# The non-tightness of the reconstruction threshold of a 4 states symmetric model with different in-block and out-block mutations

@article{Liu2019TheNO, title={The non-tightness of the reconstruction threshold of a 4 states symmetric model with different in-block and out-block mutations}, author={Wenjian Liu and Ning Ning}, journal={ArXiv}, year={2019}, volume={abs/1906.09479} }

The tree reconstruction problem is to collect and analyze massive data at the $n$th level of the tree, to identify whether there is non-vanishing information of the root, as $n$ goes to infinity. Its connection to the clustering problem in the setting of the stochastic block model, which has wide applications in machine learning and data mining, has been well established. For the stochastic block model, an "information-theoretically-solvable-but-computationally-hard" region, or say "hybrid-hard…

## One Citation

### Phase Transition of the Reconstructability of a General Model with Different In-Community and Out-Community Mutations on an Infinite Tree

- Computer ScienceSIAM J. Discret. Math.
- 2021

This paper analyzes the tree reconstruction problem by studying a general model which incorporates the characteristics of both Ising and Potts through different in-community and out-community transition probabilities, and rigorously establishing the exact conditions for reconstruction.

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