Traditionally, learning the structure of a Dynamic Bayesian Network has been centralized, with all data pooled in one location. However, in real-world scenarios, data are often dispersed among multiple parties (e.g., companies, devices) that aim to collaboratively learn a Dynamic Bayesian Network while preserving their data privacy and security. In this study, we introduce a federated learning approach for estimating the structure of a Dynamic Bayesian Network from data distributed horizontally across different parties. We propose a distributed structure learning method that leverages continuous optimization so that only model parameters are exchanged during optimization. Experimental results on synthetic and real datasets reveal that our method outperforms other state-of-the-art techniques, particularly when there are many clients with limited individual sample sizes.

Causal learning from data has received much attention in recent years. One way of capturing causal relationships is by utilizing Bayesian networks. There, one recovers a weighted directed acyclic graph, in which random variables are represented by vertices, and the weights associated with each edge represent the strengths of the causal relationships between them. This concept is extended to capture dynamic effects by introducing a dependency on past data, which may be captured by the structural equation model, which is utilized in the present contribution to formulate a score-based learning approach. A mixed-integer quadratic program is formulated and an algorithmic solution proposed, in which the pre-generation of exponentially many acyclicity constraints is avoided by utilizing the so-called branch-and-cut ("lazy constraint") method. Comparing the novel approach to the state of the art, we show that the proposed approach turns out to produce excellent results when applied to small and medium-sized synthetic instances of up to 25 time-series. Lastly, two interesting applications in bio-science and finance, to which the method is directly applied, further stress the opportunities in developing highly accurate, globally convergent solvers that can handle modest instances.

Dynamic Bayesian Networks (DBNs) are a class of Probabilistic Graphical Models that enable the modeling of a Markovian dynamic process through defining the kernel transition by the DAG structure of the graph found to fit a dataset. There are a number of structure learners than enable one to find the structure of a DBN to fit data, each of which with its own set of particular advantages and disadvantages. The structure of a DBN itself presents transparent criteria in order to identify causal discovery between variables. However, without the presence of large quantities of data, identifying a ground truth causal structure becomes unrealistic in practice. However, one can consider a procedure by which a set of graphs identifying structure are computed as approximate noisy solutions, and subsequently amortized in a broader statistical procedure fitting a mixture of DBNs. Each component of the mixture presents an alternative hypothesis on the causal structure. From the mixture weights, one can also compute the Bayes Factors comparing the preponderance of evidence between different models. This presents a natural opportunity for the development of Empirical Bayesian methods.

Dynamic Bayesian Networks (DBNs), renowned for their interpretability, have become increasingly vital in representing complex stochastic processes in various domains such as gene expression analysis, healthcare, and traffic prediction. Structure learning of DBNs from data is challenging, particularly for datasets with thousands of variables. Most current algorithms for DBN structure learning are adaptations from those used in static Bayesian Networks (BNs), and are typically focused on small-scale problems. In order to solve large-scale problems while taking full advantage of existing algorithms, this paper introduces a novel divide-and-conquer strategy, originally developed for static BNs, and adapts it for large-scale DBN structure learning. In this work, we specifically concentrate on 2 Time-sliced Bayesian Networks (2-TBNs), a special class of DBNs. Furthermore, we leverage the prior knowledge of 2-TBNs to enhance the performance of the strategy we introduce. Our approach significantly improves the scalability and accuracy of 2-TBN structure learning. Experimental results demonstrate the effectiveness of our method, showing substantial improvements over existing algorithms in both computational efficiency and structure learning accuracy. On problem instances with more than 1,000 variables, our approach improves two accuracy metrics by 74.45% and 110.94% on average , respectively, while reducing runtime by 93.65% on average.

Cryptocurrencies have gained popularity across various sectors, especially in finance and investment. The popularity is partly due to their unique specifications originating from blockchain-related characteristics such as privacy, decentralisation, and untraceability. Despite their growing popularity, cryptocurrencies remain a high-risk investment due to their price volatility and uncertainty. The inherent volatility in cryptocurrency prices, coupled with internal cryptocurrency-related factors and external influential global economic factors makes predicting their prices and price movement directions challenging. Nevertheless, the knowledge obtained from predicting the direction of cryptocurrency prices can provide valuable guidance for investors in making informed investment decisions. To address this issue, this paper proposes a dynamic Bayesian network (DBN) approach, which can model complex systems in multivariate settings, to predict the price movement direction of five popular altcoins (cryptocurrencies other than Bitcoin) in the next trading day. The efficacy of the proposed model in predicting cryptocurrency price directions is evaluated from two perspectives. Firstly, our proposed approach is compared to two baseline models, namely an auto-regressive integrated moving average and support vector regression. Secondly, from a feature engineering point of view, the impact of twenty-three different features, grouped into four categories, on the DBN's prediction performance is investigated. The experimental results demonstrate that the DBN significantly outperforms the baseline models. In addition, among the groups of features, technical indicators are found to be the most effective predictors of cryptocurrency price directions.

Motion prediction is a key factor towards the full deployment of autonomous vehicles. It is fundamental in order to assure safety while navigating through highly interactive complex scenarios. In this work, the framework IAMP (Interaction- Aware Motion Prediction), producing multi-modal probabilistic outputs from the integration of a Dynamic Bayesian Network and Markov Chains, is extended with a learning-based approach. The integration of a machine learning model tackles the limitations of the ruled-based mechanism since it can better adapt to different driving styles and driving situations. The method here introduced generates context-dependent acceleration distributions used in a Markov-chain-based motion prediction. This hybrid approach results in better evaluation metrics when compared with the baseline in the four

The problem of reinforcement learning in a non-Markov environment is explored using a dynamic Bayesian network, where conditional indepen(cid:173) dence assumptions between random variables are compactly represented by network parameters. The parameters are learned on-line, and approx(cid:173) imations are used to perform inference and to compute the optimal value function. The relative effects of inference and value function approxi(cid:173) mations on the quality of the final policy are investigated, by learning to solve a moderately difficult driving task. The two value function approx(cid:173) imations, linear and quadratic, were found to perform similarly, but the quadratic model was more sensitive to initialization. Both performed be(cid:173) low the level of human performance on the task.

The application of latent/hidden variable Dynamic Bayesian Net- works is constrained by the complexity of marginalising over latent variables. For this reason either small latent dimensions or Gaus- sian latent conditional tables linearly dependent on past states are typically considered in order that inference is tractable. We suggest an alternative approach in which the latent variables are modelled using deterministic conditional probability tables. This specialisa- tion has the advantage of tractable inference even for highly com- plex non-linear/non-Gaussian visible conditional probability tables. This approach enables the consideration of highly complex latent dynamics whilst retaining the bene(cid:12)ts of a tractable probabilistic model.

We describe an approach to building brain-computer interfaces (BCI) based on graphical models for probabilistic inference and learning. We show how a dynamic Bayesian network (DBN) can be used to infer probability distributions over brain- and body-states during planning and execution of actions. The DBN is learned directly from observed data and allows measured signals such as EEG and EMG to be interpreted in terms of internal states such as intent to move, preparatory activity, and movement execution. Unlike traditional classification-based approaches to BCI, the proposed approach (1) allows continuous tracking and predic- tion of internal states over time, and (2) generates control signals based on an entire probability distribution over states rather than binary yes/no decisions. We present preliminary results of brain- and body-state es- timation using simultaneous EEG and EMG signals recorded during a self-paced left/right hand movement task.

Functional Magnetic Resonance Imaging (fMRI) has enabled scientists to look into the active brain. However, interactivity between functional brain regions, is still little studied. In this paper, we contribute a novel framework for modeling the interactions between multiple active brain regions, using Dynamic Bayesian Networks (DBNs) as generative mod- els for brain activation patterns. This framework is applied to modeling of neuronal circuits associated with reward. The novelty of our frame- work from a Machine Learning perspective lies in the use of DBNs to reveal the brain connectivity and interactivity. Such interactivity mod- els which are derived from fMRI data are then validated through a group classification task.