Ing. Milan Papež, Ph.D.

Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution over undirected cyclic graphs. This assumption of a generic graph structure brings various computational challenges, and, more importantly, the presence of non-linearities in neural networks does not permit tractable probabilistic inference. We address these problems by proposing sum-product-set networks, an extension of probabilistic circuits from unstructured tensor data to tree-structured graph data. To this end, we use random finite sets to reflect a variable number of nodes and edges in the graph and to allow for exact and efficient inference. We demonstrate that our tractable model performs comparably to various intractable models based on neural networks.

Traditional methods for unsupervised learning of finite mixture models require to evaluate the likelihood of all components of the mixture. This quickly becomes prohibitive when the components are abundant or expensive to compute. Therefore, we propose to apply a combination of the expectation maximization and the Metropolis-Hastings algorithm to evaluate only a small number of, stochastically sampled, components, thus substantially reducing the computational cost. The Markov chain of component assignments is sequentially generated across the algorithm's iterations, having a non-stationary target distribution whose parameters vary via a gradient-descent scheme. We put emphasis on generality of our method, equipping it with the ability to train mixture models which involve complex, and possibly nonlinear, transformations. The performance of our method is illustrated on mixtures of normalizing flows.

Bayesian transfer learning (BTL) is defined in this paper as the task of conditioning a target probability distribution on a transferred source distribution. The target globally models the interaction between the source and target, and conditions on a probabilistic data predictor made available by an independent local source modeller. Fully probabilistic design is adopted to solve this optimal decision-making problem in the target. By successfully transferring higher moments of the source, the target can reject unreliable source knowledge (i.e. it achieves robust transfer). This dual-modeller framework means that the source’s local processing of raw data into a transferred predictive distribution – with compressive possibilities – is enriched by (the possible expertise of) the local source model. In addition, the introduction of the global target modeller allows correlation between the source and target tasks – if known to the target – to be accounted for. Important consequences emerge. Firstly, the new scheme attains the performance of fully modelled (i.e. conventional) multitask learning schemes in (those rare) cases where target model misspecification is avoided. Secondly, and more importantly, the new dual-modeller framework is robust to the model misspecification that undermines conventional multitask learning. We thoroughly explore these issues in the key context of interacting Gaussian process regression tasks. Experimental evidence from both synthetic and real data settings validates our technical findings: that the proposed BTL framework enjoys robustness in transfer while also being robust to model misspecification.

Type 2 diabetes (T2D) has become one of the most often encountered metabolic disorders threatening the human health. Unannounced meal intake and irregular physical activity cause abrupt changes in the blood glucose concentrations. Therefore, a reliable and accurate algorithms that account for these sudden concentration changes constitute a crucial part of automated insulin pumps and dose guiders. To this end, we develop a stochastic jump diffusion model for T2D patients, reflecting the irregular frequency and uncertain amount of consumed carbohydrates. Moreover, we design a method—combining particle Markov chain Monte Carlo and particle learning—to estimate the unknown parameters of this model, considering only continuous glucose monitoring data and amounts of injected insulin. Our approach is verified on synthetic and clinical data, demonstrating its ability to estimate the unknown parameters with a varying degree of accuracy.