Getting Started

Use this tutorial to try out main functionalities of the cits Python library and test if it has installed properly.

In this tutorial, you will be estimating the adjacency matrix of the rolled causal graph from simulated datasets. A non-zero value of \((i,j)\) entry in this adjacency matrix indicates causal relationship from variable \(i \rightarrow j\).

In neural connectomics, the rolled causal graph between neurons is referred as the causal functional connectivity between neurons.

Install the CITS package

!pip install cits

Load the CITS package

from cits import methods, simulate_timeseries

Load other packages

import time
import numpy as np
from numpy.random import default_rng
rng = default_rng(seed=111)

Simulate a dataset

Use the simulate_timeseries function to simulate a time series dataset. It also outputs the ground truth adjacency matrix of the simulated time series.

Choices of model type are as follows. For details, see the paper.

• model = ‘lingauss1’ for Linear Gaussian Model 1

• model = ‘lingauss2’ for Linear Gaussian Model 2

• model = ‘nonlinnongauss1’ for Non-linear Non-Gaussian Model 1

• model = ‘nonlinnongauss2’ for Non-linear Non-Gaussian Model 2

• model = ‘ctrnn’ for CTRNN

The following example uses model = ‘lingauss1’:

T=1000
n_neurons = 4
noise = 1
alpha = 0.05
lag=1

X, adj, adj_w = simulate_timeseries.simulate(model = 'lingauss1', noise = noise, T = T)

Estimate the adjacency matrix of the rolled causal graph of time series

• Unweighted adjacency: \((i,j)\) entry represents causal influence from \(i \rightarrow j\).

Use the cits_full to obtain the unweighted adjacency matrix.

print("True unweighted adjacency matrix: \n")
print(adj)

startime = time.time()
adj_matrix = methods.cits_full(X,lag,alpha)
out = str(time.time()-startime)
print("time taken "+ out + "\n")

print("Estimated unweighted adjacency matrix: \n")
print(adj_matrix)

• Weighted adjacency: \((i,j)\) entry has strength of causal influence from \(i \rightarrow j\).

Use the cits_full_weighted to obtain the weighted adjacency matrix.

print("True weighted adjacency matrix: \n")
print(adj_w)

startime = time.time()
adj_matrix, causaleff = methods.cits_full_weighted(X,lag,alpha)
out = str(time.time()-startime)
print("time taken "+ out + "\n")

print("Estimated weighted adjacency matrix: \n")
print(causaleff)