Title: Collaborative and Confidential Junction Trees for Hybrid Bayesian Networks
Venue: NeurIPS 2025
Accepted: yes
Keywords: Bayesian Networks

Collaboration

Secure Multi-Party Computation
Abstract: 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.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nBayesian networks are a way to represent distributions over multivariate data, each node is a variable, and a directed edge between nodes shows dependence, the network is a DAG. Collaborative Bayesian networks are when multiple parties determine individual Bayesian networks which may contain some common variables, the goal is to combine networks and perform inference on the combined Bayesian network. However we may also require that agents cannot see each others private local variables. \n\nJunction trees are a standard technique for performing inference over (non-collaborative) Bayesian networks by clustering factors in a graphical model (e.g. a Bayesian network) into nodes called cliques, within each clique one may apply variable elimination followed by message passing across cliques for exact inference, the tree structure ensures that message passing will converge in a single pass. \n\nThis paper considers the problem of performing inference over a collaborative Bayesian network while preserving confidentiality of individual parties local variables and their distributions. When there are continuous and discrete variables. \n\nThe proposed solution is a custom protocol to build a junction tree that creates two cliques for each agent, one with all agents discrete variables, and one with all the agents continuous variables, and there are two central cliques, one for communal discrete variables and communal continuous variables, and these are connected to ensure that all discrete nodes have no continuous parents. \n\nThe method is applied to 9 different datasets synthetically generated from known Bayesian network models and shows improvements over baselines.\n\nSTRENGTHS AND WEAKNESSES:\nI am familiar with graphical models and junction trees, I am not familiar with all the topics covered in the paper (SMC and I may have misunderstood details and apologize in advance for any mistakes, particularly in . \n\nIn general, I am positive about the paper and the approach seems reasonable. My comments are mostly minor. \n\n## Strengths  \n- Seems intuitive clean simple idea \n\n## Weaknesses  \n- there is no mention of [Multiply Sections Bayesian Networks](https://ieeexplore.ieee.org/document/858473), presumably one could augment this with HE for interface cliques and perform loopy belief propagation? The continuous variables require a tree structure and strong rooting hence we cannot use such a method?\n- the interface cliques must contain shared variables as well as all threshold variables (both private and shared), is there a privacy leak or can we just treat private threshold variables as invisible to irrelevant agents (see questions)?\n- it is stated that the two agent case allows each agent to infer the other agents distribution over shared variables, there is a slight data leak? \n\nhttps://ieeexplore.ieee.org/document/858473  \n- Inherits the same exponential cost in largest clique as junction trees\n\nQUESTIONS:\n- How does it work with 3+ agents? If I understand correctly, we make a star/hub and spoke network of discrete cliques with interface at the hub and one agent in each spoke, and similar hub+spokes for continuous variables cliques and link the hubs? \n\n- If the interface nodes are the only link from discrete to continuous variables, for an agent with a private discrete parent and private continuous child node, the necessary (private) message must still pass through the interface nodes. How are private threshold variables preserved if they still pass through the interface node? Is it safe to assume that they can be encrypted/ignored by all other agents as they are not required and just pass through? If so, is this equivalent to appending a private continuous clique to each private discrete clique? I understand this preserves Tree structure and strong rootedness. \n\n- What is the “#Arc”  field in the datasets table?\n\nLIMITATIONS:\n- Cost is exponential in the number of variables in each agent, (presumably one may use nested junction trees?) \n\n- In the two party case, each agent can infer information from the aligned result (which is a fundamental fact of HE and not a problem with Hybrid CCJT), I see this is mentioned in the limitations (Appendix H), this may be more prominently mentioned in the main paper.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-18"}

comments: SUMMARY:
Bayesian Networks (BN) are a tool that allows different parties to collaboratively optimize their production process. State-of-the-art frameworks for collaborative and confidential inference only support discrete data and have high communication costs, while frameworks for hybrid scenarios (mix of discrete and continuous data) are limited to single-party settings. The authors solve this by providing a collaborative and confidential framework for BNs in the hybrid setting, constructing a strongly rooted Junction Tree then running a belief-propagation-like algorithm to combine inference results confidentially. Results show 32% average improvement in predictive accuracy and up to 331× reduction in communication costs.

STRENGTHS AND WEAKNESSES:
Strengths:
1. The authors' use of Junction Trees gives a clear advantage in terms of communication costs compared to vanilla belief propagation.
2. Authors provide a proof of confidentiality under adversarial model and a clear collaborative strongly-rooted JT protocol.
3. The experimental results are strong: clear improvement in accuracy in hybrid setting, communication cost reduction in discrete setting.

Weaknesses:
1. Could the authors provide a high-level proof sketch for Proof of confidentiality would help understand why the collaborative inference protocol always hides the marginal posteriors on private variables.
2. The Collaborative inference protocol is quite sophisticated and high-level. More implementation details would be appreciated if possible.
3. Limited communication cost improvement analysis in the hybrid setting compared to the extensive discrete results (though Table 1 does show some improvements for hybrid datasets).

QUESTIONS:
Please address weaknesses.

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 4
DATE: 2025-07-03

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses the challenge of performing confidential, collaborative inference in Bayesian Networks (BNs) that span multiple parties and involve hybrid data (i.e., both discrete and continuous variables). The authors identify that existing privacy-preserving methods are typically limited to discrete-only scenarios and often incur high communication overhead.\n\nTo overcome these limitations, the paper introduces Hybrid CCJT, a novel framework for secure multi-party inference in hybrid BNs. The proposed method is twofold: first, it presents a novel technique for constructing a single, strongly rooted Junction Tree (JT) across all parties using \"interface cliques\" to connect their local network structures. Second, it develops a secure protocol based on Multi-Party Computation (MPC) to perform belief propagation on this shared JT, enabling inference while keeping model parameters and structures confidential.\n\nThe authors conduct an empirical evaluation of Hybrid CCJT on nine datasets of varying types (mixed, discrete, and continuous). They compare its performance against a state-of-the-art baseline (CCBNet) and an ablation variant of their method ($\\Delta$-CCJT), measuring prediction accuracy (using MSE for continuous and Brier score for discrete variables) and communication cost.\n\nSTRENGTHS AND WEAKNESSES:\n* Strengths\nThe paper addresses a significant and previously unaddressed challenge: confidential inference in collaborative, hybrid Bayesian Networks. It is the first to extend the Junction Tree (JT) algorithm to this domain, enabling the native handling of both discrete and continuous variables without discretization. This greatly enhances the practical relevance of collaborative probabilistic modeling, especially for industrial applications. \n\nThe proposed Hybrid CCJT methodology is technically sound, introducing \"interface cliques\" to construct a strongly-rooted JT in a distributed fashion. This is a critical feature for valid inference in hybrid Conditional Linear Gaussian (CLG) models. The paper’s design is complete, including theoretical proofs and integration of cryptographic primitives to ensure confidentiality.\n\nThe empirical evaluation is comprehensive, covering nine datasets with varying characteristics and scales. The comparison against CCBNet and an ablation variant ($\\Delta$-CCJT) clearly demonstrates the contribution of the paper’s specific innovations. The reported results show substantial performance improvements, including a 32\\% reduction in Mean Squared Error (MSE) and up to a 331x reduction in communication costs, providing strong evidence of the method’s superiority.\n\n* Weaknesses\n- Security Guarantee Scope. The security of the protocol is based on a semi-honest, non-colluding adversary model. As noted in Appendix H, the protocol cannot withstand collusion among N-1 participants. While this is a common and explicitly stated assumption, it represents a significant limitation when deployed in environments with low trust or high incentives for collusion. Briefly mentioning this boundary condition in the main text would provide readers with a clearer understanding of the threat model.\n- Practical Assumptions for Data Alignment. The successful operation of the framework relies on two key practical assumptions: (a) shared variables between parties can be correctly identified (e.g., through private set intersections on names), and (b) there is consensus on the representation of these shared variables (e.g., the states of discrete variables, applicable units, and discretization schemes). In practice, achieving semantic interoperability is a significant challenge. The importance of this as a prerequisite could be emphasized more clearly.\n- Context of the 331x Communication Improvement Claim. The paper reports a communication cost reduction of up to 331x on the Munin #2 dataset (Table 3), which is a highly impressive result. However, this peak performance figure arises under a specific, best-case scenario for the proposed method (a large, purely discrete network where the communication overhead of the baseline is maximal). While the result is technically correct and showcases the potential of the method, highlighting this peak number so prominently (e.g., in the abstract) could be slightly misleading. The average improvement across all datasets and settings might be a more representative measure of the expected gains.\n\nQUESTIONS:\n- Could the authors clarify the computational overhead introduced by the cryptographic tools used in the protocol, and how they compare with communication costs in larger models?\n- Is the local marginalization in Equation 9 the primary reason for communication efficiency compared to Variable Elimination methods like CCBNet? A brief confirmation of this mechanism would be helpful.\n- How does the protocol handle inconsistencies in data representation (e.g., mismatched units or state definitions across parties)?\n\nLIMITATIONS:\n- The paper does not provide a detailed analysis of the computational cost, especially when using cryptographic primitives, which is crucial for practical implementations.\n- Data misalignment issues are not sufficiently addressed, and there is no discussion on the protocol's sensitivity to such inconsistencies.\n- Scalability concerns with larger datasets or more participants are not fully explored.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-09"}