Belief-Combining Framework for Multi-Trace Reconstruction over Channels with Insertions, Deletions, and Substitutions

2026-01-26

AI Summary

This work addresses the exponential growth in computational complexity associated with joint methods for reconstructing multi-trace sequences under insertion, deletion, and substitution noise. To overcome this challenge, the authors propose an iterative belief fusion algorithm based on message passing that efficiently aggregates local inferences from individual traces to compute symbol-level posterior probabilities. The method achieves reconstruction accuracy comparable to that of joint maximum a posteriori estimation while reducing computational complexity from exponential to quadratic in the number of traces. Experimental results on real short-chain DNA read datasets demonstrate the superior efficiency and accuracy of the proposed approach.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

Optimal reconstruction of a source sequence from multiple noisy traces corrupted by random insertions, deletions, and substitutions typically requires joint processing of all traces, leading to computational complexity that grows exponentially with the number of traces. In this work, we propose an iterative belief-combining procedure that computes symbol-wise a posteriori probabilities by propagating trace-wise inferences via message passing. We prove that, upon convergence, our method achieves the same reconstruction performance as joint maximum a posteriori estimation, while reducing the complexity to quadratic in the number of traces. This performance equivalence is validated using a real-world dataset of clustered short-strand DNA reads.

Problem

• multi-trace reconstruction
• insertions
• deletions
• substitutions
• computational complexity

Innovation

• belief-combining
• multi-trace reconstruction
• insertion-deletion-substitution channels
• message passing
• maximum a posteriori estimation