<｜begin▁of▁sentence｜>### Instruction:
Certainly! Imagine we're strategizing a new campaign to enhance the connectivity of our brand's social network. To craft a data-driven strategy, we propose leveraging the RDPGEstimator from graspologic—an API designed to construct a Random Dot Product Graph model. Let's consider we have network data on brand interactions compiled into a networkx graph. Our goal is to use RDPGEstimator to fit this model to our network data, enabling us to examine and visualize the estimated probability matrix of connections. This will give us insights into the potential engagement patterns and help us identify areas to strengthen our brand's network. How might we execute this process to ensure our strategy is informed by the predictive architecture of the RDPG model?
### Response:
import numpy as np
from graspologic.models import RDPGEstimator
import networkx as nx

# Create a random graph
n = 200
m = 400
G = nx.gnm_random_graph(n, m)

# Convert to adjacency matrix
A = nx.to_numpy_array(G)

# Instantiate and fit the RDPG model
rdpg = RDPGEstimator(loops=False, n_components=5)
rdpg.fit(A)

# Access the estimated latent positions
latent_positions = rdpg.latent_tuple_

# Visualize the probability matrix
import matplotlib.pyplot as plt
plt.imshow(rdpg.p_mat_, cmap='viridis')
plt.colorbar()
plt.title('Estimated Probability Matrix')
plt.show()
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