However, the Aldous-Hoover theorem guarantees that these graphs are dense or…

The construction of decision-theoretic Bayesian designs for realistically-complex nonlinear models is computationally challenging, as it requires the optimization of analytically intractable expected utility functions over high-dimensional…

Though the notion of exchangeability has been discussed in the causal inference literature under various guises, it has rarely taken its original meaning as a symmetry property of probability distributions. As this property is a standard…

Finite mixtures are a flexible modeling tool for irregularly shaped densities and samples from heterogeneous populations. When modeling with mixtures using an exchangeable prior on the component features, the component labels are arbitrary…

The sparse structure of the solution for an inverse problem can be modelled using different sparsity enforcing priors when the Bayesian approach is considered. Analytical expression for the unknowns of the model can be obtained by building…

Within the framework of Gaussian graphical models, a prior distribution for the underlying graph is introduced to induce a block structure in the adjacency matrix of the graph and learning relationships between fixed groups of variables. A…

Inference for the stochastic blockmodel is currently of burgeoning interest in the statistical community, as well as in various application domains as diverse as social networks, citation networks, brain connectivity networks…

Bayesian supervised predictive classifiers, hypothesis testing, and parametric estimation under Partition Exchangeability are implemented. The two classifiers presented are the marginal classifier (that assumes test data is i.i.d.) next to…

Markov chain Monte Carlo methods for exponential family models with intractable normalizing constant, such as the exchange algorithm, require simulations of the sufficient statistics at every iteration of the Markov chain, which often…

Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately…