Bayesian Networks (BNs) are widely utilized across various industrial sectors to optimize processes, with an emerging focus on the collaboration across multiple parties. While most realistic scenarios require handling a mixture of categorical and continuous data simultaneously, the current state-of-the-art only supports collaborative inference on purely discrete models. The Junction Tree enables efficient and accurate inference on hybrid models but has not been implemented for confidential scenarios yet. To address this gap, we introduce Hybrid CCJT, an innovative framework for confidential multiparty inference in hybrid domains, offering: (i) a method to construct a collaborative, strongly-rooted junction tree for efficient and secure inference, (ii) a confidential-
preserving inference protocol for Hybrid BNs, (iii) an optimized message-passing scheme that
improves communication efficiency even in the purely discrete domain. Our extensive evaluation
show that Hybrid CCJT improves the predictive accuracy of continuous target variables by an average of 32% in Mean Squared Error and reduce the communication cost up to 86-fold, against the best state-of-the-art baseline.

Collaborative efforts in Predictive Maintenance and Control can be beneficial for manufacturers and customers in industrial environments. However, these efforts are challenged by the need for multi-dimensional sharing of information about the same type (horizontal) and piece (vertical) of equipment, privacy restrictions and the presence of heterogeneous data distributions across participants.

Existing solutions have addressed some of these challenges for forecasting or different purposes but there lacks a comprehensive approach that handles all of them for time series forecasting. To solve this problem, we introduce Time-series-based Personalized Hybrid Federated Learning (TPHFL), a hybrid federated learning (FL) strategy that combines Horizontal FL and Vertical FL to enable multi-level knowledge exchange while preserving data privacy. All participants use a personalization mechanism to make predictions that better suit their underlying data distribution.

Our approach employs a distributed model to handle vertical privacy constraints and addresses data heterogeneity across equipment through a personalisation mechanism. Through extensive experiments on four public and one industry-specific datasets, we show that TPHFL outperforms independent learning scenarios by 27.2%, providing a strong incentive for parties to collaborate.

We demonstrate the effectiveness of personalisation by showing an accuracy improvement of up to 42.7% when comparing TPHFL with personalisation to TPHFL without personalisation, and 32.7% when comparing traditional HFL methods to HFL with personalisation. Additionally, we evaluate a different configuration for personalisation and perform a detailed hyperparameter analysis to better understand the behaviour of TPHFL in different contexts.