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Causal-discovery-and-forecasting-in-nonstationary-environments

Causal discovery and forecasting in nonstationary environments with state-space models

This package contains code to the paper for causal discovery and forecasting in nonstationary environments: "Huang, B., Zhang, K., Gong, M., Glymour, C. Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models. ICML 2019."

The code is written in Matlab R2017a.

IMPORTANT FUNCTIONS

function [R, q, A, B] = cpf_saem1_new(numIter, X, N, gamma,R_init,q_init,A_init,B_Mask)

Time-varying causal model estimation when only considering the change of causal coefficients
Xt = Bt*Xt + Et, Et~N(0,R);
b_{i,j,t} = a_{i,j}*b_{i,j,t-1} + epilson_{i,j,t}, epilson_t~N(0,q_{i,j});

Input:

numIter: number of Iterations
X: observed data
N: number of sampled particles in each iteration
gamma: step length of stochastic approximation
R_init: initiation value of the noise variance
q_init: initialion value of the noise variance in the auto-regressive model of B
A_init: initiation value of the coefficients in the auto-regressive model of B
B_Mask: a pre-defined Mask of causal connectivity

Output:

R: estimated noise variance
q: estimated noise variance in the auto-regressive model of B
A: estimated coefficients in the auto-regressive model of B
B: estimated time-varying causal strength

function [q, A, beta, p, B,h] = cpf_saem2_new(numIter, X, N, gamma,q_init,A_init,beta_init,p_init,B_Mask)

Time-varying causal model estimation when considering the change of causal coefficients and noise variance
Xt = Bt*Xt + Et,
b_{i,j,t} = a_{i,j}*b_{i,j,t-1} + epilson_{i,j,t}, epilson_t~N(0,q_{i,j});
h_{i,t} = beta_{i}*h_{i,t-1} + eta_{i,t}, eta_t~N(0,p_{i});

Input:

numIter: number of Iterations
X: observed data
N: number of sampled particles in each iteration
gamma: step length of stochastic approximation
q_init: initialion value of the noise variance in the auto-regressive model of B
A_init: initiation value of the coefficients in the auto-regressive model of B
beta_init: initialion value of the noise variance in the auto-regressive model of h
p_init: initiation value of the coefficients in the auto-regressive model of h
B_Mask: a pre-defined Mask of causal connectivity

Output:

q: estimated noise variance in the auto-regressive model of B
A: estimated coefficients in the auto-regressive model of B
beta: estimated noise variance in the auto-regressive model of h
p: estimated coefficients in the auto-regressive model of h
B: estimated time-varying causal strength
h: estimated time-varying log-variance of the noise

function y_star = prediction_SSM1_new(G,Data,target_id,Bt,A,q,R)

Forecasting (only considering the change of causal coefficients)

Input:

G: causal graph
D: contain all data from 1 to time T, and from time T+1
target_id: the index of the variable that we want to predict
Bt: causal strength at time T
A: estimated coefficients in the auto-regressive model of B
q: estimated noise variance in the auto-regressive model of B
R: estimated noise variance

Output:

y_star: the predicted value at time T+1 of variable with target_id

function y_star = prediction_SSM2_new(G,Data,target_id,Bt,ht,A,q,beta,p)

Forecasting (considering both the change of causal coefficients and noise variance)

Input:

G: causal graph
D: contain all data from 1 to time T, and from time T+1
target_id: the index of the variable that we want to predict
Bt: estimated causal strength at time T
ht: estimated log-variance of the noise at time T
A: estimated coefficients in the auto-regressive model of B
q: estimated noise variance in the auto-regressive model of B
beta: estimated noise variance in the auto-regressive model of h
p: estimated coefficients in the auto-regressive model of h

Output:

y_star: the predicted value at time T+1 of variable with target_id

EXAMPLE

example1.m and example2.m give two example of using this package.

CITATION

If you use this code, please cite the following paper: "Huang, B., Zhang, K., Gong, M., Glymour, C. Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models. ICML 2019."

If you have problems or questions, do not hesitate to send an email to biweih@andrew.cmu.edu