Bayesian Network models are a powerful tool to collaboratively optimize production processes in various manufacturing industries. When interacting, collaborating parties must preserve their business secrets by maintaining the confidentiality of their model structures and parameters. While most realistic industry scenarios involve hybrid settings, handling both discrete and continuous data, current state-of-the-art methods for collaborative and confidential inference only support discrete data and have high communication costs. In a centralized setting, Junction Trees enable efficient inference even in hybrid scenarios without discretizing continuous variables, but no extension for collaborative and confidential scenarios exists. To address this research gap, we introduce Hybrid CCJT, the first framework for confidential multiparty inference in hybrid domains with semi-honest, non-colluding adversaries, comprising: (i) a method to construct a strongly-rooted Junction Tree across collaborating parties through a novel construct of interface cliques; and, (ii) a protocol for confidential inference built upon multiparty computation primitives comprising a one-time alignment phase and a belief propagation system for combining the inference results across the Junction Tree cliques. Extensive evaluation on nine datasets shows that Hybrid CCJT improves the predictive accuracy of continuous target variables by 32% on average compared to the state-of-the-art, while reducing communication costs by a median 10.4x under purely discrete scenarios.

Phenotypic variation in the copy number of gene products expressed by cells or tissues has been the focus of intense investigation. To what extent the observed differences in cellular expression levels are persistent or transient is an intriguing question. Here, we develop a quantitative framework that resolves the expression variation into stable and unstable components. The difference between the expression means in two cohorts isolated from any cell population is shown to converge to an asymptotic value, with a characteristic time, τT, that measures the timescale of the unstable dynamics. The asymptotic difference in the means, relative to the initial value, measures the stable proportion of the original population variance [Formula: see text]. Empowered by this insight, we analysed the T-cell receptor (TCR) expression variation in CD4 T cells. About 70% of TCR expression variance is stable in a diverse polyclonal population, while over 80% of the variance in an isogenic TCR transgenic population is volatile. In both populations the TCR levels fluctuate with a characteristic time of 32 hours. This systematic characterisation of the expression variation dynamics, relying on time series of cohorts' means, can be combined with technologies that measure gene or protein expression in single cells or in bulk.