Causal discovery and forecasting in nonstationary environments with state-space models
Copyright (c) 2018-2019 Biwei Huang
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.
- 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
- 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
- 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
example1.m and example2.m give two example of using this package.
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