MMSB (Mixed Membership Stochastic Blockmodel) Documentation

🔍 Overview

MMSB is a probabilistic generative model for graph data where each node is represented by a distribution over latent communities (blocks). Each edge is generated based on sampled community assignments from Dirichlet-distributed memberships and a block interaction matrix B.

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⚙️ Class Definition

Class Name: MMSB

This class implements a simplified version of MMSB for sampling synthetic graphs.

class MMSB:
    def __init__(self, n_nodes: int, n_blocks: int, alpha: float = 0.5):
        ...

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📋 Parameters

Parameter	Type	Default	Description
n_nodes	int	—	Number of graph nodes
n_blocks	int	—	Number of latent blocks (communities)
alpha	float	0.5	Dirichlet prior parameter for membership

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💻 Using Example

from soft_clustering._mmsb._mmsb import MMSB

model = MMSB(n_nodes=6, n_blocks=3, alpha=0.5)
Y = model.sample_graph()
pi = model.get_memberships()
B = model.get_block_matrix()

print("Adjacency Matrix:", Y)
print("Memberships:", pi)
print("Block Matrix:", B)

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📥 Input / 📤 Output

• Input: None required at inference time (sampling model)

• Returns:

  • Y (Tensor): Adjacency matrix (n_nodes x n_nodes)

  • pi (Tensor): Membership matrix (n_nodes x n_blocks)

  • B (Tensor): Block interaction matrix (n_blocks x n_blocks)

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🛠️ Methods

• sample_graph(): Generates a synthetic adjacency matrix from MMSB

• get_memberships(): Returns Dirichlet-distributed node memberships

• get_block_matrix(): Returns the B matrix of interaction probabilities

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📝 Implementation Notes

• Memberships are sampled from Dirichlet distributions

• Each pair of nodes samples latent community assignments

• Edge presence determined by Bernoulli trials from B matrix

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📚 Reference

1. Airoldi, E. M., Blei, D. M., Fienberg, S. E., & Lafferty, J. D. (2008). Mixed Membership Stochastic Blockmodels. Journal of Machine Learning Research 9.